Is there any way to tell whether a filter is high pass or low pass by observing only it's time domain samples or coefficients?
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$\begingroup$ Do you mean to ask "… without transforming it to a frequency domain representation?", or do you mean to ask "… or are there other things than the time domain coefficients that make up the filter's characteristics?" $\endgroup$– Marcus MüllerCommented Jan 30, 2018 at 19:57
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$\begingroup$ @MarcusMüller Yes, without transforming it to a frequency domain representation $\endgroup$– Jubaer HossainCommented Jan 31, 2018 at 8:29
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2 Answers
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To elaborate a bit on Fat32's answer: the most straightforward thing to do is to compute (or estimate) the following two sums:
$$H(e^{j 0})=\sum_nh[n]\tag{1}$$
and
$$H(e^{j \pi})=\sum_n(-1)^nh[n]\tag{2}$$
where $(1)$ is the value of the frequency response at DC (i.e., $\omega=0$), and $(2)$ is the value of the frequency response at Nyquist (i.e., at $\omega=\pi$).
A low pass filter should have a relatively large value for $(1)$ and a very small value (ideally zero) for $(2)$. For a high pass filter the opposite is the case. If both values are small (and if $h[n]$ is not zero) then it's probably a band pass filter, and if both values are relatively large, it's probably a band stop filter. This of course only applies if you can assume that the filter approximates some standard frequency selective filter characteristic.
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$\begingroup$ Thanks for the clarification. It really helped me a lot! $\endgroup$ Commented Jan 31, 2018 at 8:37
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Yes. For example if the sum of the filter coefficients is (close to) zero, then it will not pass any DC signals, hence it cannot be a low-pass filter. Then such a filter will be a highpass filter (it can also be band-pass but I assume you deal with only a lowpass or highpass decision..)
