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MyModule.py
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MyModule.py
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import math
import matplotlib.pyplot as plt
import numpy as np
import cmath
import time
def conv(h, x):
y = [0] * (len(x) + len(h) -1)
for n in range(len(y)):
for k in range(len(h)):
if(n - k >= 0 and n - k < len(x)):
y[n] = y[n] + x[n-k] * h[k];
return (y);
'''conv(x,h)=ifft(fft(x)*fft(h)), if len(y)<=len(x) and len(h)'''
def cconv(x, h):
'''circular convolution'''
N=len(x)
y = np.zeros(N,dtype=complex)
for i in range(N):
y[i]=0+0j
for k in range(N):
y[i] = y[i] + x[(i-k+N)%N] * h[k];
return (y);
def real_dft(x):
N=len(x)
X=[0+0j]*N
for m in range(N):
for n in range(N):
X[m]=X[m]+x[n]*complex(math.cos(2*math.pi*m*n/N),-1.0*math.sin(2*math.pi*m*n/N))
return(X)
def complex_dft(x):
'''complex input DFT'''
N=len(x)
X=[0+0j]*N
for m in range(N):
for n in range(N):
X[m]=X[m]+x[n]*cmath.exp(-1j*2*math.pi*m*n/N)
return(X)
def complex_idft(X):
'''complex input inverse DFT,scaled by 1/N'''
N=len(X)
x=[0+0j]*N
for n in range(N):
for m in range(N):
x[n]=x[n]+X[m]*cmath.exp(1j*2*math.pi*m*n/N)
x[n]=x[n]/N
return(x)
def dftplot(x,X):
N=len(X)
Xreal=[0.0]*N
Ximag=[0.0]*N
Xamp=[0.0]*N
Xphase=[0.0]*N
Xdb=[0,0]*N
for i in range(len(X)):
Xreal[i]=X[i].real
Ximag[i]=X[i].imag
Xamp[i],Xphase[i]=cmath.polar(X[i])
if Xamp[i]<1e-10:
Xphase[i]=0
if Xamp[i] !=0.0:
Xdb[i]=20*cmath.log10(Xamp[i])
f,axarr=plt.subplots(3,2)
f.suptitle('figtitle')
axarr[0,0].plot(x,'o-')
axarr[0,1].plot(Xdb,'o-')
axarr[1,0].plot(Xreal,'o-')
axarr[2,0].plot(Ximag,'o-')
axarr[1,1].plot(Xamp,'o-')
axarr[2,1].plot(Xphase,'o-')
plt.show
def fft(x):
N=len(x)
if (N==1):
X=x
else:
halfN=N//2
xeven=np.zeros((halfN),dtype=complex)
xodd=np.zeros((halfN),dtype=complex)
for i in range(halfN):
xeven[i]=x[2*i]
xodd[i]=x[2*i+1]
Xeven=fft(xeven)
Xodd=fft(xodd)
X=np.zeros((N),dtype=complex)
for m in range(N):
X[m]=Xeven[m % halfN]+Xodd[m %halfN]*cmath.exp(-1j*2*math.pi*m/N)
return(X)
def ifftnoscale(X):
N=len(X)
if (N==1):
x=X
else:
halfN=N//2
Xeven=np.zeros((halfN),dtype=complex)
Xodd=np.zeros((halfN),dtype=complex)
for i in range(halfN):
Xeven[i]=X[2*i]
Xodd[i]=X[2*i+1]
xeven=ifftnoscale(Xeven)
xodd=ifftnoscale(Xodd)
x=np.zeros((N),dtype=complex)
for m in range(N):
x[m]=xeven[m % halfN]+xodd[m %halfN]*cmath.exp(1j*2*math.pi*m/N)
return(x)
def ifft(X):
x=ifftnoscale(X)
N=len(x)
for i in range(N):
x[i]=x[i]/N
return(x)
def fft2d(f):
(Nr,Nc)=f.shape
F=np.zeros((Nr,Nc),dtype=complex)
for m in range(Nr):
F[m,:]=fft(f[m,:])
for n in range(Nc):
F[:,n]=fft(F[:,n])
return(F)
def ifft2d(F):
(Nr,Nc)=F.shape
f=np.zeros((Nr,Nc),dtype=complex)
for m in range(Nr):
f[m,:]=ifft(F[m,:])
for n in range(Nc):
f[:,n]=ifft(f[:,n])
return(f)
def shift(Img):
(Nr, Nc) = Img.shape
Imgshift = np.zeros((Nr,Nc), dtype=complex)
for i in range(Nr):
for j in range(Nc):
Imgshift[i,j] = Img[(i+Nr//2) % Nr, (j+Nc//2) % Nc]
return(Imgshift)
def trim(Img, radius):
(Nr, Nc) = Img.shape
for i in range(Nr):
for j in range(Nc):
if (((i-Nr//2)**2 + (j-Nc//2)**2) > radius**2):
Img[i,j] = 0.0 +0.0j
return(Img)
def convlong(x,h,Nfft):
'''convolute a long signal segment by segment'''
Nsegment=Nfft-len(h)
hseq=np.zeros((Nfft))
hseq[:len(h)]=h[:]
Hseq=fft(hseq)
yiffted=np.zeros((len(x)+Nfft),dtype=x.dtype)
for s in range(len(x)//Nsegment+1):
xseq=np.zeros((Nfft))
if (s+1)*Nsegment<=len(x):
reallen=Nsegment
else:
reallen=len(x)-s*Nsegment
xseq[:reallen]=x[s*Nsegment:s*Nsegment+reallen]
Xseq=fft(xseq)
seqiffted=ifft(Hseq*Xseq)
l=s*Nsegment
r=l+len(seqiffted)
yiffted[l:r]=yiffted[l:r]+seqiffted[:]
return(yiffted)