Parameter

Example

For example, a parametric equaliser is a tone control circuit that allows the frequency of maximum cut or boost to be set by one control, and the size of the cut or boost by another. These settings, the frequency and level of the peak or trough, are two of the parameters of a frequency response curve, and in a two-control equaliser they completely describe the curve. More elaborate parametric equalisers may allow other parameters to be varied, such as skew. These parameters each describe some aspect of the response curve seen as a whole, over all frequencies. By way of contrast, a graphic equaliser provides individual level controls for various frequency bands, each of which acts only on that particular frequency band.

Types of parameter

Mathematical

In mathematics there is little difference in meaning between a parameter and an argument of a function. It is usually a matter of convention (and therefore a historical accident) whether some or all the arguments of a function are called parameters.

Computer science

When the terms formal parameter and actual parameter are used, they generally correspond with the definitions used in computer science. In the definition of a function such as

f(x) = x + 2,

y = f(3) + 5,

In computing the parameters passed to a function subroutine are more normally called arguments.

Logic

In logic, the parameters passed to (or operated on by) an open predicate are called parameters by some authors (e.g. Prawitz, "Natural Deduction"; Paulson, "Designing a theorem prover"). Parameters locally defined within the predicate are called variables. This extra distinction pays off when defining substitution (without this distinction special provision has to be made to avoid variable capture). Others (maybe most) just call parameters passed to (or operated on by) an open predicate variables, and when defining substitution have to distinguish between free variables and bound variables.

Analytic geometry

In analytic geometry, curves are often given as the image of some function. The argument of the function is invariably called "the parameter". A circle of radius 1 centered at the origin can be specified in more than one form: