irfftn

irfftn is a function in various numerical computing libraries, such as NumPy in Python, that computes the inverse of the complex-to-complex Fast Fourier Transform (FFT) for multi-dimensional arrays. Specifically, irfftn is designed to compute the inverse of rfftn, which computes the real to complex FFT. This means irfftn takes an array of complex numbers representing the result of a real-to-complex FFT and transforms it back into a real-valued array. The "ir" prefix denotes inverse, "fftn" indicates a multi-dimensional FFT.

The primary advantage of using irfftn (and its related rfftn) over a standard complex-to-complex FFT (like fftn) is efficiency. When dealing with real-valued input data, the FFT inherently has a conjugate symmetric property in its output. rfftn exploits this symmetry to compute the FFT using roughly half the computational effort and storing only the unique components. Consequently, irfftn is the correct function to use to reconstruct the original real data from the output of rfftn. Using a standard complex-to-complex inverse FFT on the output of rfftn would result in an incorrect, complex-valued array. The dimensionality of the input array determines the dimensionality of the FFT performed by irfftn.