Frequency transformations allow design of other filters.

For IIR filters, the classical analog filter design methods together with the bilinear transformation, that maps the analog s-plane into the Z-plane, are used to design low-pass filters. The filter design consists in specifying a desired magnitude or impulse response followed by rational or polynomial approximation to obtain a stable and realizable filter. These discrete filters are implemented using software or dedicated hardware and minimal direct, cascade, and parallel forms. In the discrete-time domain, two types of filters designs are possible: the infinite impulse response (IIR) filter resulting from rational approximation, and the finite impulse response (FIR) filter that results from polynomial approximation. Luis Chaparro, in Signals and Systems Using MATLAB (Second Edition), 2015 AbstractĪccording to the eigenfunction property of LTI systems, filtering changes the frequency content of an input signal. The convolution integral is approximated using the MATLAB function conv. The following script simulates the convolution of a sinusoid x( t) of frequency Ω = 20 π, amplitude 10, and random phase with the impulse response h( t) (a modulated decaying exponential) of an LTI system. As in the eigenfunction property, the frequency of the output coincides with the frequency of the input, however, the magnitude and the phase of the input signal is changed by the response of the system at the input frequency.

Eigenfunction property of lti systems