在数字滤波器的MATLAB与FPGA实现中，作者用MATLAB定点仿真了混频器(Mixer)的波形图。由于最近在熟练python的使用，花了点时间，把该程序用python跑了出来。两种语言略有区别，所以代码上也会有一些不同。 基本原理是两个sine函数相乘后，频率会搬移，形成DC分量以及更高的频率分量。在程序中，也仿真了没有滤除DC分量时的情况。可以看出，量化比特对于性能的影响很明显。下面分别是量化比特为2和量化比特位10的时候的仿真图。

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代码如下： from __future__ import division from pylab import * #system parameter fi = 625000 #input signal frequency fo = 625000 # local oscillator Fs = 5000000 #sampling frequency L = 1024 # data length N = 10 # quantization bit t = linspace(0,1/Fs*L,L) theta = 2*pi*rand() # random phase si = sin(2*pi*fi*t + theta) #input sine wave so = sin(2*pi*fo*t) # local oscillator sm = si * so # ideal without quantization loss sm_no_dc = sm - mean(sm) #reduce DC component si = (si * (2**(N-1))).round() #quantization so = (so * (2**(N-1))).round() sm_loss = si * so # with loss sm_loss_no_dc = sm_loss - mean(sm_loss) # - DC #normalization si = si / max(abs(si)) so = so / max(abs(so)) sm = sm / max(abs(sm)) sm_loss = sm_loss / max(abs(sm_loss)) sm_loss_no_dc = sm_loss_no_dc / max(abs(sm_loss_no_dc)) #calculate FFT and normalization # with DC component f_sm = fft(sm,L) f_sm = f_sm / max(abs(f_sm)) f_sm = concatenate([f_sm[L/2:],f_sm[0:L/2]],0) f_sm_loss = fft(sm_loss,L) f_sm_loss = f_sm_loss / max(abs(f_sm_loss)) f_sm_loss = concatenate([f_sm_loss[L/2:],f_sm_loss[0:L/2]],0) # calculate FFT, DC component filtered out f_sm_no_dc = fft(sm_no_dc,L) f_sm_no_dc = f_sm_no_dc / max(abs(f_sm_no_dc)) f_sm_loss_no_dc = fft(sm_loss_no_dc,L) f_sm_loss_no_dc = f_sm_loss_no_dc / max(abs(f_sm_loss_no_dc)) # picture axis = arange(-L/2,L/2,1)*Fs/L*(10**(-6)) fig,ax = subplots(2,2) ax[0,0].set_title("%d bit quantization" %N) ax[0,0].plot(axis,f_sm) ax[0,0].set_xlabel(r'frequency without quantization') ax[0,1].plot(axis,f_sm_loss) ax[0,1].set_title("Frequency Amplitude") ax[0,1].set_xlabel(r'frequency with quantization') ax[1,0].plot(axis,f_sm_no_dc) ax[1,0].set_xlabel(r'No quant and DC') ax[1,1].plot(axis,f_sm_loss_no_dc) ax[1,1].set_xlabel(r'quantization but no DC') t = t * (10**6) fig1,ax1 = subplots(2,2) ax1[0,0].set_title("%d bit quantization" %N) ax1[0,0].plot(t[1:32],si[1:32]) ax1[0,0].set_xlabel(r'input sine') ax1[0,1].plot(t[1:32],sm[1:32]) ax1[0,1].set_title("Time Wave") ax1[0,1].set_xlabel(r'mix sine no loss') ax1[1,0].plot(t[1:32],sm_loss[1:32]) ax1[1,0].set_xlabel(r'mix sine quantization loss') ax1[1,1].plot(t[1:32],sm_loss_no_dc[1:32]) ax1[1,1].set_xlabel(r'quantization but no DC') show()