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 [CT].

Fourier analysis is fundamentally a method for expressing a function as a sum of periodic components, and for recovering the function from those components. When both the function and its Fourier transform are replaced with discretized counterparts, it is called the discrete Fourier transform (DFT).

Compute the one-dimensional discrete Fourier Transform for real input. This function computes the one-dimensional n -point discrete Fourier Transform (DFT) of a real-valued array by means of an efficient algorithm called the Fast Fourier Transform (FFT).

This function computes the n-dimensional discrete Fourier Transform over any axes in an M-dimensional array by means of the Fast Fourier Transform (FFT). By default, the transform is computed over the last two axes of the input array, i.e., a 2-dimensional FFT.

Compute the one-dimensional inverse discrete Fourier Transform. This function computes the inverse of the one-dimensional n -point discrete Fourier transform computed by fft . In other words, ifft(fft(a)) == a to within numerical accuracy.

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 [CT].

Compute the N-dimensional discrete Fourier Transform. This function computes the N -dimensional discrete Fourier Transform over any number of axes in an M -dimensional array by means of the Fast Fourier Transform (FFT).

This function computes the inverse of the 2-dimensional discrete Fourier Transform over any number of axes in an M-dimensional array by means of the Fast Fourier Transform (FFT). In other words, ifft2(fft2(a)) == a to within numerical accuracy.

This function computes the inverse of the one-dimensional n-point discrete Fourier Transform of real input computed by rfft. In other words, irfft(rfft(a), len(a)) == a to within numerical accuracy. (See Notes below for why len(a) is necessary here.)

Convolve two arrays using the Fast Fourier Transform. scipy.linalg.toeplitz. Used to construct the convolution operator. polymul. Polynomial multiplication. Same output as convolve, but also accepts poly1d objects as input.