In some cases, a linear filter is designed by expressing how it modifies the spectral distribution. It could amplify some frequencies, while suppressing others. In this case, the filter is defined in terms of a *transfer function*, which is applied as follows: 1) transforming the original signal using the Fourier transform, 2) multiplying the result by the transfer function to obtain the distorted spectral distribution, and then 3) applying the inverse Fourier transform to obtain the result as a function of time. The transfer function can be calculated from the linear filter by applying the discrete Laplace transform (called *z-transform*) to the finite impulse response [11,191].

Steven M LaValle 2020-11-11