TD_DFFT (Discrete Fast Fourier Transform) takes a time or space series as an input, and produces a result series containing the computed Fourier transform coefficients. The computed coefficients can be output in rectangular (real, imaginary) or polar (amplitude, phase) forms
The function is a version of the Fourier transform algorithm that is designed to handle discrete, finite-length signals. It is used in signal processing, image processing, audio signal processing, and telecommunications.
The DFFT algorithm operates on a sequence of N complex numbers, x[0], x[1], ..., x[N-1], and computes a corresponding sequence of N1 complex numbers, X[0], X[1], ..., X[N-1]. The DFFT algorithm has a computational complexity of 0(N log N), which makes it faster than the 0(N2) complexity of the naive DFT algorithm.
The TD_DFFT algorithm works by recursively parsing the input signal into smaller and smaller segments, and then combining the results to compute the final output. The algorithm takes advantage that a sequence can be expressed in terms of the Fourier transforms of its subsequences.
- Use TD_DFFT on series 1 and series 2 to get a tables named dfftRes1 and dfftRes2, respectively.
- Use TD_BINARYSERIESOP to do point-wise multiplication using dfftRes1 and dfftRes2, and name the resultant table freqRes.
- Use TD_IDFFT on freqRes to get the convolved result of the two series.