Computing the FFT in Python

 

To analyze the frequency content of a data stream, we use the Fast Fourier Transform (FFT), which efficiently computes the Discrete Fourier Transform (DFT). One of the most widely used FFT algorithms is the Cooley–Tukey algorithm, which is a radix-2 divide-and-conquer method. It breaks down a DFT of size N (where N$N$ is a power of 2) into smaller DFTs of size $N/2$, recursively, which reduces computational complexity from 

$O(N^2)$ to $O(N \log_2 N)$.

 

Python Code for FFT 

To use this code, you need a sampled signal and the corresponding sampling frequency.

    def compute_fft(self, signal):
        fft_result = np.fft.fft(signal)
        freq = np.fft.fftfreq(len(signal), d=1/self.samplingFrequency)
        return np.abs(fft_result), freq 

 

In our case, we will perform the Fast Fourier Transform (FFT) on sine, cosine, rectangular, and triangular signals.

 

Example code to compute the Fourier Transform of sine, cosine, rectangular, and triangular waveforms:

 

 

 

 

 

 

 

Get the complete python code 

 

Output

 

 

Further Reading

1.