# Transforms

Fourier, chirp Z, DCT, Hilbert, cepstrum, Walsh-Hadamard

Signal Processing Toolbox™ provides functions that let you compute widely used forward and inverse transforms, including the fast Fourier transform (FFT), the discrete cosine transform (DCT), and the Walsh-Hadamard transform. Extract signal envelopes and estimate instantaneous frequencies using the analytic signal. Analyze signals in the time-frequency domain. Investigate magnitude-phase relationships, estimate fundamental frequencies, and detect spectral periodicity using the cepstrum. Compute discrete Fourier transforms using the second-order Goertzel algorithm.

## Funktionen

alle erweitern

 `abs` Absoluter Wert und komplexer Betrag `angle` Phasenwinkel `fft` Fast Fourier transform `ifft` Inverse fast Fourier transform `fftshift` Shift zero-frequency component to center of spectrum `ifftshift` Inverse zero-frequency shift `dftmtx` Discrete Fourier transform matrix `fft2` 2-D fast Fourier transform `ifft2` 2-D inverse fast Fourier transform `instfreq` Estimate instantaneous frequency `czt` Chirp Z-transform `goertzel` Discrete Fourier transform with second-order Goertzel algorithm `dct` Discrete cosine transform `idct` Inverse discrete cosine transform
 `envelope` Signal envelope `fwht` Fast Walsh-Hadamard transform `ifwht` Inverse Fast Walsh-Hadamard transform `hilbert` Discrete-time analytic signal using Hilbert transform
 `emd` Empirical mode decomposition `fsst` Fourier synchrosqueezed transform `ifsst` Inverse Fourier synchrosqueezed transform `hht` Hilbert-Huang transform `pspectrum` Analyze signals in the frequency and time-frequency domains `spectrogram` Spectrogram using short-time Fourier transform `xspectrogram` Cross-spectrogram using short-time Fourier transforms `stft` Short-time Fourier transform `dlstft` Deep learning short-time Fourier transform (Seit R2021a) `stftLayer` Short-time Fourier transform layer (Seit R2021b) `istftLayer` Inverse short-time Fourier transform layer (Seit R2024a) `stftmag2sig` Signal reconstruction from STFT magnitude (Seit R2020b) `istft` Inverse short-time Fourier transform `dlistft` Deep learning inverse short-time Fourier transform (Seit R2024a) `vmd` Variational mode decomposition (Seit R2020a) `wvd` Wigner-Ville distribution and smoothed pseudo Wigner-Ville distribution `xwvd` Cross Wigner-Ville distribution and cross smoothed pseudo Wigner-Ville distribution
 `cceps` Complex cepstral analysis `icceps` Inverse complex cepstrum `rceps` Real cepstrum and minimum-phase reconstruction
 `bitrevorder` Permute data into bit-reversed order `digitrevorder` Permute input into digit-reversed order