# 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?" Jan 30 '18 at 19:57
• @MarcusMüller Yes, without transforming it to a frequency domain representation 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! 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. 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..)