# Low pass and High pass filter Coefficient

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?

• 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?" – Marcus Müller Jan 30 '18 at 19:57
• @MarcusMüller Yes, without transforming it to a frequency domain representation – Jubaer Hossain Jan 31 '18 at 8:29

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.

• Thanks for the clarification. It really helped me a lot! – Jubaer Hossain Jan 31 '18 at 8:37
• @JubaerHossain: You can accept one of the answers by clicking on the check mark to the left of the answer. – Matt L. Jan 31 '18 at 9:45

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..)