I need to convert this 12 Tap Low Pass Filter to a High Pass Filter.

The coefficients of the Low Pass Filter are as follows:

h[k] = [0.022 -0.083 -0.083 0.083 0.311 0.417 0.311 0.083 -0.083 -0.083 0.022 0.083]

My understanding is that if its an even-tap - We Multiply the coeffs by -1.

However the answer is:

hT[k] = [-0.022 -0.083 0.083 -0.083 -0.083 0.311 -0.417 0.311 -0.083 0.083 -0.083 -0.022 0.083]

I do not know how this came about. I looked for answers online alot but did not get the answer. Any help is appreciated


1 Answer 1



It looks like they shifted the frequency response by half the sampling frequency, i.e.,


Frequency shifting corresponds to modulation (multiplication) in the time domain. Now you just have to figure out the modulation sequence that achieves the correct frequency shift.


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