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.
When you open prewarping.sq from Sysquake (menu File/Open), two figures are
displayed
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.
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.
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.
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.