# Discrete Varying Lowpass

Discrete Butterworth filter with varying coefficients

Libraries:
Control System Toolbox / Linear Parameter Varying

## Description

The block implements the Tustin discretization of a continuous-time Nth-order Butterworth filter. The result is a digital filter with unit DC gain and varying cutoff frequency that you provide as an input to the block.

Use this block and the other blocks in the Linear Parameter Varying library to implement common control elements with variable parameters or coefficients. For more information, see Model Gain-Scheduled Control Systems in Simulink.

Caution

Avoid making the cutoff frequency depend on the block output y. If you have such dependence, the resulting filter causes an algebraic loop, because computing the block output value requires knowing the block output value. This algebraic loop is prone to instability and divergence.

## Ports

### Input

expand all

Lowpass filter input signal.

Continuous-time value of the cutoff frequency, specified in rad/s.

### Output

expand all

Lowpass filter output signal.

## Parameters

expand all

Lowpass filter order, specified as a positive integer.

Pre-warping frequency, specified as a positive scalar. Discretization of the continuous-time Butterworth filter can shift the cutoff frequency when it is close to the Nyquist frequency. To ensure that the analog and digital filters have matching frequency response near a particular frequency `w0`, set this parameter to `w0`. The default value `w0 = 0` corresponds to the bilinear (Tustin) transformation without pre-warp:

`$s=\frac{2}{{T}_{s}}\left(\frac{z-1}{z+1}\right),$`

where Ts is the block sample time, specified with the Sample time Ts parameter.

Block sample time, specified as a positive scalar. This block does not support inherited sample time, because it requires a specified sample time to compute the discretization of the Butterworth filter.

## Version History

Introduced in R2017b