Given the following poles and zeros map I have to identify qualitatively, which filter type is represented (Low-Pass, High-Pass, ...). In the solution it says, that this is a high pass filter.

Poles and zeros Map

However, I plotted the amplitude response (see below) and to me this looks more like a notch filter or a band stop.

Where is my mistake in reasoning?

Thank You!

Amplitude response in dB

Linear amplitude response


1 Answer 1


Your pole-zero plot depicts a linear phase, real valued, three coefficient FIR filter, if we assume the zeros are complex conjugates on the unit circle.

The frequency response magnitude is exactly zero at the angle of the zeros on the unit circle. Because of these exact zeros, the log magnitude of the frequency response tends to minus infinity at those frequencies, which gives an impression of notch, however the frequency response is not narrow enough for a typical notch filter. Adding two poles close to those zeros would make it a strong notch filter.

Because of the location of zeros, the frequency response magnitude is larger towards frequencies $\pm \pi$ and smaller at low frequencies and for this reason it is classified as a highpass filter. However it's not a very successful highpass filter either.


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