Matlab 到 Python 代码转换 - 输出不匹配

Question

我已成功将 MATLAB 源代码转换为 Python - 但绘图输出不匹配。我已经在 Python 和 Octave 中双重验证了每个变量 bot 的值 - 它们也是相同的。

八度曲线输出：

Python Matplotlib 输出：

八度码：

clear
N  = 10^3; % number of symbols
am = 2*(rand(1,N)>0.5)-1 + j*(2*(rand(1,N)>0.5)-1); % generating random binary sequence
fs = 10; % sampling frequency in Hz

% defining the sinc filter
sincNum = sin(pi*[-fs:1/fs:fs]); % numerator of the sinc function
sincDen = (pi*[-fs:1/fs:fs]); % denominator of the sinc function
sincDenZero = find(abs(sincDen) < 10^-10);
sincOp = sincNum./sincDen;
sincOp(sincDenZero) = 1; % sin(pix/(pix) =1 for x =0

% raised cosine filter
alpha = 0.5;
cosNum = cos(alpha*pi*[-fs:1/fs:fs]);
cosDen = (1-(2*alpha*[-fs:1/fs:fs]).^2);
cosDenZero = find(abs(cosDen)<10^-10);
cosOp = cosNum./cosDen;
cosOp(cosDenZero) = pi/4;

gt_alpha5 = sincOp.*cosOp;

alpha = 1;
cosNum = cos(alpha*pi*[-fs:1/fs:fs]);
cosDen = (1-(2*alpha*[-fs:1/fs:fs]).^2);
cosDenZero = find(abs(cosDen)<10^-10);
cosOp = cosNum./cosDen;
cosOp(cosDenZero) = pi/4;
gt_alpha1 = sincOp.*cosOp;

% upsampling the transmit sequence
amUpSampled = [am;zeros(fs-1,length(am))];
amU = amUpSampled(:).';

% filtered sequence
st_alpha5 = conv(amU,gt_alpha5);
st_alpha1 = conv(amU,gt_alpha1);

% taking only the first 10000 samples
st_alpha5 = st_alpha5([1:10000]);
st_alpha1 = st_alpha1([1:10000]);

st_alpha5_reshape = reshape(st_alpha5,fs*2,N*fs/20).';
st_alpha1_reshape = reshape(st_alpha1,fs*2,N*fs/20).';

close all
figure;
st_alpha5_reshape
plot([0:1/fs:1.99],real(st_alpha5_reshape).','b');  
title('eye diagram with alpha=0.5');
xlabel('time')
ylabel('amplitude')
axis([0 2 -1.5 1.5])
grid on

figure;
plot([0:1/fs:1.99],real(st_alpha1_reshape).','b'); 
title('eye diagram with alpha=1')
xlabel('time')
ylabel('amplitude')
axis([0 2 -1.5 1.5 ])
grid on

Python 代码：

j = np.complex(0,1)
N = 10**3
#% number of symbols
am = 2.*(np.random.rand(1., N) > 0.5)-1.+np.dot(j, 2.*(np.random.rand(1., N) > 0.5)-1.)
#% generating random binary sequence
fs = 10.
#% sampling frequency in Hz
#% defining the sinc filter
sincNum = np.sin(np.dot(np.pi, np.array(np.hstack((np.arange(-fs, (fs)+(1./fs), 1./fs))))))
#% numerator of the sinc function
sincDen = np.dot(np.pi, np.array(np.hstack((np.arange(-fs, (fs)+(1./fs), 1./fs)))))
#% denominator of the sinc function
sincDenZero = np.where(abs(sincDen) < 10**-10);
sincOp=sincNum/sincDen
sincOp[int(sincDenZero[0])-1] = 1.
#% raised cosine filter
alpha = 0.5
cosNum = np.cos(np.dot(np.dot(alpha, np.pi), np.array(np.hstack((np.arange(-fs, (fs)+(1./fs), 1./fs))))))
cosDen = 1.-np.dot(2.*alpha, np.array(np.hstack((np.arange(-fs, (fs)+(1./fs), 1./fs)))))**2.
cosDenZero = np.where(abs(cosDen)<10**-10);
cosOp = cosNum/cosDen
cosOp[int(cosDenZero[0][0])-1] = np.pi/4.
cosOp[int(cosDenZero[0][1])-1] = np.pi/4.
gt_alpha5 = sincOp*cosOp
alpha = 1.
cosNum = np.cos(np.dot(np.dot(alpha, np.pi), np.array(np.hstack((np.arange(-fs, (fs)+(1./fs), 1./fs))))))
cosDen = 1.-np.dot(2.*alpha, np.array(np.hstack((np.arange(-fs, (fs)+(1./fs), 1./fs)))))**2.
cosDenZero = np.where(abs(cosDen)<10**-10);
cosOp = cosNum/cosDen
cosOp[int(cosDenZero[0][0])-1] = np.pi/4.
cosOp[int(cosDenZero[0][1])-1] = np.pi/4.
gt_alpha1 = sincOp*cosOp
#% upsampling the transmit sequence
#amUpSampled = np.array(np.vstack((np.hstack((am)), np.hstack((np.zeros((fs-1.), len(am)))))))
amUpSampled = np.append(am,np.zeros((fs-1,am.size)))
amU = amUpSampled.flatten(0)
#% filtered sequence
st_alpha5 = np.convolve(amU, gt_alpha5)
st_alpha1 = np.convolve(amU, gt_alpha1)
#% taking only the first 10000 samples
st_alpha5 = st_alpha5[0:10000:1]
st_alpha1 = st_alpha1[0:10000:1]
#st_alpha5_reshape = np.reshape(st_alpha5, (fs*2.), (np.dot(N, fs)/20.)).T
st_alpha5_reshape = np.reshape(st_alpha5, (-1,500)).T
#st_alpha1_reshape = np.reshape(st_alpha1, (fs*2.), (np.dot(N, fs)/20.)).T
st_alpha1_reshape = np.reshape(st_alpha1, (-1,500)).T
plt.close('all')
plt.figure(1)
plt.plot(np.array(np.hstack((np.arange(.1, (1.99)+(1./fs), 1./fs)))), np.real(st_alpha5_reshape).T, 'b')
plt.title('eye diagram with alpha=0.5')
plt.xlabel('time')
plt.ylabel('amplitude')
plt.axis(np.array(np.hstack((0., 2., -1.5, 1.5))))
plt.grid('on')
plt.figure(2)
plt.plot(np.array(np.hstack((np.arange(.1, (1.99)+(1./fs), 1./fs)))), np.real(st_alpha1_reshape).T, 'b')
plt.title('eye diagram with alpha=1')
plt.xlabel('time')
plt.ylabel('amplitude')
plt.axis(np.array(np.hstack((0., 2., -1.5, 1.5))))
plt.grid('on')
plt.show()

请让我知道问题出在哪里以及仅在 Python 代码中解决了什么问题？

Answer 1

一些事情。尽管您说“我已经在 Python 和 Octave 中双重验证了每个变量 bot 的值 - 它们也是相同的”。 -- 根本不是这样的。

首先，当您从 MATLAB 移植到 numpy 时，有次您需要从索引中减去 1，但您的代码没有这些。

所以你到处都有类似的东西：

sincOp[int(sincDenZero[0])-1] = 1.

改成

sincOp[int(sincDenZero[0])] = 1

简而言之，这是因为 np.where 的输出已经是 0 索引的，所以当你减去 1 时，你就会过度补偿。

接下来，您在所有地方都使用np.array(np.hstack((np.arange(-fs, (fs)+(1./fs), 1./fs))))，所以让我们创建一个变量并构建一次：

fsrange = np.array(np.hstack((np.arange(-fs, (fs)+(1./fs), 1./fs))))

但这可能只是：

fsrange = np.arange(-fs, fs+(1./fs), 1./fs)

同样，这条大线：

cosNum = np.cos(np.dot(np.dot(alpha, np.pi), np.array(np.hstack((np.arange(-fs, (fs)+(1./fs), 1./fs))))))

只能是：

cosNum = np.cos(alpha * np.pi * fsrange) 

还有这一行：

amUpSampled = np.append(am,np.zeros((fs-1,am.size)))

应该只是（所以你不要修改am，并正确地将args指定为zeros）：

amUpSampled = np.vstack([ am, np.zeros([(fs-1.), am.size]) ])

您在此处指定了错误的展平顺序：

amU = amUpSampled.flatten(0)

应该使用 FORTRAN 顺序（MATLAB 使用的）将其展平：

amU = amUpSampled.flatten('F')

reshape 也是一样，需要指定 FORTRAN 顺序：

st_alpha5_reshape = np.reshape(st_alpha5, [(fs*2.), (N * fs / 20.)], 'F').T
st_alpha1_reshape = np.reshape(st_alpha1, [(fs*2.), (N * fs / 20.)], 'F').T

所以你更正的python代码应该是这样的：

import numpy as np
import matplotlib.pyplot as plt


j = np.complex(0,1)
N = 10**3
#% number of symbols
am = 2.*(np.random.rand(1., N) > 0.5)-1.+np.dot(j, 2.*(np.random.rand(1., N) > 0.5)-1.)
#% generating random binary sequence
fs = 10.
fsrange = np.arange(-fs, fs+(1./fs), 1./fs)

#% sampling frequency in Hz
#% defining the sinc filter
sincNum = np.sin(np.dot(np.pi, fsrange))
#% numerator of the sinc function
sincDen = np.dot(np.pi, fsrange)
#% denominator of the sinc function
sincDenZero = np.where(np.abs(sincDen) < 10**-10);
sincOp=sincNum/sincDen
sincOp[int(sincDenZero[0])] = 1.


#% raised cosine filter
alpha = 0.5
cosNum = np.cos(alpha * np.pi * fsrange)
cosDen = 1.-np.dot(2.*alpha, fsrange)**2.
cosDenZero = np.nonzero(abs(cosDen)<10**-10);
cosOp = cosNum/cosDen
cosOp[int(cosDenZero[0][0])] = np.pi/4.
cosOp[int(cosDenZero[0][1])] = np.pi/4.
gt_alpha5 = sincOp*cosOp

alpha = 1.
cosNum = np.cos(alpha * np.pi * fsrange)
cosDen = 1.-np.dot(2.*alpha, fsrange)**2.
cosDenZero = np.where(abs(cosDen)<10**-10);
cosOp = cosNum/cosDen
cosOp[int(cosDenZero[0][0])] = np.pi/4.
cosOp[int(cosDenZero[0][1])] = np.pi/4.
gt_alpha1 = sincOp*cosOp


#% upsampling the transmit sequence
amUpSampled = np.vstack([ am, np.zeros([(fs-1.), am.size]) ])
amU = amUpSampled.flatten('F')
#% filtered sequence
st_alpha5 = np.convolve(amU, gt_alpha5)
st_alpha1 = np.convolve(amU, gt_alpha1)
#% taking only the first 10000 samples
st_alpha5 = st_alpha5[0:10000]
st_alpha1 = st_alpha1[0:10000]
st_alpha5_reshape = np.reshape(st_alpha5, [(fs*2.), (N * fs / 20.)], 'F').T
st_alpha1_reshape = np.reshape(st_alpha1, [(fs*2.), (N * fs / 20.)], 'F').T
plt.close('all')
X = np.arange(0,1.99, 1.0/fs)
plt.figure(1)
plt.plot(X, np.real(st_alpha5_reshape).T, 'b')
plt.title('eye diagram with alpha=0.5')
plt.xlabel('time')
plt.ylabel('amplitude')
plt.axis(np.array(np.hstack((0., 2., -1.5, 1.5))))
plt.grid('on')

plt.figure(2)
plt.plot(X, np.real(st_alpha1_reshape).T, 'b')
plt.title('eye diagram with alpha=1')
plt.xlabel('time')
plt.ylabel('amplitude')
plt.axis(np.array(np.hstack((0., 2., -1.5, 1.5))))

plt.grid('on')
plt.show()

这会产生您预期的数字。

旁注：

如果您在 MATLAB 中有一个数组/矩阵（假设它被称为 varname），您可以使用 save varname（在 MATLAB 中）将其保存到一个 .mat 文件中。

然后您可以在 python 中加载该数组/矩阵：

import scipy.io
mat = scipy.io.loadmat("<path of .mat file>")
varname = mat[varname]

您也可以对整个 MATLAB 工作区执行此操作，只需 save -- 在 python 中，mat 仍然只是一个以变量名称为键的字典，因此您可以像访问单个工作区变量一样访问以上。

您可以使用它来逐步验证 numpy 生成的内容与您期望生成的内容，并找出您做错了什么。