傅里叶变换（python)

import cv2import matplotlib.pyplot as pltimport matplotlib.cm as cm%matplotlib inlinedef imshow(img):    plt.imshow(img,cm.gray_r,interpolation='nearest')import numpy as npdim=31img=np.zeros((dim,dim))mx=int(dim/2)for i in range(dim):    for j in range(dim):        if ((i-mx)*(i-mx)+(j-mx)*(j-mx))<10:            img[i,j]=255imshow(img)

F[i,j]=∑Mp=1∑Nq=1f(p,q)e−2πi(ipM+jqN)

lv=np.complex(0,1)def FT(img):    w,h=img.shape    res=np.zeros((h,w))    for i in range(h):        for j in range(w):            temp=-1*lv*2*np.pi            for p in range(h):                for q in range(w):                    res[i,j]+=img[p,q]*np.exp(temp*(i*p/h+j*q/w))            res[i,j]=np.abs(res[i,j])    return resft=FT(img)imshow(ft)

b=np.fft.fft2(img)b=np.abs(b)imshow(b)