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sinc

Sinc function

Syntax

Description

example

y = sinc(x) returns an array, y, whose elements are the sinc of the elements of the input, x. y is the same size as x.

Input Arguments

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x — Input arrayscalar value | vector | matrix | N-D array

Input array, specified as a real-valued or complex-valued scalar, vector, matrix, or N-D array. When x is nonscalar, sinc is an element-wise operation.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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y — Sinc of inputscalar value | vector | matrix | N-D array

Sinc of the input array, x, returned as a real-valued or complex-valued scalar, vector, matrix, or N-D array of the same size as x.

Examples

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Ideal Bandlimited Interpolation

Perform ideal bandlimited interpolation of a random signal sampled at integer spacings.

Assume that the signal to interpolate, x, is 0 outside of the given time interval and has been sampled at the Nyquist frequency. Reset the random number generator for reproducibility.

rng default

t = 1:10;
x = randn(size(t))';
ts = linspace(-5,15,600);
[Ts,T] = ndgrid(ts,t);
y = sinc(Ts - T)*x;

plot(t,x,'o',ts,y)
xlabel Time, ylabel Signal
legend('Sampled','Interpolated','Location','SouthWest')
legend boxoff

More About

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Sinc

The sinc function is defined by

This analytic expression corresponds to the continuous inverse Fourier transform of a rectangular pulse of width 2π and height 1:

The space of functions bandlimited in the frequency range is spanned by the countably infinite set of sinc functions shifted by integers. Thus, you can reconstruct any such bandlimited function g(t) from its samples at integer spacings:

See Also

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