Discrete Fourier Transform implementation using Python - Infinite loop

Question

I need to program the Discrete Fourier Transform using python. (I cannot use the numpy function for fft). You can find the numpy fft function in my code, but it is just for verification. Not sure why, but it seems that my code is getting in a infinite loop (I have to Keyboard Interrupt). Any ideas?

import matplotlib.pyplot as plt
import numpy as np
import cmath

Fs = 40000;  # sampling
Ts = 1.0/Fs; # sampling period
t = np.arange(0,1,Ts) # time vector

f = 100;   # frequencia do sinal
x1_n = np.sin(2*np.pi*f*t + 0)
f = 1000;
x2_n = np.sin(2*np.pi*f*t + 180)

x_n = x1_n + x2_n

n = len(x_n) # signal length
k = np.arange(n) #vetor em k
T = n/Fs
frq = k/T # both sides of the frequency vetor
frq = frq[range(int(n/2))] # one side of the frequency vector

X = np.fft.fft(x_n)/n # fft using numpy and normalization

print("A")
print(X) # printing the results for numpy fft

m = len(x_n)
output = []
for k in range(m):  # For each output element
    s = complex(0)
    for t in range(m):  # For each input element
        angle = 2j * cmath.pi * t * k / m
        s += x_n[t] * cmath.exp(-angle)
    output.append(s)

print("B") #printing the results for the fft implementation using for loops
print(output)

Tim Roberts · Accepted Answer · 2022-09-21 22:56:46Z

1

It's not an infinite loop, but since m = 40000, your inner loop is going to run 1.6 billion times. That's going to take a LOT of time, which is why FFTs are not implemented in Python. On my machine, it does about 5 outer loops per second, so it's going to take 3 hours to run.

answered Sep 21, 2022 at 22:56

Tim Roberts

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2 Comments

Matheus Torres Over a year ago

ooh! that makes sense. Not sure how to implement that then :(

Tim Roberts Over a year ago

One choice, of course, is to let it run for 3 hours. If it's just a proof of concept, that's viable.

Frank Yellin · Accepted Answer · 2022-09-21 23:07:25Z

0

You've written a perfectly good implementation of a Fourier transform. You have not written a fast Fourier Transform, which specifically involves a series of techniques to bring the runtime town from O(n^2) to (n log n).

This is what made the FFT so revolutionary when it was discovered. Hard problems that could only be used using a Fourier Transform suddenly became a lot faster.

answered Sep 21, 2022 at 23:07

Frank Yellin

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2 Comments

Matheus Torres Over a year ago

yea, it makes sense. But not sure how to write that in python. This is an assignment for my class.

Frank Yellin Over a year ago

pythonnumericalmethods.berkeley.edu/notebooks/… This shows a very short implementation of an FFT for powers of 2.

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