# why type 2 FIR cannot be used to design high pass filter

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

• Have a look at this answer, where the 4 types of linear phase FIR filters are compared. – Matt L. Jan 14 '16 at 12:50
• please clarify how presence of a zero at Z=-1 prevent us from using type two FIR filter for designing HPF or BSF – pavan sunder Jan 14 '16 at 14:25
• $z=-1$ 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. – Matt L. Jan 14 '16 at 14:28
• How can you determine Z=-1 is the highest possible frequency? – pavan sunder Jan 14 '16 at 14:39

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.