信息处理 - 使用 Python 进行模数转换 - 吾爱随笔录

我是初学者。我尝试使用 Python 模拟模拟信号转换为数字（包括按时间采样和按电平量化）。这是我的代码：

import numpy as np
import matplotlib.pyplot as plt

time_of_view        = 1.; # s.
analog_time         = np.linspace (0, time_of_view, 10e5); # s.

sampling_rate       = 20.; # Hz
sampling_period     = 1. / sampling_rate; # s
sample_number       = time_of_view / sampling_period;
sampling_time       = np.linspace (0, time_of_view, sample_number);

carrier_frequency   = 9.;
amplitude           = 1;
phase               = 0;

quantizing_bits     = 4;
quantizing_levels   = 2 ** quantizing_bits / 2;
quantizing_step     = 1. / quantizing_levels;

def analog_signal (time_point):
    return amplitude * np.cos (2 * np.pi * carrier_frequency * time_point + phase);
sampling_signal     = analog_signal (sampling_time);
quantizing_signal   = np.round (sampling_signal / quantizing_step) * quantizing_step;


fig = plt.figure ()
plt.plot (analog_time,   analog_signal (analog_time) );
#plt.stem (sampling_time, sampling_signal);
plt.stem (sampling_time, quantizing_signal, linefmt='r-', markerfmt='rs', basefmt='r-');
plt.title("Analog to digital signal conversion")
plt.xlabel("Time")
plt.ylabel("Amplitude")

plt.show()

总的来说，我对此感到满意：如果我使用变量，那么结果对我来说是预期的。除了一件事：根据清单sampling_rate = 20，carrier_frequency = 9因为sampling_rate / carrier_frequency > 2我希望转换成功，但我得到了失真的信号（看图片：输出信号的包络已经清楚地表达了幅度调制）。我的错误在哪里？我的实现是否正确？

Fs = 20; % Sampling frequency T = 1/Fs; % Sample time L = length(sampling_signal); % Length of signal t = (0:L-1)*T; % Time vector y = sampling_signal; % Sinusoids plus quantization noise NFFT = 2^nextpow2(L); Y = fft(y,NFFT)/L; f = Fs/2*linspace(0,1,NFFT/2+1); plot(f,2*abs(Y(1:NFFT/2+1))) title('Single-Sided Amplitude Spectrum of y(t)') xlabel('Frequency (Hz)') ylabel('|Y(f)|')