0
$\begingroup$

I know that for linear phase filters, all frequency components have equal delay times. That is, there is no distortion of signal due to the time delay of frequencies relative to one another.

However, for filters generalised linear phase, where the phase is of the form $a\omega+b$, and $b$ is not zero. Will the same be true for them? Thanks in advance!

Improve this question
$\endgroup$
3
  • $\begingroup$ @hotpaw2: OK, so is there phase distortion? $\endgroup$
    – meta_warrior
    Commented Feb 13, 2014 at 1:32
  • $\begingroup$ @hotpaw2, that doesn't sound right. The phase response $\phi=a\omega + b$ produces a delay of $d\phi / d\omega = a$, so a is nonzero for non-trivial causal filters. On the other hand, $b$ introduces a global phaseshift which requires a complex filter unless $b=n \pi$ for natural $n$. That is unless you allow a discontinuity of $b$ at $\omega=0$, which would not be obvious from what the OP stated. $\endgroup$
    – Jazzmaniac
    Commented Feb 13, 2014 at 15:17
  • $\begingroup$ @Jazzmaniac: Can you provide an answer for my question above? Thanks! $\endgroup$
    – meta_warrior
    Commented Feb 13, 2014 at 15:41

2 Answers 2

Reset to default
2
$\begingroup$

Yes. The time delay of real-coefficient linear-phase N-point FIR filter is (N-1)/2 samples. The time delay of complex-coefficient generalized-linear-phase N-point FIR filter is also (N-1)/2 samples.

You can prove this to yourself. Design a narrowband linear-phase lowpass FIR filter, and plot its group delay. Then multiply that filter's coefficients by a complex exponential whose frequency is one fourth the sample rate, creating a complex-coefficient filter. Now plot the group delay of the complex filter. Compare the two group delay plots.

Improve this answer
$\endgroup$
1
$\begingroup$

Yes the same will be true for generalized linear phase. The only difference is that there will be a processing delay, due to the filter being casual like hotpaw2 said. Normally for FIR filters this delays is half the number of coefficients of the filter.

Improve this answer
$\endgroup$
8
  • $\begingroup$ Will the waveform of the signal be retained? Can you show an ezample ? $\endgroup$
    – meta_warrior
    Commented Feb 13, 2014 at 5:08
  • $\begingroup$ Absolutely not. Unless the magnitude of the frequency response is flat for all frequencies, which added to the linear phase makes a fancy delay line, which is pretty pointless. The whole point of filtering is modifying the waveform somehow, in order to obtain a desireable result out of it. $\endgroup$
    – bone
    Commented Feb 13, 2014 at 5:12
  • $\begingroup$ Ok, but for strictly linear phase filters, the waveform of the signal will be retained? $\endgroup$
    – meta_warrior
    Commented Feb 13, 2014 at 5:23
  • 1
    $\begingroup$ No. Bone's answer is correct. Unless the filter is a pure delay (linear phase AND flat frequency response) the waveform will change. $\endgroup$
    – Hilmar
    Commented Feb 13, 2014 at 9:55
  • $\begingroup$ But there will be no phase distortion for both cases ? @Hilmar $\endgroup$
    – meta_warrior
    Commented Feb 13, 2014 at 11:50

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.