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When looking at the response of a digital filter, typically the magnitude and phase response of the filter is plotted. While the use of the magnitude plot is obvious, as it shows how each frequency is amplified or attenuated, I'm not as clear on what the use of the phase plot is. This is especially this case for linear phase response filters.

So, what is the practical use of looking at the phase response of a filter?

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1 Answer 1

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  • Can (will) affect stability.
    A filter with enough phase shift is called an oscillator :-) :-(.

  • When multiple frequencies are involved the waveform of the output signal will be affected by variations in phase delay of its components. eg to use the obvious example, a square edge becomes rounded as the phase, equivalent to delays, of component fequencies vary.

  • This effect is important enough that eg the classic Butterworth, Bessel and Chebychev transfer functions have been considered worth dealing with, designing for and talking about for decades.

  • Butterworth - maximally flat, phase response of components vary somewhat but amplitude flatness is more important in the related application.

  • Bessel - maximally constant delay - phase MATTERS even if flatness and absolute cuttoff rates are not well controlled.

  • Chebychev - maximal amplitude cutoff rate. We don't want no stinkin phase considerations, ie the ability to drop off the edge of the passband suddenly is most important.

Note that at "any distance" from the filter edge the amplitude response per pole of each type is essentially the same at6dB/octave, 20 dB/decade.

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  • \$\begingroup\$ that 1st point especially pertains to when your amplifier is part of a feedback control system. \$\endgroup\$
    – JustJeff
    Commented Oct 18, 2011 at 11:13
  • \$\begingroup\$ A filter by itself is not a oscillator. Stability is only a issue if the filter is part of the overall feedback loop. You might want to qualify your point 1. It gives the impression that a filter with large phase shift put in line with a loudspeaker, for example, would cause oscillation. I know you don't mean that, but the OP and others might not. \$\endgroup\$ Commented Oct 18, 2011 at 11:39
  • \$\begingroup\$ @Olin Lathrop: It's pretty common in some analog settings to have filter with internal feedback paths, such that the impulse response would include a decaying sine wave at the filter's cutoff frequency. On some such filters, the feedback was adjustable (and touchy), and if adjusted too high the filter would, in fact, self-oscillate. The only thing that distinguishes a high-Q filter from an oscillator is that the cutoff-frequency gain of the former is less than one, while that of the latter is greater than one (at least at low amplitudes). \$\endgroup\$
    – supercat
    Commented Oct 18, 2011 at 14:40

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