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Recursive Formula (Filter)

In DSP, this is a type of mathematical operation in which values (samples) obtained at earlier points in time are used along with current samples to determine subsequent calculations. In digital audio much of the processing that must be done to the signal requires mathematical computation. This computation appears in the form of equations where quite often a series of samples are compared to one another on a continuing basis, such that (for example) the value of a given sample may get added to or subtracted from the following sample, and then that result may be added to or subtracted from the next, and so on. There are many different types of functions, but the category of recursive functions specifically refers to preceding samples (their values and calculations based on them) being used to manipulate subsequent ones. This is a very common way to do filtering and equalization in the digital domain. A “Non Recursive Formula” would therefore be one in which these preceding values are not utilized. Volume and pan are examples of non-recursive operations.

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