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.

`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 |

`bitrevorder` |
Permute data into bit-reversed order |

`digitrevorder` |
Permute input into digit-reversed order |

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.

**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.

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

**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.

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