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.

Explore the primary tool of digital signal processing.

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

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.

The Hilbert transform helps form the analytic signal.

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

Extract the envelope of a signal using the `hilbert`

and
`envelope`

functions.

**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.

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

**Walsh-Hadamard Transform for Spectral Analysis and Compression of ECG Signals**

Use an electrocardiogram signal to illustrate the Walsh-Hadamard transform.

**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.

Apply the complex cepstrum to detect echo in a signal.