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The Dirichlet Function

The function diric computes the Dirichlet function, sometimes called the periodic sinc or aliased sinc function, for an input vector or matrix x. The Dirichlet function is defined by

D(x)={sin(Nx/2)Nsin(x/2),x2πk,(-1)k(N-1),x=2πk,k=0,±1,±2,±3,

where N is a user-specified positive integer. For N odd, the Dirichlet function has a period of 2π; for N even, its period is 4π. The magnitude of this function is 1/N times the magnitude of the discrete-time Fourier transform of the N-point rectangular window.

To plot the Dirichlet function between 0 and 4π for N=7 and N=8, use

x = linspace(0,4*pi,300);

subplot(2,1,1)
plot(x/pi,diric(x,7))
title('N = 7')

subplot(2,1,2)
plot(x/pi,diric(x,8))
title('N = 8')
xlabel('x / \pi')

Figure contains 2 axes objects. Axes object 1 with title N = 7 contains an object of type line. Axes object 2 with title N = 8 contains an object of type line.

See Also

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