sinc

Signal Processing Toolbox

Sinc or sin(

t)/

t function.

y = sinc(x)

Description

sinc computes the sinc function of an input vector or array, where the sinc function is

This function is the continuous inverse Fourier transform of the rectangular pulse of width 2

and height 1:

y = sinc(x)

returns an array y the same size as x, whose elements are the sinc function of the elements of x.

The space of functions bandlimited in the frequency band

is spanned by the infinite (yet countable) set of sinc functions shifted by integers. Thus any such bandlimited function g(t) can be reconstructed from its samples at integer spacings:

Example

Perform ideal bandlimited interpolation by assuming that the signal to be interpolated is 0 outside of the given time interval and that it has been sampled at exactly the Nyquist frequency:

t = (1:10)';           % a column vector of time samples
x = randn(size(t));    % a column vector of data
% ts is times at which to interpolate data
ts = linspace(-5,15,600)';
y = sinc(ts(:,ones(size(t))) - t(:,ones(size(ts)))')*x;
plot(t,x,'o',ts,y)

See Also


`chirp`	Swept-frequency cosine generator.
`cos`	Cosine of vector/matrix elements (see MATLAB Function Reference).
`diric`	Dirichlet or periodic sinc function.
`gauspuls`	Gaussian-modulated sinusoidal pulse generator.
`pulstran`	Pulse train generator.
`rectpuls`	Sampled aperiodic rectangle generator.
`sawtooth`	Sawtooth or triangle wave generator.
`sin`	Sine of vector/matrix elements (see MATLAB Function Reference).
`square`	Square wave generator.
`tripuls`	Sampled aperiodic triangle generator.

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