Transforms
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.
Functions
Topics
Discrete Fourier and Cosine Transforms
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.
Hilbert and Walsh-Hadamard Transforms
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.
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.
Apply the complex cepstrum to detect echo in a signal.
