Fast Fourier Transform Implementation with numpy

fast_fourier_transform_impl.py

import numpy as np
import matplotlib.pyplot as plt
from skimage import color

def fft(length_x,width_y,v,y,image,inner=True):
    expVector=np.exp(-2j*np.pi/width_y*(v@y)) if inner else np.exp(-2j*np.pi/length_x*(v@y))
    if inner:
        return image @ expVector
    else:
        return expVector @ image
        
def fft2d(grayImage):
    length_x = grayImage.shape[0] 
    width_y= grayImage.shape[1]

    y=np.arange(width_y).reshape(1,-1)
    v = np.arange(width_y).reshape(-1,1)

    firstLevel=fft(length_x,width_y,v,y,grayImage,True)

    u = np.arange(length_x).reshape(-1,1)
    x = np.arange(length_x).reshape(1,-1)

    return fft(length_x,width_y,u,x,firstLevel,False)

image=plt.imread('filename')
grayImage=color.rgb2gray(image)

transformedImage=fft2d(grayImage)

magnitude = np.log(np.abs(fourierimage)+1))
angle = np.angle(fourierimage))

f,axxr = plt.subplots(nrows=1,ncols=2,figsize=(15,15))
axxr[0].imshow(magnitude),plt.title('Magnitude')
axxr[1].imshow(angle),plt.title('Angle')

This implementation only works with grayscale 2d images.