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the group delay is D=(N-1)/2=20 samples No. Group delay is a function of frequency. Assigning a single number to group delay is somewhat questionable. While the phase is indeed piece wise linear, at the "dips" of the combfilter, the phase jumps from $-\pi$ /2 to $\pi/2$. This is a real discontinuity, not a wrapping issue. At these frequencies the group ...


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Since this is an FIR, the group delay is D=(N-1)/2=20 samples. No, since this is a linear phase (i.e. symmetric or anti-symmetric) filter, the group delay is half the length! (being a FIR isn't sufficient.) The issue is that I get too peaks in the cross correlation, one at zero lag and another at 20 lag. Write down the formula for auto-correlation at ...


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Yeah, I answered my own question. So tried the same filter adding zeros to a total of 32 taps. Plays great now and spectrum is better in the highs. So this is the filter: 1, -0.15, 0.026, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (Total taps: 32)


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Real-valued and causal FIR filters have a (generalized) linear phase response if and only if their coefficients satisfy either $$h[n]=h[N-1-n]\tag{1}$$ or $$h[n]=-h[N-1-n]\tag{2}$$ where $N$ is the filter length (number of taps). There are four types of linear phase FIR filters, depending on the type of symmetry (even as in $(1)$ or odd as in $(2)$), ...


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The output variable holds the current output value given the current input value value. It is just the weighted sum of the current and ntaps-1 past input values. Note that this is not the most optimized version of an FIR filter routine.


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Note that this is not about general limitations of FIR filters, but about the special case of linear-phase FIR filters. If you understand why a type-II linear-phase FIR filter has a zero at $z=-1$, then the limitations of the other types should be obvious too. It's always about zeros at either $z=1$ (DC) or $z=-1$ (Nyquist). Given the transfer function $$H(...


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It stores the last $ntap$ samples of the input. So it's $x[n], x[n-1], ..., x[n-N+1]$


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A real coefficient, minimum phase, FIR filter will have the following property : $$ H(z) = H^*(z^*) = H(\frac{1}{z}) = H^*(\frac{1}{z^*}) $$ which implies that for every zero $z_0$ of $H(z)$ there will be three more zeros at $z_0^*$, $1/z_0$, and $1/z_0^*$; at conjugate, reciprocal, and conjugate-reciprocal locations respectively. Note that the reciprocal ...


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In order for H(z) to be a linear phase filter, it must zeros both on the inside of the unit circle and at the complementary locations (1/z) which are outside the unit circle. Therefore a linear phase circle has no stable causal inverse (since this would necessitate poles outside of the unit circle.) Note that a linear phase filter can be decomposed into ...


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