The Dirichlet and sinc functions are related by . Show this relationship for . Avoid indeterminate expressions by specifying that the ratio of sinc functions is for , where is an integer.
The Dirichlet function, or periodic sinc function, is
for any nonzero integer N.
This function has period 2π for odd N and period
4π for even N. Its maximum value is 1 for all
N, and its minimum value is –1 for even N. The
magnitude of the function is 1/N times the magnitude of the discrete-time Fourier transform of the
N-point rectangular window.
Extended Capabilities
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