prewarping.sq

Effect of the frequency prewarping on the bilinear transform

Conversion from continuous time to discrete time with bilinear transformation and frequency prewarping. The frequency where the frequency response is preserved can be manipulated interactively, as well as the Nyquist or sampling frequency.

First contact

When you open prewarping.sq from Sysquake (menu File/Open), two figures are displayed: the frequency response magnitude and the step response. Each figure shows a third-order continuous-time system in black, and its discrete-time equivalent in red. The discrete-time function transfer is obtained with the bilinear transform with prewarping, which gives an exact match for the frequency response at the prewarping frequency. In the frequency response figure, the blue line represents the sampling frequency, the green line the Nyquist frequency, and the magenta (pink) line the prewarping frequency. You can move them to the right or to the left to change them. Observe the non-linear change of scale when you change the prewarping frequency.

Figures

Bode Magnitude

The magnitude of the continuous-time transfer function is displayed in black, and the magnitude of the discrete-time transfer function is displayed in red. The Nyquist frequency and the sampling frequency, which can be manipulated, are displayed as green and blue vertical lines, respectively.

Bode Phase

The phase of the continuous-time transfer function is displayed in black, and the phase of the discrete-time transfer function is displayed in red. The Nyquist frequency and the sampling frequency, which can be manipulated, are displayed as green and blue vertical lines, respectively.

Step Response

The step response of the continuous-time transfer function is displayed in black, and the samples of the step response of the discrete-time transfer function are displayed as red circles. The samples can be dragged to the right or to the left to change the sampling period.

Settings

Continuous-Time TF

The continuous-time transfer function can be entered in a dialog box as two vectors containing the coefficients of the numerator and denominator, respectively, highest power first.


Copyright 1998-2014, Calerga.
All rights reserved.