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Kindly explain why type 2 FIR filter cannot be used to design high pass filter.

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  • $\begingroup$ Have a look at this answer, where the 4 types of linear phase FIR filters are compared. $\endgroup$ – Matt L. Jan 14 '16 at 12:50
  • $\begingroup$ please clarify how presence of a zero at Z=-1 prevent us from using type two FIR filter for designing HPF or BSF $\endgroup$ – pavan sunder Jan 14 '16 at 14:25
  • $\begingroup$ $z=-1$ corresponds to the Nyquist (i.e. highest possible) frequency. If the filter's frequency response is zero at the highest frequency (and of course decays on the way there), you can't have a high pass or band stop filter, which are supposed to pass high frequencies. $\endgroup$ – Matt L. Jan 14 '16 at 14:28
  • $\begingroup$ How can you determine Z=-1 is the highest possible frequency? $\endgroup$ – pavan sunder Jan 14 '16 at 14:39
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Type 2 filters are even and symmetric. A signal with a frequency of $f_s/2$ is just a scaled version of [+1,-1,+1,-1,+1,...].

That means, at $f_s/2$, the response of a type 2 filter will always be zero as the coefficients of the same magnitude are an even number of samples apart so they cancel each other out.

A filter with a magnitude frequency response of zero at $f_s/2$ makes a very poor high pass filter.

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