The square wave response of a dynamic system measures how the dynamic system responds when a square wave is applied to its input. Generally a unit step function is applied defined by the following equation:

Laplace transform and Fourier transform both are use for analysis of aperiodic signals. Laplace yields the result in s-domain where as Fourier transform yields it in frequency domain. Laplace is more often used because in s-domian it is easier to analyze the performance of the system by looking at the poles and the zeros.

The Laplace transform is usually used in the context of one-sided signals, i.e. signals that are zero for all values ofnbsp.tnbsp.less than some value. Usually, this start time is set to zero, for convenience and without loss of generality, with the transform integral being taken from zero to infinity. The Fourier transform is used for analyzing systems that process signals that are infinite in extent, such as modulated sinusoids. (LTI)

The signal is compared both in frequency and time domain, before and after filtering. As seen in the graphs the amplitude of the signal after filtering is 1. The amplitude thus decreases from 2 to 1, showing 3dB attenuation. In frequency domain the higher frequency coefficients are zero. They cover almost half the total bandwidth. Thus the half band filter has made half of the coefficients zero with 3dB