Fourier Transform with NumPy

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What is Fourier Transform?

Fourier Transform is a mathematical operation that transforms a signal from the time domain to the frequency domain. It is a powerful tool for analyzing data across many applications, including signal processing, image processing, speech recognition, and medical imaging.

The formula for the Fourier Transform of a function f(x) is given by:

where i is the imaginary unit, ω is the frequency variable, and f(x) is the function being transformed. The Fourier Transform of a function f(x) gives us a representation of the function in terms of its frequency components.

Fourier Transform in NumPy

NumPy provides support for Fourier Transform through its numpy.fft module. The module provides functions for computing the one-dimensional n-point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm.Here are some of the functions provided by NumPy for Fourier Transform:

numpy.fft.fft(a, n=None, axis=-1, norm=None): Compute the one-dimensional discrete Fourier Transform. This function computes the one-dimensional n-point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm.

numpy.fft.fftfreq(n, d=1.0): Return the Discrete Fourier Transform sample frequencies…