MATLAB SIGNAL PROCESSING TOOLBOX 6 Manuel d'utilisateur télécharger pdf (Page 23)

The Dirichlet Function

2-15

The Dirichlet Function

The toolbox 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, D(x) is:

D x

N x

x k k

k N

( )

sin( / )

, , , , , ,...

( ) ,

( )

π = ± ± ±

2 0 1 2 3

== = ± ± ±

2 0 1 2 3

k k, , , , ,...

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 over the range 0 to 4π for N=7 and N=8, use

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

subplot(2,1,1)

plot(x,diric(x,7))

axis tight

title('n = 7')

subplot(2,1,2)

plot(x,diric(x,8))

axis tight

title('n = 8')

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MATLAB SIGNAL PROCESSING TOOLBOX 6 Manuel d'utilisateur Page 23