sinc

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The cardinal sine.

Library

EngeeDSP

Syntax

Function call

y = sinc(x) — returns an array y, whose elements are the cardinal sinuses of the elements of the input array x. Output array y has the same size as x.

Arguments

Input arguments

# x — input data

+ scalar | vector | the matrix

Details

Input data specified as a real or complex scalar, vector, or matrix. If x if not a scalar, then sinc Applies to each element.

Data types	`Float32`, `Float64`
Support for complex numbers	Yes

Output arguments

# y is the value of the cardinal sinuses of the input data

+ scalar | vector | the matrix

Details

Cardinal sinuses x, returned as a real or complex scalar, vector, or matrix of the same dimension as x.

Data types	`Float32`, `Float64`
Support for complex numbers	Yes

Additional information

The cardinal sine function

Details

The cardinal sine function is defined as:

This analytical expression corresponds to the continuous inverse Fourier transform of a rectangular pulse of width and height 1:

The space of functions with a limited bandwidth in the frequency range is covered by a countably infinite set of functions sinc, shifted by integers. Thus, it is possible to recover any such function with limited bandwidth from its samples at integer intervals: