OVERVIEW

Asignal is any useful information and noise is the not so useful information, invariably, a part of the signal. The signals, seemingly arbitrary in nature, may be thought of as sinusoidal functions (the fundamental and the harmonics), as described by Fourier. You can imagine what would happen to signal frequencies, if they were passed through a system of energy storage elements (such as the linear time invariant systems we have been studying, which have within them an impulse response in the form of sinusoidal functions), obviously, the matching frequencies in the signal and the system would be enhanced, and the unmatched frequencies would subside. The result is a filter, separating the desired frequencies from the undesired. We can tailor the response of such systems to our wishes, by physically choosing the components (in case of an analog system) or the coefficients (in case of a digital system). This is the basics of the filter design: suppressing or enhancing a specific frequency or a set of frequencies by passing a signal source through a system of energy storage elements. Filters modify signals in ways specified by the filter's frequency response.

In essence, a filter is a system capable of generating response based on the frequency selection. An analog filter is an electrical network comprising physical components of the resistors, capacitors, and inductors, whereas, a digital filter is a computer software algorithm producing the filter response. Filters can either amplify or suppress a specific frequency or range of frequencies, but...