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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.


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absAbsolute value and complex magnitude
anglePhase angle
fftFast Fourier transform
ifftInverse fast Fourier transform
fftshiftShift zero-frequency component to center of spectrum
ifftshiftInverse zero-frequency shift
dftmtxDiscrete Fourier transform matrix
fft22-D fast Fourier transform
ifft22-D inverse fast Fourier transform
instfreqEstimate instantaneous frequency
cztChirp Z-transform
goertzelDiscrete Fourier transform with second-order Goertzel algorithm
dctDiscrete cosine transform
idctInverse discrete cosine transform
envelopeSignal envelope
fwhtFast Walsh-Hadamard transform
ifwhtInverse Fast Walsh-Hadamard transform
hilbertDiscrete-time analytic signal using Hilbert transform
emdEmpirical mode decomposition
fsstFourier synchrosqueezed transform
ifsstInverse Fourier synchrosqueezed transform
hhtHilbert-Huang transform
pspectrumAnalyze signals in the frequency and time-frequency domains
spectrogramSpectrogram using short-time Fourier transform
xspectrogramCross-spectrogram using short-time Fourier transforms
stftShort-time Fourier transform
dlstftDeep learning short-time Fourier transform (Since R2021a)
stftLayerShort-time Fourier transform layer (Since R2021b)
istftLayerInverse short-time Fourier transform layer (Since R2024a)
stftmag2sigSignal reconstruction from STFT magnitude (Since R2020b)
istftInverse short-time Fourier transform
dlistftDeep learning inverse short-time Fourier transform (Since R2024a)
vmdVariational mode decomposition (Since R2020a)
wvdWigner-Ville distribution and smoothed pseudo Wigner-Ville distribution
xwvdCross Wigner-Ville distribution and cross smoothed pseudo Wigner-Ville distribution
ccepsComplex cepstral analysis
iccepsInverse complex cepstrum
rcepsReal cepstrum and minimum-phase reconstruction
bitrevorderPermute data into bit-reversed order
digitrevorderPermute input into digit-reversed order


Discrete Fourier and Cosine Transforms

Hilbert and Walsh-Hadamard Transforms

Cepstral Analysis