Chapter 4: DFT (Magnitude spectrum)

This demo shows the Discrete Fourier Transformation (DFT) of length \(M\) of an audio input signal \(x[k]\) according to $$ X[\mu] = \sum_{k=0}^{M-1}\tilde x[k]\omega_M^{\mu k}, $$ with the twiddle factor (Drehfaktor) \(\omega_M=\mathrm e^{-\mathrm{j}\frac{2\pi}{M}}\) and \(\tilde x[k]\), being a window of \(x[k]\) of length \(M\).

Input Signal \(x[k]\) Lalala Elise Armstrong Snare Position (0...1): 0.8 DFT-Length \(M\):

4096 8192 16384

Recompute

Input \(x[k]\)

Window \(\tilde x[k]\)