Simulink®

Discrete Filter - Model IIR and FIR filters

Library

Discrete

Description

The Discrete Filter block models Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) filters using a direct form II structure (also known as "control canonical form"). You specify the filter as a ratio of polynomials in z^-1. You can specify that the block have a scalar output or vector output where the elements correspond to a set of filters that have the same denominator polynomial but different numerator polynomials.

Use the Numerator coefficient parameter to specify the coefficients of the discrete filter's numerator polynomial or polynomials. Use a vector to specify the coefficients for a single numerator polynomial. Use a matrix to specify the coefficients of multiple numerator polynomials where each row contains the coefficients of one of the polynomials. Use the Denominator coefficient parameter to specify the coefficients of the function's denominator polynomial. The value of the Denominator coefficient parameter must be a vector of coefficients.

You must specify the coefficients of the numerator and denominator polynomials in ascending powers of z^-1. The order of the denominator must be greater than or equal to the order of the numerator.

If you specify a single numerator polynomial, i.e., a vector as the value of the Numerator coefficient parameter, the block's output is a scalar signal. If you specify multiple numerator polynomials, i.e., a matrix as the value of the Numerator coefficient parameter, the block's output is a vector signal whose width equals the number of matrix rows, i.e., the number or numerator polynomials.

The Discrete Filter block lets you use polynomials in z^-1 (the delay operator) to represent a discrete system, a method typically used by signal processing engineers. By contrast, the Discrete Transfer Fcn block lets you use polynomials in z to represent a discrete system, the method typically used by control engineers. The two methods are identical when the numerator and denominator polynomials have the same length.

The block displays the numerator and denominator according to how they are specified. For a discussion of how Simulink^® software displays the icon, see Transfer Fcn.

Data Type Support

The Discrete Filter block accepts and outputs a real signal of type single or double.

Parameters and Dialog Box

Numerator coefficient

A vector of polynomial coefficients or a matrix of coefficients where each row of coefficients corresponds to a distinct numerator polynomial. You must specify the polynomial coefficients in ascending powers of z^-1. If you specify a vector of coefficients, i.e., a single numerator polynomial, the output of the block is a scalar signal. If you specify a matrix of coefficients, i.e., multiple polynomials, the block's output is a vector of signals, each corresponding to the filter consisting off the corresponding numerator polynomial and the denominator polynomial specified by the Denominator coefficient parameter. The default is [1].

Denominator coefficient

The vector of denominator coefficients. The default is [1 0.5]. The width of the vector, i.e., the order of the denominator, must be greater than or equal to the width of the numerator vector or matrix rows, i.e., the order of the numerator.

Sample time

The time interval between samples. See Specifying Sample Time.

The State Attributes pane of this block pertains to code generation and has no effect on model simulation. See Block State Storage and Interfacing in the Real-Time Workshop^® User's Guide for more information.

Characteristics

Discrete Derivative

Discrete FIR Filter