Square wave and Nonlinear phase filter

Cuthbert Nyack
If a square wave is passed through a filter with ideal amplitude but nonlinear phase characteristic, then depending on the nonlinearity, there can be a "ringing" at the rising edge of the pulse. This phenomenon is a common occurence in electronic circuits.

The effect is illustrated in the applet below. With gain = 1, the vertical scale for phase is -3p to +p.
The output is shown in green, the nonlinear phase in cyan. The part of the square wave spectrum that passes through the filter is in green, the part that is rejected is in red and the ideal filter amplitude characteristic in magenta.
Nonlin = 1.0 corresponds to linear phase. When the phase is linear all spectral components are delayed by the same amount in time so the whole square wave shifts to the right depending on the MaxPhase.
eg parameters (1.0, 3.0, -3.0p, 1.0), the signal is delayed by p = T/2.
eg parameters (3.5, 30.0, -3.0p, 1.0), the component at n = 30 is delayed by 3p, component at n = 1 is unaffected.

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

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COPYRIGHT 2005 Cuthbert Nyack.