Suitability of filter test input.

In the end, digital filters are manifest entities that are expected to perform to some standard. This performance can be affected by sampling errors, round off errors and implementation errors. In order to confidently use a digital filter, it must not only be designed from a proper theoretical point of view, the actual implementation must be rigorously tested.

A key point to this testing comes from the design of filters. These filters look at the input as a sum of different frequencies. While discussing the topic with a friend, the question was posed “Why not use a voltage source and a potentiometer” to provide the input. This would be inadequate to actually test a filter, because the Fourier decomposition of a ramp has relatively few frequencies. And a rigorous test would involve applying all possible frequencies to the digital filter. Luckily, there is a type of signal that manifests all frequencies and phases: Noise.