Parametric Modeling :: Special Topics (Signal Processing Toolbox)

Signal Processing Toolbox

Parametric Modeling

Parametric modeling techniques find the parameters for a mathematical model describing a signal, system, or process. These techniques use known information about the system to determine the model. Applications for parametric modeling include speech and music synthesis, data compression, high-resolution spectral estimation, communications, manufacturing, and simulation.

The toolbox parametric modeling functions operate with the rational transfer function model. Given appropriate information about an unknown system (impulse or frequency response data, or input and output sequences), these functions find the coefficients of a linear system that models the system.

One important application of the parametric modeling functions is in the design of filters that have a prescribed time or frequency response. These functions provide a data-oriented alternative to the IIR and FIR filter design functions discussed in Filter Design and Implementation.

Here is a summary of the parametric modeling functions in this toolbox. Note that the System Identification Toolbox provides a more extensive collection of parametric modeling functions.

Domain
Functions
Description

Time
arburg
Generate all-pole filter coefficients that model an input data sequence using the Levinson-Durbin algorithm.

arcov
Generate all-pole filter coefficients that model an input data sequence by minimizing the forward prediction error.

armcov
Generate all-pole filter coefficients that model an input data sequence by minimizing the forward and backward prediction errors.

aryule
Generate all-pole filter coefficients that model an input data sequence using an estimate of the autocorrelation function.

lpc, levinson
Linear Predictive Coding. Generate all-pole recursive filter whose impulse response matches a given sequence.

prony
Generate IIR filter whose impulse response matches a given sequence.

stmcb
Find IIR filter whose output, given a specified input sequence, matches a given output sequence.

Frequency
invfreqz, invfreqs
Generate digital or analog filter coefficients given complex frequency response data.

Domain	Functions	Description
Time	`arburg`	Generate all-pole filter coefficients that model an input data sequence using the Levinson-Durbin algorithm.
`arcov`	Generate all-pole filter coefficients that model an input data sequence by minimizing the forward prediction error.
`armcov`	Generate all-pole filter coefficients that model an input data sequence by minimizing the forward and backward prediction errors.
`aryule`	Generate all-pole filter coefficients that model an input data sequence using an estimate of the autocorrelation function.
`lpc`, `levinson`	Linear Predictive Coding. Generate all-pole recursive filter whose impulse response matches a given sequence.
`prony`	Generate IIR filter whose impulse response matches a given sequence.
`stmcb`	Find IIR filter whose output, given a specified input sequence, matches a given output sequence.
Frequency	`invfreqz`, `invfreqs`	Generate digital or analog filter coefficients given complex frequency response data.

Because yulewalk is geared explicitly toward ARMA filter design, it is discussed in Filter Design and Implementation.

pburg and pyulear are discussed in Statistical Signal Processing along with the other (nonparametric) spectral estimation methods.

Chebyshev Window Time-Domain Based Modeling