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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 based on the Hilbert-transform. Investigate magnitude-phase relationships, estimate fundamental frequencies, and detect spectral periodicity using the cepstrum. Compute discrete Fourier transforms using the second-order Goertzel algorithm.

Functions

abs Absolute value (magnitude)
angle Phase angle
fft Fast Fourier transform
ifft Inverse fast Fourier transform
fftshift Shift zero-frequency component to center of spectrum
dftmtx Discrete Fourier transform matrix
fft2 2-D fast Fourier transform
ifft2 2-D inverse fast Fourier transform
czt Chirp Z-transform
goertzel Discrete Fourier transform with second-order Goertzel algorithm
dct Discrete cosine transform (DCT)
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
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

Topics

Discrete Fourier and Cosine Transforms

Discrete Fourier Transform

Explore the primary tool of digital signal processing.

Chirp Z-Transform

Use the CZT to evaluate the Z-transform outside of the unit circle and to compute transforms of prime length.

Discrete Cosine Transform

Compute discrete cosine transforms and learn about their energy compaction properties.

DCT for Speech Signal Compression

Use the discrete cosine transform to compress speech signals.

Hilbert and Walsh-Hadamard Transforms

Hilbert Transform

The Hilbert transform helps form the analytic signal.

Analytic Signal for Cosine

Determine the analytic signal for a cosine and verify its properties.

Envelope Extraction Using the Analytic Signal

Extract the envelope of a signal using the magnitude of its analytic signal.

Analytic Signal and Hilbert Transform

Generate the analytic signal for a finite block of data using the hilbert function and an FIR Hilbert transformer.

Hilbert Transform and Instantaneous Frequency

Estimate the instantaneous frequency of a monocomponent signal using the Hilbert transform. Show that the procedure does not work for multicomponent signals.

Single-Sideband Amplitude Modulation

Perform single-sideband amplitude modulation of a signal using the Hilbert transform. Single-sideband AM signals have less bandwidth than normal AM signals.

Walsh-Hadamard Transform

Learn about the Walsh-Hadamard transform, a non-sinusoidal, orthogonal transformation technique.

Cepstral Analysis

Complex Cepstrum -- Fundamental Frequency Estimation

Use the complex cepstrum to estimate a speaker's fundamental frequency. Compare the result with the estimate obtained with a zero-crossing method.

Cepstrum Analysis

Apply the complex cepstrum to detect echo in a signal.

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