Fourier Series, Square wave Response of Ideal Filter.

Cuthbert Nyack
The frequency characteristic of an ideal band pass filter is shown in the plot below. The gain changes from 0 to 1 at the lower frequency F1 and from 1 to 0 at the higher frequency F2. The characteristic can also have a phase delay which changes linearly from +A to -A over the bandwidth of the filter. Ideal filters are not acheivable in practice but are used as a reference to gauge the performance of real filters.

The applet below shows the output from an ideal band pass filter when the input is a square wave shown in orange.
The Ideal Filter characteristic is shown in magenta and the input signal spectrum in green . The spectrum components which pass unattenuated through the filter and the output in the time domain is shown in red. Phase changes from +Phase to -Phase where Phase is shown on applet. Lower and upper frequency are given in units of the fundamental frequency.
Some eg parameters are:-
(0.5, 20.5, 0.0p, 1.0) this shows the output containing spectral components from 1 to 20 and approximating the square wave.
(2.5, 25.5, 0.0p, 1.0) this shows the output containing spectral components from 3 to 25 and approximating the square wave minus the fundamental.
(16.5, 17.5, 0.0p, 12.0) this shows the output containing a single spectral component n = 17(17 periods fit in 1 period of the fundamental).
(16.5, 19.5, 0.0p, 6.0) this shows the output containing 2 spectral components n = 17 and n = 19 and the result is a beating between the 2 frequencies.
(16.5, 21.5, 0.0p, 6.0) this shows the output containing 3 spectral components n = 17 n = 19 and n = 21 and the result is a beating between the 3 frequencies.




When activated the following gif image show how the applet should appear.

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COPYRIGHT © 1996 Cuthbert Nyack.