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.
||Absolute value (magnitude)|
||Fast Fourier transform|
||Inverse fast Fourier transform|
||Shift zero-frequency component to center of spectrum|
||Discrete Fourier transform matrix|
||2-D fast Fourier transform|
||2-D inverse fast Fourier transform|
||Discrete Fourier transform with second-order Goertzel algorithm|
||Discrete cosine transform|
||Inverse discrete cosine transform|
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.
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 magnitude of its analytic signal.
Generate the analytic signal for a finite block of
data using the
hilbert function and an FIR Hilbert
Estimate the instantaneous frequency of a monocomponent signal using the Hilbert transform. Show that the procedure does not work for multicomponent signals.
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.
Use an electrocardiogram signal to illustrate the Walsh-Hadamard transform.
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.