new lab
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anna
parent
572f42e895
commit
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3.6.1Спектр/Data_l.xlsx
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3.6.1Спектр/Data_l.xlsx
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3.6.1Спектр/Laba.py
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3.6.1Спектр/Laba.py
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# -*- coding: utf-8 -*-
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import numpy as np
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import matplotlib.pyplot as plt
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import csv
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from scipy.optimize import curve_fit
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def read_csv(file_name):
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with open(file_name) as file:
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reader = list(csv.reader(file, delimiter=';',
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quotechar=',', quoting=csv.QUOTE_MINIMAL))
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return reader
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def make_latex_table(data):
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table = []
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table.append("\\begin{table}".replace('//', '\\'))
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table.append("\label{}".replace('/', '\\'))
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table.append('\caption{}'.replace('/', '\\'))
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leng = len(data[0])
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stroka = 'c'.join(['|' for _ in range(leng+1)])
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table.append('\\begin{tabular}{'.replace('//', '\\')+stroka+'}')
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table.append('\hline')
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for i in range(len(data)):
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table.append(' & '.join(data[i]) + ' \\\\')
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table.append('\hline')
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table.append("\end{tabular}".replace('/', '\\'))
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table.append("\end{table}".replace('/', '\\'))
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return table
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def make_point_grafic(x, y, xlabel, ylabel, caption, xerr, yerr,
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subplot=None, color=None, center=None, s=15):
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if not subplot:
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subplot = plt
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if type(yerr) == float or type(yerr) == int:
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yerr = [yerr for _ in y]
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if type(xerr) == float or type(xerr) == int:
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xerr = [xerr for _ in x]
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if xerr[1] != 0 or yerr[1] != 0:
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subplot.errorbar(x, y, yerr=yerr, xerr=xerr, linewidth=4,
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linestyle='', label=caption, color=color,
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ecolor=color, elinewidth=1, capsize=3.4,
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capthick=1.4)
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else:
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subplot.scatter(x, y, linewidth=0.005, label=caption,
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color=color, edgecolor='black', s=s)
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# ax = plt.subplots()
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# ax.grid())
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if not center:
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plt.xlabel(xlabel)
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plt.ylabel(ylabel)
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else:
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ax = plt.gca()
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ax.spines['top'].set_visible(False)
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ax.spines['right'].set_visible(False)
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ax.spines['bottom'].set_position('zero')
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ax.spines['left'].set_position('zero')
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ax.set_xlabel(ylabel, labelpad=-180, fontsize=14) # +
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ax.set_ylabel(xlabel, labelpad=-260, rotation=0, fontsize=14)
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def make_line_grafic(xmin, xmax, xerr, yerr, xlabel, ylabel, k, b, caption,
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subplot=None, color=None, linestyle='-'):
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if not subplot:
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subplot = plt
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x = np.arange(xmin, xmax, (xmax-xmin)/10000)
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subplot.plot(x, k*x+b, label=caption, color=color, linewidth=1.4,
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linestyle=linestyle)
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def make_graffic(x, y, xlabel, ylabel, caption_point, xerr, yerr, k=None,
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b=None, filename=None, color=None, koef=[0.9, 1.1], s=None):
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if not color:
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color = ['limegreen', 'indigo']
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if not s:
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make_point_grafic(x, y, xlabel=xlabel,
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ylabel=ylabel, caption=caption_point,
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xerr=xerr, yerr=yerr, subplot=plt, color=color[0])
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else:
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make_point_grafic(x, y, xlabel=xlabel,
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ylabel=ylabel, caption=caption_point,
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xerr=xerr, yerr=yerr, subplot=plt, color=color[0], s=s)
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if k and b:
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make_line_grafic(xmin=min(x)-1, xmax=max(x)+1, xerr=xerr, yerr=yerr,
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xlabel='', ylabel='', k=k, b=b,
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caption='Theoretical dependence', subplot=plt,
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color='red')
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if type(yerr) == float or type(yerr) == int:
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yerr = [yerr for _ in y]
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k, b, sigma = approx(x, y, b, yerr)
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sigma[0] = abs(k*((sigma[0]/k)**2+(np.mean(yerr)/np.mean(y))**2 +
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(np.mean(xerr)/np.mean(x))**2)**0.5)
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if (b != 0):
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sigma[1] = abs(b*((sigma[1]/b)**2+(np.mean(yerr)/np.mean(y))**2 +
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(np.mean(xerr)/np.mean(x))**2)**0.5)
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else:
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sigma[1] = 0
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make_line_grafic(xmin=min(x)*koef[0], xmax=max(x)*koef[1], xerr=xerr,
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yerr=yerr, xlabel='', ylabel='', k=k, b=b, caption=None,
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subplot=plt, color=color[1])
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plt.legend()
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return k, b, sigma
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def approx(x, y, b, sigma_y, f=None):
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if sigma_y[0] != 0:
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sigma_y = [1/i**2 for i in sigma_y]
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else:
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sigma_y = np.array([1 for _ in y])
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if f is None:
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if b == 0:
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def f(x, k):
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return k*x
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k, sigma = curve_fit(f, xdata=x, ydata=y, sigma=sigma_y)
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sigma = np.sqrt(np.diag(sigma))
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return k, b, [sigma, 0]
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else:
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def f(x, k, b):
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return x*k + b
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k, sigma = curve_fit(f, xdata=x, ydata=y, sigma=sigma_y)
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sigma_b = np.sqrt(sigma[1][1])
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b = k[1]
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k = k[0]
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sigma = np.sqrt(sigma[0][0])
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return k, b, [sigma, sigma_b]
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else:
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k, sigma = curve_fit(f, xdata=x, ydata=y, sigma=sigma_y)
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sigma = np.sqrt(np.diag(sigma))
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b = k[1]
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k = k[0]
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return k, b, sigma
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def find_delivation(data):
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data = np.array(data).astype(np.float)
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s = sum(data)/len(data)
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su = 0
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for i in data:
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su += (i-s)**2
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return (su/(len(data)-1))**0.5
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def make_dic(filename):
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data = np.array(read_csv(filename))
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data = np.transpose(data)
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dic = {}
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for i in range(len(data)):
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dic[data[i][0]] = np.array(data[i][1:]).astype(np.float)
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data = dic
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return data
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def make_fun(A0, T):
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def f(t, k, b):
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return A0/(1+A0*b*t)-k*0*A0*t/T
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return f
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def make_fun_grafic(xmin, xmax, xerr, yerr, xlabel, ylabel, f, k, b, caption,
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subplot=None, color=None):
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if not subplot:
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subplot = plt
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x = np.arange(xmin, xmax, (xmax-xmin)/10000)
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subplot.plot(x, f(x, k, b), label=caption, color=color)
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def make_all():
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part_1_1()
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part_1_2()
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part_2()
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part_3()
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def part_1_1():
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plt.figure(dpi=500, figsize=(8, 5))
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data = make_dic("dnu(tau).csv")
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x = 1 / data["tau"]*100
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y = data['d_nu']/10**4
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xlabel = "1/"+greek_letters[48]+'$,10^4$Гц'
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ylabel = greek_letters[0]+greek_letters[41]+'$,10^4$ Гц'
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k, b, sigma = make_graffic(x, y, xlabel, ylabel,
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caption_point='', xerr=0, yerr=0, s=40)
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print(k, sigma[0])
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plt.savefig("dnu(tau)")
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plt.show()
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def part_1_2():
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fig, ax = plt.subplots(figsize=(10, 6))
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data = make_dic("a(n).csv")
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v = 1000
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t = 50 * 10 **- 6
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T = 1 / v
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N = 200
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V0 = 300
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vu = [n/T for n in range(2, N)]
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c = [abs(V0*t/T*np.sin(n*t*np.pi/T)/(n*t*np.pi/T)) for n in range(2, N)]
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for i in range(len(vu)):
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plt.scatter(vu[i], c[i], linewidth=0.005, label='',
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color='purple', s=15)
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ax.vlines(vu[i], 0, c[i], colors='purple')
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ax.set_xlabel(greek_letters[41]+', Hz')
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ax.set_ylabel("$a_n$, мВ")
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plt.savefig("a(n)")
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plt.show()
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def part_2():
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plt.figure(dpi=500, figsize=(8, 5))
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data = make_dic("T(dnu).csv")
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x = 1 / data["T"]*10**3
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y = data['dnu']
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xlabel = "1/"+greek_letters[48]+'$, $Гц'
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ylabel = greek_letters[0]+greek_letters[41]+'$,10^4$ Гц'
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k, b, sigma = make_graffic(x, y, xlabel, ylabel,
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caption_point='', xerr=0, yerr=0, s=40)
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print(k, sigma[0], -sigma[0]/k*100)
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plt.savefig("T(dnu)")
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plt.show()
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def part_3():
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plt.figure(dpi=500, figsize=(8, 5))
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data = make_dic("a(m).csv")
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otn = data['a_b']/data['a_c']
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k, b, sigma = make_graffic(data['m']/100, otn, 'm', '$а_{бок}/a_{осн}$',
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caption_point='', xerr=0, yerr=0, s=40)
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print(k, sigma[0])
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plt.savefig("a(m)")
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plt.show()
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greek_letters=[chr(code) for code in range(916,980)]
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print(greek_letters)
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make_all()
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11
3.6.1Спектр/T(dnu).csv
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3.6.1Спектр/T(dnu).csv
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T;dnu;T_1;dnu_1
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0.2;6250;0.5;125
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1;2778;1;247
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1.5;4167;2;490
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2;1042;3;714
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2.5;1190;4;892
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3;735;4;892
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3.5;893;4;892
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4;1000;4;892
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4.5;1042;4;892
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5;1190;4;892
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3.6.1Спектр/T(dnu).png
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3.6.1Спектр/T(dnu).png
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3.6.1Спектр/a(m).csv
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3.6.1Спектр/a(m).csv
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m;a_b;a_c
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50;186;738
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10;38;738
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20;74;738
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30;110;738
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40;150;738
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60;222;738
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70;258;738
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80;298;738
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90;334;738
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100;370;738
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3.6.1Спектр/a(m).png
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3.6.1Спектр/a(n).csv
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3.6.1Спектр/a(n).csv
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a;nu;n
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90;8200;2
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53;7800;3
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39;7200;4
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30;7800;5
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24;6400;6
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21;6200;7
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3.6.1Спектр/a(n).png
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3.6.1Спектр/dnu(tau).csv
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3.6.1Спектр/dnu(tau).csv
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d_nu;tau
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50200;20
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25200;40
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17200;60
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13000;80
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10200;100
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8600;120
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7400;140
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6600;160
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5800;180
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5000;200
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3.6.1Спектр/dnu(tau).png
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3.6.1Спектр/dnu(tau).png
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3.6.1Спектр/rect.png
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3.6.1Спектр/Спектр.aux
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3.6.1Спектр/Спектр.aux
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\relax
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\providecommand\hyper@newdestlabel[2]{}
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\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
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\HyperFirstAtBeginDocument{\ifx\hyper@anchor\@undefined
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\global\let\oldcontentsline\contentsline
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\gdef\contentsline#1#2#3#4{\oldcontentsline{#1}{#2}{#3}}
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\global\let\oldnewlabel\newlabel
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\gdef\newlabel#1#2{\newlabelxx{#1}#2}
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\gdef\newlabelxx#1#2#3#4#5#6{\oldnewlabel{#1}{{#2}{#3}}}
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\AtEndDocument{\ifx\hyper@anchor\@undefined
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\let\contentsline\oldcontentsline
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\let\newlabel\oldnewlabel
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\fi}
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\fi}
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\global\let\hyper@last\relax
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\gdef\HyperFirstAtBeginDocument#1{#1}
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\providecommand\HyField@AuxAddToFields[1]{}
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\providecommand\HyField@AuxAddToCoFields[2]{}
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\providecommand\babel@aux[2]{}
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\@nameuse{bbl@beforestart}
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\catcode `"\active
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\babel@aux{russian}{}
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\@writefile{toc}{\contentsline {section}{\numberline {1}Аннотация}{1}{section.1}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\numberline {2}Введение}{1}{section.2}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\numberline {3}Поставка задачи}{1}{section.3}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\numberline {4}Теоретические сведения}{1}{section.4}\protected@file@percent }
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\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Периодическая последовательность прямоугольных импульсов}}{2}{figure.1}\protected@file@percent }
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\newlabel{rect}{{1}{2}{Периодическая последовательность прямоугольных импульсов}{figure.1}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Периодическая последовательность цуг}}{3}{figure.2}\protected@file@percent }
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\newlabel{цуги}{{2}{3}{Периодическая последовательность цуг}{figure.2}{}}
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\@writefile{toc}{\contentsline {section}{\numberline {5}Методика измерений}{3}{section.5}\protected@file@percent }
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\@writefile{toc}{\contentsline {section}{\numberline {6}Измерения и обработка данных}{3}{section.6}\protected@file@percent }
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\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces Спектры прямоугольных импульсов}}{4}{figure.3}\protected@file@percent }
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\newlabel{прямоуг}{{3}{4}{Спектры прямоугольных импульсов}{figure.3}{}}
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||||
defining Unicode char U+0432 (decimal 1074)
|
||||
defining Unicode char U+0433 (decimal 1075)
|
||||
defining Unicode char U+0434 (decimal 1076)
|
||||
defining Unicode char U+0435 (decimal 1077)
|
||||
defining Unicode char U+0436 (decimal 1078)
|
||||
defining Unicode char U+0437 (decimal 1079)
|
||||
defining Unicode char U+0438 (decimal 1080)
|
||||
defining Unicode char U+0439 (decimal 1081)
|
||||
defining Unicode char U+043A (decimal 1082)
|
||||
defining Unicode char U+043B (decimal 1083)
|
||||
defining Unicode char U+043C (decimal 1084)
|
||||
defining Unicode char U+043D (decimal 1085)
|
||||
defining Unicode char U+043E (decimal 1086)
|
||||
defining Unicode char U+043F (decimal 1087)
|
||||
defining Unicode char U+0440 (decimal 1088)
|
||||
defining Unicode char U+0441 (decimal 1089)
|
||||
defining Unicode char U+0442 (decimal 1090)
|
||||
defining Unicode char U+0443 (decimal 1091)
|
||||
defining Unicode char U+0444 (decimal 1092)
|
||||
defining Unicode char U+0445 (decimal 1093)
|
||||
defining Unicode char U+0446 (decimal 1094)
|
||||
defining Unicode char U+0447 (decimal 1095)
|
||||
defining Unicode char U+0448 (decimal 1096)
|
||||
defining Unicode char U+0449 (decimal 1097)
|
||||
defining Unicode char U+044A (decimal 1098)
|
||||
defining Unicode char U+044B (decimal 1099)
|
||||
defining Unicode char U+044C (decimal 1100)
|
||||
defining Unicode char U+044D (decimal 1101)
|
||||
defining Unicode char U+044E (decimal 1102)
|
||||
defining Unicode char U+044F (decimal 1103)
|
||||
defining Unicode char U+0450 (decimal 1104)
|
||||
defining Unicode char U+0451 (decimal 1105)
|
||||
defining Unicode char U+0452 (decimal 1106)
|
||||
defining Unicode char U+0453 (decimal 1107)
|
||||
defining Unicode char U+0454 (decimal 1108)
|
||||
defining Unicode char U+0455 (decimal 1109)
|
||||
defining Unicode char U+0456 (decimal 1110)
|
||||
defining Unicode char U+0457 (decimal 1111)
|
||||
defining Unicode char U+0458 (decimal 1112)
|
||||
defining Unicode char U+0459 (decimal 1113)
|
||||
defining Unicode char U+045A (decimal 1114)
|
||||
defining Unicode char U+045B (decimal 1115)
|
||||
defining Unicode char U+045C (decimal 1116)
|
||||
defining Unicode char U+045D (decimal 1117)
|
||||
defining Unicode char U+045E (decimal 1118)
|
||||
defining Unicode char U+045F (decimal 1119)
|
||||
defining Unicode char U+0490 (decimal 1168)
|
||||
defining Unicode char U+0491 (decimal 1169)
|
||||
defining Unicode char U+0492 (decimal 1170)
|
||||
defining Unicode char U+0493 (decimal 1171)
|
||||
defining Unicode char U+0496 (decimal 1174)
|
||||
defining Unicode char U+0497 (decimal 1175)
|
||||
defining Unicode char U+0498 (decimal 1176)
|
||||
defining Unicode char U+0499 (decimal 1177)
|
||||
defining Unicode char U+049A (decimal 1178)
|
||||
defining Unicode char U+049B (decimal 1179)
|
||||
defining Unicode char U+049C (decimal 1180)
|
||||
defining Unicode char U+049D (decimal 1181)
|
||||
defining Unicode char U+04A0 (decimal 1184)
|
||||
defining Unicode char U+04A1 (decimal 1185)
|
||||
defining Unicode char U+04A2 (decimal 1186)
|
||||
defining Unicode char U+04A3 (decimal 1187)
|
||||
defining Unicode char U+04A4 (decimal 1188)
|
||||
defining Unicode char U+04A5 (decimal 1189)
|
||||
defining Unicode char U+04AA (decimal 1194)
|
||||
defining Unicode char U+04AB (decimal 1195)
|
||||
defining Unicode char U+04AE (decimal 1198)
|
||||
defining Unicode char U+04AF (decimal 1199)
|
||||
defining Unicode char U+04B0 (decimal 1200)
|
||||
defining Unicode char U+04B1 (decimal 1201)
|
||||
defining Unicode char U+04B2 (decimal 1202)
|
||||
defining Unicode char U+04B3 (decimal 1203)
|
||||
defining Unicode char U+04B6 (decimal 1206)
|
||||
defining Unicode char U+04B7 (decimal 1207)
|
||||
defining Unicode char U+04B8 (decimal 1208)
|
||||
defining Unicode char U+04B9 (decimal 1209)
|
||||
defining Unicode char U+04BA (decimal 1210)
|
||||
defining Unicode char U+04BB (decimal 1211)
|
||||
defining Unicode char U+04C0 (decimal 1216)
|
||||
defining Unicode char U+04C1 (decimal 1217)
|
||||
defining Unicode char U+04C2 (decimal 1218)
|
||||
defining Unicode char U+04D0 (decimal 1232)
|
||||
defining Unicode char U+04D1 (decimal 1233)
|
||||
defining Unicode char U+04D2 (decimal 1234)
|
||||
defining Unicode char U+04D3 (decimal 1235)
|
||||
defining Unicode char U+04D4 (decimal 1236)
|
||||
defining Unicode char U+04D5 (decimal 1237)
|
||||
defining Unicode char U+04D6 (decimal 1238)
|
||||
defining Unicode char U+04D7 (decimal 1239)
|
||||
defining Unicode char U+04D8 (decimal 1240)
|
||||
defining Unicode char U+04D9 (decimal 1241)
|
||||
defining Unicode char U+04DA (decimal 1242)
|
||||
defining Unicode char U+04DB (decimal 1243)
|
||||
defining Unicode char U+04DC (decimal 1244)
|
||||
defining Unicode char U+04DD (decimal 1245)
|
||||
defining Unicode char U+04DE (decimal 1246)
|
||||
defining Unicode char U+04DF (decimal 1247)
|
||||
defining Unicode char U+04E2 (decimal 1250)
|
||||
defining Unicode char U+04E3 (decimal 1251)
|
||||
defining Unicode char U+04E4 (decimal 1252)
|
||||
defining Unicode char U+04E5 (decimal 1253)
|
||||
defining Unicode char U+04E6 (decimal 1254)
|
||||
defining Unicode char U+04E7 (decimal 1255)
|
||||
defining Unicode char U+04E8 (decimal 1256)
|
||||
defining Unicode char U+04E9 (decimal 1257)
|
||||
defining Unicode char U+04EC (decimal 1260)
|
||||
defining Unicode char U+04ED (decimal 1261)
|
||||
defining Unicode char U+04EE (decimal 1262)
|
||||
defining Unicode char U+04EF (decimal 1263)
|
||||
defining Unicode char U+04F0 (decimal 1264)
|
||||
defining Unicode char U+04F1 (decimal 1265)
|
||||
defining Unicode char U+04F2 (decimal 1266)
|
||||
defining Unicode char U+04F3 (decimal 1267)
|
||||
defining Unicode char U+04F4 (decimal 1268)
|
||||
defining Unicode char U+04F5 (decimal 1269)
|
||||
defining Unicode char U+04F8 (decimal 1272)
|
||||
defining Unicode char U+04F9 (decimal 1273)
|
||||
defining Unicode char U+200C (decimal 8204)
|
||||
defining Unicode char U+2013 (decimal 8211)
|
||||
defining Unicode char U+2014 (decimal 8212)
|
||||
defining Unicode char U+2018 (decimal 8216)
|
||||
defining Unicode char U+2019 (decimal 8217)
|
||||
defining Unicode char U+201C (decimal 8220)
|
||||
defining Unicode char U+201D (decimal 8221)
|
||||
defining Unicode char U+201E (decimal 8222)
|
||||
defining Unicode char U+2030 (decimal 8240)
|
||||
defining Unicode char U+2031 (decimal 8241)
|
||||
defining Unicode char U+2116 (decimal 8470)
|
||||
defining Unicode char U+2329 (decimal 9001)
|
||||
defining Unicode char U+232A (decimal 9002)
|
||||
defining Unicode char U+2423 (decimal 9251)
|
||||
defining Unicode char U+27E8 (decimal 10216)
|
||||
defining Unicode char U+27E9 (decimal 10217)
|
||||
defining Unicode char U+FB00 (decimal 64256)
|
||||
defining Unicode char U+FB01 (decimal 64257)
|
||||
defining Unicode char U+FB02 (decimal 64258)
|
||||
defining Unicode char U+FB03 (decimal 64259)
|
||||
defining Unicode char U+FB04 (decimal 64260)
|
||||
defining Unicode char U+FB05 (decimal 64261)
|
||||
defining Unicode char U+FB06 (decimal 64262)
|
||||
)
|
||||
\symT2Aletters=\mathgroup6
|
||||
)
|
||||
LaTeX Font Info: Trying to load font information for T2A+cmr on input line 1
|
||||
12.
|
||||
|
||||
(C:\Users\anna\AppData\Roaming\MiKTeX\tex/latex/cyrillic\t2acmr.fd
|
||||
File: t2acmr.fd 2001/08/11 v1.0a Computer Modern Cyrillic font definitions
|
||||
))
|
||||
(C:\Program Files\MiKTeX\tex/latex/base\inputenc.sty
|
||||
Package: inputenc 2021/02/14 v1.3d Input encoding file
|
||||
\inpenc@prehook=\toks19
|
||||
\inpenc@posthook=\toks20
|
||||
)
|
||||
(C:\Program Files\MiKTeX\tex/generic/babel\babel.sty
|
||||
Package: babel 2021/06/02 3.60 The Babel package
|
||||
|
||||
(C:\Program Files\MiKTeX\tex/generic/babel\babel.def
|
||||
File: babel.def 2021/06/02 3.60 Babel common definitions
|
||||
\babel@savecnt=\count270
|
||||
\U@D=\dimen155
|
||||
\l@unhyphenated=\language79
|
||||
|
||||
(C:\Program Files\MiKTeX\tex/generic/babel\txtbabel.def)
|
||||
\bbl@readstream=\read2
|
||||
)
|
||||
\bbl@dirlevel=\count271
|
||||
|
||||
*************************************
|
||||
* Local config file bblopts.cfg used
|
||||
*
|
||||
(C:\Program Files\MiKTeX\tex/latex/arabi\bblopts.cfg
|
||||
File: bblopts.cfg 2005/09/08 v0.1 add Arabic and Farsi to "declared" options of
|
||||
babel
|
||||
)
|
||||
(C:\Program Files\MiKTeX\tex/latex/babel-english\english.ldf
|
||||
Language: english 2017/06/06 v3.3r English support from the babel system
|
||||
Package babel Info: Hyphen rules for 'canadian' set to \l@english
|
||||
(babel) (\language0). Reported on input line 102.
|
||||
Package babel Info: Hyphen rules for 'australian' set to \l@ukenglish
|
||||
(babel) (\language73). Reported on input line 105.
|
||||
Package babel Info: Hyphen rules for 'newzealand' set to \l@ukenglish
|
||||
(babel) (\language73). Reported on input line 108.
|
||||
)
|
||||
(C:\Users\anna\AppData\Roaming\MiKTeX\tex/latex/babel-russian\russianb.ldf
|
||||
File: russianb.ldf 2021/01/10 1.3m Russian support for the Babel system
|
||||
Language: russian 2020/09/09 1.3k Russian support for the Babel system
|
||||
Package babel Info: Making " an active character on input line 124.
|
||||
Package babel Info: Default for \cyrdash is provided on input line 163.
|
||||
))
|
||||
(C:\Program Files\MiKTeX\tex/latex/amsmath\amsmath.sty
|
||||
Package: amsmath 2021/04/20 v2.17j AMS math features
|
||||
\@mathmargin=\skip50
|
||||
|
||||
For additional information on amsmath, use the `?' option.
|
||||
(C:\Program Files\MiKTeX\tex/latex/amsmath\amstext.sty
|
||||
Package: amstext 2000/06/29 v2.01 AMS text
|
||||
|
||||
(C:\Program Files\MiKTeX\tex/latex/amsmath\amsgen.sty
|
||||
File: amsgen.sty 1999/11/30 v2.0 generic functions
|
||||
\@emptytoks=\toks21
|
||||
\ex@=\dimen156
|
||||
))
|
||||
(C:\Program Files\MiKTeX\tex/latex/amsmath\amsbsy.sty
|
||||
Package: amsbsy 1999/11/29 v1.2d Bold Symbols
|
||||
\pmbraise@=\dimen157
|
||||
)
|
||||
(C:\Program Files\MiKTeX\tex/latex/amsmath\amsopn.sty
|
||||
Package: amsopn 2016/03/08 v2.02 operator names
|
||||
)
|
||||
\inf@bad=\count272
|
||||
LaTeX Info: Redefining \frac on input line 234.
|
||||
\uproot@=\count273
|
||||
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|
||||
LaTeX Info: Redefining \overline on input line 399.
|
||||
\classnum@=\count275
|
||||
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|
||||
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|
||||
LaTeX Info: Redefining \dots on input line 499.
|
||||
LaTeX Info: Redefining \cdots on input line 620.
|
||||
\Mathstrutbox@=\box51
|
||||
\strutbox@=\box52
|
||||
\big@size=\dimen158
|
||||
LaTeX Font Info: Redeclaring font encoding OML on input line 743.
|
||||
\symOMLletters=\mathgroup7
|
||||
LaTeX Font Info: Redeclaring font encoding OMS on input line 744.
|
||||
\symOMSletters=\mathgroup8
|
||||
\macc@depth=\count277
|
||||
\c@MaxMatrixCols=\count278
|
||||
\dotsspace@=\muskip17
|
||||
\c@parentequation=\count279
|
||||
\dspbrk@lvl=\count280
|
||||
\tag@help=\toks22
|
||||
\row@=\count281
|
||||
\column@=\count282
|
||||
\maxfields@=\count283
|
||||
\andhelp@=\toks23
|
||||
\eqnshift@=\dimen159
|
||||
\alignsep@=\dimen160
|
||||
\tagshift@=\dimen161
|
||||
\tagwidth@=\dimen162
|
||||
\totwidth@=\dimen163
|
||||
\lineht@=\dimen164
|
||||
\@envbody=\toks24
|
||||
\multlinegap=\skip51
|
||||
\multlinetaggap=\skip52
|
||||
\mathdisplay@stack=\toks25
|
||||
LaTeX Info: Redefining \[ on input line 2923.
|
||||
LaTeX Info: Redefining \] on input line 2924.
|
||||
)
|
||||
(C:\Program Files\MiKTeX\tex/latex/amsfonts\amsfonts.sty
|
||||
Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
|
||||
\symAMSa=\mathgroup9
|
||||
\symAMSb=\mathgroup10
|
||||
LaTeX Font Info: Redeclaring math symbol \hbar on input line 98.
|
||||
LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
|
||||
(Font) U/euf/m/n --> U/euf/b/n on input line 106.
|
||||
)
|
||||
(C:\Program Files\MiKTeX\tex/latex/amsfonts\amssymb.sty
|
||||
Package: amssymb 2013/01/14 v3.01 AMS font symbols
|
||||
)
|
||||
(C:\Users\anna\AppData\Roaming\MiKTeX\tex/latex/amscls\amsthm.sty
|
||||
Package: amsthm 2020/05/29 v2.20.6
|
||||
\thm@style=\toks26
|
||||
\thm@bodyfont=\toks27
|
||||
\thm@headfont=\toks28
|
||||
\thm@notefont=\toks29
|
||||
\thm@headpunct=\toks30
|
||||
\thm@preskip=\skip53
|
||||
\thm@postskip=\skip54
|
||||
\thm@headsep=\skip55
|
||||
\dth@everypar=\toks31
|
||||
)
|
||||
(C:\Users\anna\AppData\Roaming\MiKTeX\tex/latex/mathtools\mathtools.sty
|
||||
Package: mathtools 2021/04/12 v1.27 mathematical typesetting tools
|
||||
|
||||
(C:\Program Files\MiKTeX\tex/latex/tools\calc.sty
|
||||
Package: calc 2017/05/25 v4.3 Infix arithmetic (KKT,FJ)
|
||||
\calc@Acount=\count284
|
||||
\calc@Bcount=\count285
|
||||
\calc@Adimen=\dimen165
|
||||
\calc@Bdimen=\dimen166
|
||||
\calc@Askip=\skip56
|
||||
\calc@Bskip=\skip57
|
||||
LaTeX Info: Redefining \setlength on input line 80.
|
||||
LaTeX Info: Redefining \addtolength on input line 81.
|
||||
\calc@Ccount=\count286
|
||||
\calc@Cskip=\skip58
|
||||
)
|
||||
(C:\Users\anna\AppData\Roaming\MiKTeX\tex/latex/mathtools\mhsetup.sty
|
||||
Package: mhsetup 2021/03/18 v1.4 programming setup (MH)
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||||
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|
||||
LaTeX Info: Thecontrolsequence`\('isalreadyrobust on input line 130.
|
||||
LaTeX Info: Thecontrolsequence`\)'isalreadyrobust on input line 130.
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||||
LaTeX Info: Thecontrolsequence`\['isalreadyrobust on input line 130.
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||||
LaTeX Info: Thecontrolsequence`\]'isalreadyrobust on input line 130.
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||||
\g_MT_multlinerow_int=\count287
|
||||
\l_MT_multwidth_dim=\dimen167
|
||||
\origjot=\skip59
|
||||
\l_MT_shortvdotswithinadjustabove_dim=\dimen168
|
||||
\l_MT_shortvdotswithinadjustbelow_dim=\dimen169
|
||||
\l_MT_above_intertext_sep=\dimen170
|
||||
\l_MT_below_intertext_sep=\dimen171
|
||||
\l_MT_above_shortintertext_sep=\dimen172
|
||||
\l_MT_below_shortintertext_sep=\dimen173
|
||||
\xmathstrut@box=\box53
|
||||
\xmathstrut@dim=\dimen174
|
||||
)
|
||||
(C:\Users\anna\AppData\Roaming\MiKTeX\tex/latex/titlesec\titlesec.sty
|
||||
Package: titlesec 2021/07/05 v2.14 Sectioning titles
|
||||
\ttl@box=\box54
|
||||
\beforetitleunit=\skip60
|
||||
\aftertitleunit=\skip61
|
||||
\ttl@plus=\dimen175
|
||||
\ttl@minus=\dimen176
|
||||
\ttl@toksa=\toks32
|
||||
\titlewidth=\dimen177
|
||||
\titlewidthlast=\dimen178
|
||||
\titlewidthfirst=\dimen179
|
||||
)
|
||||
(C:\Users\anna\AppData\Roaming\MiKTeX\tex/latex/wasysym\wasysym.sty
|
||||
Package: wasysym 2020/01/19 v2.4 Wasy-2 symbol support package
|
||||
\symwasy=\mathgroup11
|
||||
LaTeX Font Info: Overwriting symbol font `wasy' in version `bold'
|
||||
(Font) U/wasy/m/n --> U/wasy/b/n on input line 93.
|
||||
)
|
||||
(C:\Program Files\MiKTeX\tex/latex/l3backend\l3backend-pdftex.def
|
||||
File: l3backend-pdftex.def 2021-05-07 L3 backend support: PDF output (pdfTeX)
|
||||
\l__color_backend_stack_int=\count288
|
||||
\l__pdf_internal_box=\box55
|
||||
)
|
||||
(Спектр.aux)
|
||||
\openout1 = `Спектр.aux'.
|
||||
|
||||
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 35.
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||||
LaTeX Font Info: ... okay on input line 35.
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||||
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 35.
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||||
LaTeX Font Info: ... okay on input line 35.
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||||
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||||
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||||
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||||
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||||
LaTeX Font Info: ... okay on input line 35.
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||||
LaTeX Font Info: Checking defaults for T2A/cmr/m/n on input line 35.
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||||
LaTeX Font Info: ... okay on input line 35.
|
||||
(C:\Program Files\MiKTeX\tex/context/base/mkii\supp-pdf.mkii
|
||||
[Loading MPS to PDF converter (version 2006.09.02).]
|
||||
\scratchcounter=\count289
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||||
\scratchdimen=\dimen180
|
||||
\scratchbox=\box56
|
||||
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||||
\nofMParguments=\count291
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|
||||
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|
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\MPscratchDim=\dimen181
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||||
\MPnumerator=\count293
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||||
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|
||||
) (C:\Program Files\MiKTeX\tex/latex/epstopdf-pkg\epstopdf-base.sty
|
||||
Package: epstopdf-base 2020-01-24 v2.11 Base part for package epstopdf
|
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Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4
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|
||||
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\BOOKMARK [2][-]{subsection.6.2}{\376\377\004\030\004\101\004\101\004\073\004\065\004\064\004\076\004\062\004\060\004\075\004\070\004\065\000\040\004\101\004\077\004\065\004\072\004\102\004\100\004\060\000\040\004\063\004\060\004\100\004\074\004\076\004\075\004\070\004\107\004\065\004\101\004\072\004\070\004\105\000\040\004\101\004\070\004\063\004\075\004\060\004\073\004\076\004\062\000,\000\040\004\074\004\076\004\064\004\103\004\073\004\070\004\100\004\076\004\062\004\060\004\075\004\075\004\113\004\105\000\040\004\077\004\076\000\040\004\060\004\074\004\077\004\073\004\070\004\102\004\103\004\064\004\065}{section.6}% 8
|
||||
\BOOKMARK [1][-]{section.7}{\376\377\004\022\004\113\004\062\004\076\004\064\004\113}{}% 9
|
||||
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|
||||
\documentclass[a4paper,12pt]{article} % тип документа
|
||||
|
||||
% report, book
|
||||
|
||||
% Рисунки
|
||||
\usepackage{graphicx}
|
||||
\usepackage{wrapfig}
|
||||
\usepackage{mathtext}
|
||||
\usepackage[left=2cm,right=2cm,
|
||||
top=2cm,bottom=2cm,bindingoffset=0cm]{geometry}
|
||||
|
||||
\usepackage{hyperref}
|
||||
\usepackage[rgb]{xcolor}
|
||||
\hypersetup{ % Гиперссылки
|
||||
colorlinks=true, % false: ссылки в рамках
|
||||
urlcolor=blue % на URL
|
||||
}
|
||||
|
||||
% Русский язык
|
||||
\usepackage[T2A]{fontenc} % кодировка
|
||||
\usepackage[utf8]{inputenc} % кодировка исходного текста
|
||||
\usepackage[english,russian]{babel} % локализация и переносы
|
||||
|
||||
|
||||
% Математика
|
||||
\usepackage{amsmath,amsfonts,amssymb,amsthm,mathtools}
|
||||
\usepackage{titlesec}
|
||||
\titlelabel{\thetitle.\quad}
|
||||
|
||||
\usepackage{wasysym}
|
||||
|
||||
\author{Анна Назарчук Б02-109}
|
||||
\title{3.6.1 Спектральный анализ электрических сигналов}
|
||||
\date{}
|
||||
\begin{document}
|
||||
\maketitle
|
||||
\section{Аннотация}
|
||||
В работе исследуются спектры периодических сигналов: модулированный по амплитуде, прямоугольные импульсы и цуги. Проверяются теоретические зависимости параметров спектра на практике.
|
||||
|
||||
|
||||
\section{Введение}
|
||||
Задача описания поведения некоторой системы во времени зачастую
|
||||
сводится к выяснению связи между "сигналом", подаваемым на "вход"
|
||||
системы (обозначим его как $f(t)$), и её реакцией на "выходе" $g(t)$). Если произвольную функцию $f(t)$ удастся представить в виде
|
||||
некоторой суммы ряда (конечного или бесконечного) гармонических
|
||||
слагаемых, то при известной частотной характеристике $\lambda(\omega)$) задача
|
||||
о связи воздействия и отклика системы будет решена. Такое разложение
|
||||
называют спектральным. Оно имеет физический смысл: высоко добротный колебательный контур выделяет из подаваемого на него сигнала те спектральные компоненты, частоты которых близки к его собственной. Возможность разложить произвольную функцию $f(t)$ в ряд (или интеграл)
|
||||
Фурье единственным и однозначным способом подразумевает и
|
||||
возможность "собрать" сигнал любой формы, используя гармонические
|
||||
колебания с подобранными амплитудами и фазами. В последнее время повсеместное распространение получила цифровая
|
||||
обработка сигналов. Спектральный состав оцифрованного сигнала
|
||||
может быть найден численно. Это и планируется проследить в работе.
|
||||
|
||||
|
||||
\section{Поставка задачи}
|
||||
Сгенерировать и получить на осциллографе спектры различных периодических сигналов. Проверить экспериментально соотношение неопределенности и отношения амплитуд гармоник при модулированных по амплитуде сигналах.
|
||||
|
||||
\section{Теоретические сведения}
|
||||
Задача описания поведения некоторой системы во времени зачастую
|
||||
сводится к выяснению связи межу «сигналом», подаваемым на «вход»
|
||||
системы (обозначим его как $f(t)$), и её реакцией на «выходе» ($g(t)$).
|
||||
Для линейных стационарных фильтров: $g = \hat{\Lambda}[f]$, $\hat{\Lambda}$ - линейное преобразование. Из линейности системы: $f=\sum c_nf_n$, $g_n = c_n \cdot \hat{\Lambda}[f_n]$
|
||||
\begin{equation}
|
||||
g(t) = \sum c_n \hat{\Lambda}[f_n]
|
||||
\end{equation}
|
||||
Выбор элементарных слагаемых - собственные векторы.
|
||||
\begin{equation}
|
||||
f(t) = \sum_n c_n e^{i\omega_n t}
|
||||
\end{equation}
|
||||
Такое представление - ряд Фурье.
|
||||
\subsection*{Спект периодического процесса}
|
||||
Периодический процесс - $f(t)=f(t+T)$
|
||||
\begin{equation}
|
||||
f(t) = \sum_{n=-\inf}^{\inf} c_n e^{in\omega_0 t}
|
||||
\end{equation}
|
||||
Набор коэффициентов можно найти, домножив обе части прошлого равенства на $e^{-im\omega_0 t}$ и проинтегрировав по периоду:
|
||||
\begin{equation}
|
||||
c_n = \frac{1}{T}\int_0^T f(t)e^{-in\omega_0 t}dt
|
||||
\end{equation}
|
||||
\begin{figure}[h!]
|
||||
\includegraphics[width=0.4\textwidth]{rect}
|
||||
\caption{Периодическая последовательность прямоугольных импульсов} \label{rect}
|
||||
\end{figure}
|
||||
Рассмотрим спектр периодической последовательности прямоугольных импульсов (рис. \ref{rect}):
|
||||
\begin{equation}
|
||||
c_n = \frac{1}{T}\int_{-\tau / 2}^{\tau / 2} e^{-in\omega_0 t}dt = \dfrac{sin(\pi n \tau / T))}{\pi n}
|
||||
\end{equation}
|
||||
|
||||
\subsection*{Свойства спектров}
|
||||
Справедливо для произвольного сигнала соотношение неопределенностей:
|
||||
\begin{equation}
|
||||
\Delta \omega \cdot \Delta t \sim 2\pi
|
||||
\end{equation}
|
||||
Рассмотрим спектр обрывка синусоиды (цуг):
|
||||
\begin{equation}
|
||||
f(t) = f_0(t)\cos(\omega_0 t)
|
||||
\end{equation}
|
||||
Из спектра прямоугольного импульса:
|
||||
\begin{equation}
|
||||
F(\omega) = \dfrac{\tau}{2}\left[\dfrac{\sin(\omega-\omega_0)\tau /2}
|
||||
{(\omega-\omega_0)\tau /2}
|
||||
+ \dfrac{\sin(\omega+\omega_0)\tau /2}{\omega+\omega_0)\tau /2}\right]
|
||||
\end{equation}
|
||||
Получим спектр периодической последовательности цугов (рис. \ref{цуги}):
|
||||
\begin{equation}
|
||||
F(\omega) = \dfrac{\tau}{2T}\left[\dfrac{\sin(\omega-\omega_0)\tau /2}
|
||||
{(\omega-\omega_0)\tau /2}
|
||||
+ \dfrac{\sin(\omega+\omega_0)\tau /2}{(\omega+\omega_0)\tau /2}\right]
|
||||
\end{equation}
|
||||
|
||||
\begin{figure}[h!]
|
||||
\begin{center}
|
||||
\includegraphics[width=0.4\textwidth]{цуги}
|
||||
\caption{Периодическая последовательность цуг} \label{цуги}
|
||||
\end{center}
|
||||
\end{figure}
|
||||
\subsection*{Модуляция}
|
||||
Модулированные колебания:
|
||||
\begin{equation}
|
||||
f(t) = a(t) \cos (\omega_0 t+\varphi(t))
|
||||
\end{equation}
|
||||
Простейшее амплитудно-модулированное колебание:
|
||||
\begin{equation}
|
||||
f(t)= a(t) \cos (\omega_0 t), \hspace{3mm} a(t) = a_0(1+m\cos(\Omega t))
|
||||
\end{equation}
|
||||
В выражении $0 < m \leq 1$ - глубина модуляции, выражается:
|
||||
\begin{equation}
|
||||
m = \dfrac{a_{max}-a_{min}}{a_{max}+a_{min}}
|
||||
\end{equation}
|
||||
Из прошлой формулы можно получить:
|
||||
\begin{equation}
|
||||
f(t) = a_0 \cos (\omega_0 t) +\dfrac{ma_0}{2}\cos (\omega_0 +\Omega)t++\dfrac{ma_0}{2}\cos (\omega_0 -\Omega)t
|
||||
\end{equation}
|
||||
|
||||
\section{Методика измерений}
|
||||
В работе используются генератор сигналов произвольной формы, цифровой осциллограф с функцией быстрого преобразования Фурье.
|
||||
|
||||
\section{Измерения и обработка данных}
|
||||
\subsection*{Исследования спектра периодической последовательности прямоугольных импульсов}
|
||||
На генераторе создается сигнал с разными параметрами, по которому на экране осциллографа получается спектр (рис. \ref{прямоуг})
|
||||
|
||||
\begin{figure}[h!]
|
||||
\begin{minipage}[h!]{0.47\linewidth}
|
||||
\center{\includegraphics[width=1\linewidth]{1_1}} a) $\nu_{повт} = 1000 Гц, \tau = 50 мкс$\\
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}[h!]{0.47\linewidth}
|
||||
\center{\includegraphics[width=1\linewidth]{1_2}} \\b) $\nu_{повт} = 1400 Гц, \tau = 50 мкс$
|
||||
\end{minipage}
|
||||
\vfill
|
||||
\begin{minipage}[h!]{0.47\linewidth}
|
||||
\center{\includegraphics[width=1\linewidth]{1_3}} c) $\nu_{повт} = 700 Гц, \tau = 50 мкс$ \\
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}[h!]{0.47\linewidth}
|
||||
\center{\includegraphics[width=1\linewidth]{1_4}} d) $\nu_{повт} = 1000 Гц, \tau = 70 мкс$ \\
|
||||
\end{minipage}
|
||||
\caption{Спектры прямоугольных импульсов}
|
||||
\label{прямоуг}
|
||||
\end{figure}
|
||||
При $\nu_{повт} = 700 Гц$ проведены измерения ширины спектра. Результаты
|
||||
представлены в таблице \ref{dnu(tau)_tbl} и на рисунке \ref{dnu(tau)_img}.
|
||||
\begin{table}[h!]
|
||||
\caption{Зависимость ширины спектра от длительности спектра} \label{dnu(tau)_tbl}
|
||||
\begin{tabular}{|l|l|}
|
||||
\hline
|
||||
$\Delta\nu$, Hz & $\tau$, мкс \\ \hline
|
||||
50200 & 20 \\ \hline
|
||||
25200 & 40 \\ \hline
|
||||
17200 & 60 \\ \hline
|
||||
13000 & 80 \\ \hline
|
||||
10200 & 100 \\ \hline
|
||||
8600 & 120 \\ \hline
|
||||
7400 & 140 \\ \hline
|
||||
6600 & 160 \\ \hline
|
||||
5800 & 180 \\ \hline
|
||||
5000 & 200 \\ \hline
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
|
||||
\begin{figure}[h!]
|
||||
\begin{center}
|
||||
\includegraphics[width=\textwidth]{dnu(tau)}
|
||||
\caption{Зависимость ширины спектра от длительности спектра} \label{dnu(tau)_img}
|
||||
\end{center}
|
||||
\end{figure}
|
||||
Рассчитаем коэффициент наклона прямой:
|
||||
\begin{equation}
|
||||
k = 0.9997 \pm 0.0039
|
||||
\end{equation}
|
||||
Полученное значение близко к $1$, что подтверждает соотношение неопределенностей.
|
||||
|
||||
|
||||
Для одного из сигналов (a) рассчитаем теоретическую зависимость и изобразим на графике \ref{теор}. Теоретический и экспериментальный спектр похожи.
|
||||
|
||||
\begin{figure}[h!]
|
||||
\begin{center}
|
||||
\includegraphics[width=\textwidth]{a(n)}
|
||||
\caption{Теоретический спектр прямоугольных импульсов} \label{теор}
|
||||
\end{center}
|
||||
\end{figure}
|
||||
|
||||
\subsection{Исследование спектра периодической последовательности цугов гармонических колебаний}
|
||||
На генераторе создается сигнал последовательности синусоидальных цугов с разными параметрами, по которому на экране осциллографа получается спектр. (рис. \ref{спектр_цуги})
|
||||
|
||||
\begin{figure}[h!]
|
||||
\begin{minipage}[h!]{0.47\linewidth}
|
||||
\center{\includegraphics[width=1\linewidth]{2_1}} a) $\nu = 50 кГц, T = 1 мс, N = 5$\\
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}[h!]{0.47\linewidth}
|
||||
\center{\includegraphics[width=1\linewidth]{2_2}} \\b) $\nu = 50 кГц, T = 1 мс, N = 3$
|
||||
\end{minipage}
|
||||
\vfill
|
||||
\begin{minipage}[h!]{0.47\linewidth}
|
||||
\center{\includegraphics[width=1\linewidth]{2_3}} c) $\nu = 50 кГц, T = 3 мс, N = 5$ \\
|
||||
\end{minipage}
|
||||
\hfill
|
||||
\begin{minipage}[h!]{0.47\linewidth}
|
||||
\center{\includegraphics[width=1\linewidth]{2_4}} d) $\nu = 30 кГц, T = 1 мс, N = 5$ \\
|
||||
\end{minipage}
|
||||
\vfill
|
||||
\begin{minipage}[h!]{0.47\linewidth}
|
||||
\center{\includegraphics[width=1\linewidth]{2_5}} \\e) $\nu = 70 кГц, T = 1 мс, N = 5$
|
||||
\end{minipage}
|
||||
\caption{Вид спектра при разных параметрах спектра}
|
||||
\label{спектр_цуги}
|
||||
\end{figure}
|
||||
|
||||
При фиксированной длительности импульсов $\tau$ = 50 мкс измерим расстояния между соседними спектральными компонентами от периода повторения импульсов (табл. \ref{dnu(T)_tbl}, рис. \ref{dnu(T)_img})
|
||||
|
||||
\begin{table}[h!]
|
||||
\caption{Зависимость расстояния между соседними спектральными компонентами от периода повторения импульсов} \label{dnu(T)_tbl}
|
||||
\begin{tabular}{|l|l|}
|
||||
\hline
|
||||
T, ms & $\delta \nu$, Hz \\ \hline
|
||||
0.2 & 6250 \\ \hline
|
||||
1 & 2778 \\ \hline
|
||||
1.5 & 4167 \\ \hline
|
||||
2 & 1042 \\ \hline
|
||||
2.5 & 1190 \\ \hline
|
||||
3 & 735 \\ \hline
|
||||
3.5 & 893 \\ \hline
|
||||
4 & 1000 \\ \hline
|
||||
4.5 & 1042 \\ \hline
|
||||
5 & 1190 \\ \hline
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
|
||||
\begin{figure}[h!]
|
||||
\begin{center}
|
||||
\includegraphics[width=0.9\textwidth]{T(dnu)}
|
||||
\caption{Зависимость расстояния между соседними спектральными компонентами от периода повторения импульсов} \label{dnu(T)_img}
|
||||
\end{center}
|
||||
\end{figure}
|
||||
|
||||
Точки должны хорошо ложиться на прямую, однако из графика видно, что это не так. Проблема заключается в снятии данных (был выбран неверный канал при курсорных измерениях). Поэтому подтвердить справедливость соотношения неопределенности невозможно.
|
||||
|
||||
\subsection{Исследование спектра гармонических сигналов, модулированных по амплитуде}
|
||||
На генераторе создается сигнал, модулированных по амплитуде, по которому на экране осциллографа получается спектр (\ref{мод}).
|
||||
\begin{figure}[h!]
|
||||
\begin{center}
|
||||
\includegraphics[width=\textwidth]{3}
|
||||
\caption{Спектр сигнала, модулированного по амплитуде} \label{мод}
|
||||
\end{center}
|
||||
\end{figure}
|
||||
Измерим с помощью осциллографа глубину модуляции:
|
||||
\begin{equation}
|
||||
m = \dfrac{A_{max}-A_{min}}{A_{max}+A_{min}} = \dfrac{1.54 - 0.04}{1.54 + 0.04} = 0.5, что сходится с установленным на генераторе
|
||||
\end{equation}
|
||||
Изменяя глубину модуляции, измерим $\dfrac{a_{бок}}{а_{осн}}$ (табл. \ref{mod_tbl} и рис. \ref{mod_img}).
|
||||
|
||||
\begin{table}[h!]
|
||||
\caption{Зависимость $\dfrac{a_{бок}}{а_{осн}}$ от $m$}
|
||||
\label{mod_tbl}
|
||||
\begin{tabular}{|l|l|l|}
|
||||
\hline
|
||||
m & a\_бок & a\_центр \\ \hline
|
||||
50 & 186 & 738 \\ \hline
|
||||
10 & 38 & 738 \\ \hline
|
||||
20 & 74 & 738 \\ \hline
|
||||
30 & 110 & 738 \\ \hline
|
||||
40 & 150 & 738 \\ \hline
|
||||
60 & 222 & 738 \\ \hline
|
||||
70 & 258 & 738 \\ \hline
|
||||
80 & 298 & 738 \\ \hline
|
||||
90 & 334 & 738 \\ \hline
|
||||
100 & 370 & 738 \\ \hline
|
||||
\end{tabular}
|
||||
\end{table}
|
||||
\begin{figure}[h!]
|
||||
\begin{center}
|
||||
\includegraphics[width=0.9\textwidth]{a(m)}
|
||||
\caption{Зависимость $\dfrac{a_{бок}}{а_{осн}}$ от $m$} \label{mod_img}
|
||||
\end{center}
|
||||
\end{figure}
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Определим коэффициент наклона прямой:
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\begin{equation}
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k = 0.502 \pm 0.002
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\end{equation}
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Результат сходится с предсказанным теоретически (0.5).
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\section{Выводы}
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|
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|
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1. При исследовании последовательности прямоугольных импульсов получена зависимость ширины спектра от длительности импульса, что подтверждает соотношение неопределенностей: $\tau \cdot \Delta\nu \sim 1$.
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2. Проверены теоретические расчеты спектра при прямоугольных импульсах (теоретическая и экспериментальная картины схожи).
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|
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3. При обработке данных от спектра периодической последовательности цугов была обнаружена ошибка при снятии данных, что не позволило проверить соотношение неопределенностей.
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4. Получен угол наклона графика зависимости $\dfrac{a_{бок}}{а_{осн}}$ от $m$ (0.5), подтверждено теоретическое значение этого угла (0.5).
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\end{document}
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3.6.1Спектр/Цуги.png
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3.6.1Спектр/Цуги.png
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