Discrete Varying Lowpass
Discrete Butterworth filter with varying coefficients
Control System Toolbox / Linear Parameter Varying
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.
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.
u — Filter input
Lowpass filter input signal.
freq — Cutoff frequency
Continuous-time value of the cutoff frequency, specified in rad/s.
y — Filter output
Lowpass filter output signal.
Filter order — Lowpass filter order
1 (default) | positive integer
Lowpass filter order, specified as a positive integer.
Pre-warping frequency w0 (rad/s) — Pre-warping frequency
0 (default) | positive scalar
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 = 0 corresponds to the bilinear (Tustin)
transformation without pre-warp:
where Ts is the block sample time, specified with the Sample time Ts parameter.
Sample time Ts — Sample time
1 (default) | positive scalar
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.
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Introduced in R2017b