Time-domain description and convolution

Abstract

In the previous chapter we saw how the Fourier and Laplace transforms can be used to represent signals and calculate the response of a linear system to a fairly general input signal. If we use Laplace or Fourier transforms to represent signals or systems we are said to be working in the ‘frequency domain’ or ‘transform domain’. In contrast, the original signal x(t) is said to be in the ‘time-domain’. To calculate the response of a system to the signal x(t) we first transform the signal to the frequency domain. We then multiply the transform of the input by the frequency response or transfer function of the system to get the output (in the frequency domain). Finally we inverse transform to get back to the time-domain.