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 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
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:
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