# Discrete Fourier transforms (scipy.fft)¶

## Fast Fourier Transforms (FFTs)¶

 fft(x[, n, axis, norm, overwrite_x]) Compute the one-dimensional discrete Fourier Transform. ifft(x[, n, axis, norm, overwrite_x]) Compute the one-dimensional inverse discrete Fourier Transform. fft2(x[, s, axes, norm, overwrite_x]) Compute the 2-dimensional discrete Fourier Transform ifft2(x[, s, axes, norm, overwrite_x]) Compute the 2-dimensional inverse discrete Fourier Transform. fftn(x[, s, axes, norm, overwrite_x]) Compute the N-dimensional discrete Fourier Transform. ifftn(x[, s, axes, norm, overwrite_x]) Compute the N-dimensional inverse discrete Fourier Transform. rfft(x[, n, axis, norm, overwrite_x]) Compute the one-dimensional discrete Fourier Transform for real input. irfft(x[, n, axis, norm, overwrite_x]) Compute the inverse of the n-point DFT for real input. rfft2(x[, s, axes, norm, overwrite_x]) Compute the 2-dimensional FFT of a real array. irfft2(x[, s, axes, norm, overwrite_x]) Compute the 2-dimensional inverse FFT of a real array. rfftn(x[, s, axes, norm, overwrite_x]) Compute the N-dimensional discrete Fourier Transform for real input. irfftn(x[, s, axes, norm, overwrite_x]) Compute the inverse of the N-dimensional FFT of real input. hfft(x[, n, axis, norm, overwrite_x]) Compute the FFT of a signal that has Hermitian symmetry, i.e., a real spectrum. ihfft(x[, n, axis, norm, overwrite_x]) Compute the inverse FFT of a signal that has Hermitian symmetry. hfft2(x[, s, axes, norm, overwrite_x]) Compute the 2-dimensional FFT of a Hermitian complex array. ihfft2(x[, s, axes, norm, overwrite_x]) Compute the 2-dimensional inverse FFT of a real spectrum. hfftn(x[, s, axes, norm, overwrite_x]) Compute the N-dimensional FFT of Hermitian symmetric complex input, i.e. ihfftn(x[, s, axes, norm, overwrite_x]) Compute the N-dimensional inverse discrete Fourier Transform for a real spectum.

## Discrete Sin and Cosine Transforms (DST and DCT)¶

 dct(x[, type, n, axis, norm, overwrite_x]) Return the Discrete Cosine Transform of arbitrary type sequence x. idct(x[, type, n, axis, norm, overwrite_x]) Return the Inverse Discrete Cosine Transform of an arbitrary type sequence. dctn(x[, type, shape, axes, norm, overwrite_x]) Return multidimensional Discrete Cosine Transform along the specified axes. idctn(x[, type, shape, axes, norm, overwrite_x]) Return multidimensional Discrete Cosine Transform along the specified axes. dst(x[, type, n, axis, norm, overwrite_x]) Return the Discrete Sine Transform of arbitrary type sequence x. idst(x[, type, n, axis, norm, overwrite_x]) Return the Inverse Discrete Sine Transform of an arbitrary type sequence. dstn(x[, type, shape, axes, norm, overwrite_x]) Return multidimensional Discrete Sine Transform along the specified axes. idstn(x[, type, shape, axes, norm, overwrite_x]) Return multidimensional Discrete Sine Transform along the specified axes.

## Helper functions¶

 fftshift(x[, axes]) Shift the zero-frequency component to the center of the spectrum. ifftshift(x[, axes]) The inverse of fftshift. fftfreq(n[, d]) Return the Discrete Fourier Transform sample frequencies. rfftfreq(n[, d]) Return the Discrete Fourier Transform sample frequencies (for usage with rfft, irfft). next_fast_len(target[, dtype]) Find the next fast size of input data to fft, for zero-padding, etc.