Inverse Discrete Fourier Transform
An inverse DFT is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence.
The discrete Fourier transform is an invertible, linear transformation
F:CN --> CN
with C denoting the set of complex numbers. Its inverse is known as Inverse Discrete Fourier Transform (IDFT). In other words, for any N>0, an N-dimensional complex vector has a DFT and an IDFT which are in turn N-dimensional complex vectors.
The inverse transform is given by:
The step-by-step values for the provided input is shown at the bottom of the page: