DTFT, Time Limited Square Wave.

Cuthbert Nyack
The Z transform of M periods of a sampled square wave with 2N samples per period is shown below.
Substituting Z = ejwT gives Z(w), the DTFT below.
For Comparison the Fourier Transform G(w) of M periods of a square wave with period 2t is:-

The applet below shows how the DTFT and FT spectrum of the above Time Limited Square Wave changes as N and M changes. Plots are divided by N and M to maintain constant amplitude.

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© 2000 Cuthbert A. Nyack.