Filter design is the process of designing a signal processing filter that satisfies a set of requirements, some of which may be conflicting. The purpose is to find a realization of the filter that meets each of the requirements to an acceptable degree.

The filter design process can be described as an optimization problem. Certain parts of the design process can be automated, but an experienced designer may be needed to get a good result.

The design of digital filters is a complex topic. Although filters are easily understood and calculated, the practical challenges of their design and implementation are significant and are the subject of advanced research.

Typical requirements which may be considered in the design process are:

The required frequency response is an important parameter. The steepness and complexity of the response curve determines the filter order and feasibility.

A first-order recursive filter will only have a single frequency-dependent component. This means that the slope of the frequency response is limited to 6 dB per octave. For many purposes, this is not sufficient. To achieve steeper slopes, higher-order filters are required.

In relation to the desired frequency function, there may also be an accompanying weighting function, which describes, for each frequency, how important it is that the resulting frequency function approximates the desired one.

Typical examples of frequency function are: