sinc

Sinc function

Syntax

y = sinc(x)

Description

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

Examples

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

Input Arguments

x — Input array

scalar value | vector | matrix | N-D array | gpuArray object

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

See Run MATLAB Functions on a GPU (Parallel Computing Toolbox) and GPU Support by Release (Parallel Computing Toolbox) for details on gpuArray (Parallel Computing Toolbox) objects.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

y — Sinc of input

scalar value | vector | matrix | N-D array | gpuArray object

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

More About

sinc

The sinc function is defined by

$$\mathrm{sinc}t=\{\begin{array}{cc}\frac{\sin \pi t}{\pi t}& t\ne 0,\\ 1& t=0.\end{array}$$

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

$$\mathrm{sinc}t=\frac{1}{2\pi }{\displaystyle {\int }_{-\pi }^{\pi }{e}^{j\omega t}d\omega .}$$

The space of functions bandlimited in the frequency range $$\omega =(-\pi ,\pi ]$$ 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:

$$g(t)={\displaystyle \sum _{n=-\infty }^{\infty }g(n)\mathrm{sinc}(t-n)}.$$

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).