For example, we have a baseband signal which is passed through a low pass filter with 3-dB bandwidth of 5 GHz, and if the same filter (all other parameter same like filter loss, filter order etc) 3 dB bandwidth increased to lets say 7 GHz, will the signal experience different time delays for filter with 5 GHz and 7 GHz bandwidth or not?
In general, how is filter bandwidth and signal time delay related to each other?
Dear Shahid
The delay experienced by the signal will depend on the phase response of the filter. For a helpful discussion along with mathematical relations, please see: https://dsp.stackexchange.com/questions/34934/how-to-read-phase-response-graph
As a general rule, a phase lag (i.e. a delay) is required for a low-pass filtering effect. So I would expect the time delay to increase as the filter bandwidth decreases. The complex response (i.e. phase and magnitude) of the filter is required to compute the delay. The magnitude response only gives a crude indication. For a linear-phase FIR filter, with an odd number of taps, the delay is equal to half the filter order. High sidelobes would suggest a low-order FIR filter, so I would expect a lower delay in that case.
Filtering is an operation that consists in separating (or modifying) the components of a signal according to their frequencies. As a general rule, a filter does not change the shape of the signal passing through it, but selects a part of the frequency content of the signal. We are talking about high-pass, low-pass, band-pass, and notch filters depending on the sorted frequency ranges.
The filters often lead to a phase shift, either early or late, between the input and output signals. Depending on the location of the filter in the system, this feature may be harmful or undesirable, forcing circuit designers to take this into account.
This phase shift represents the delay of the output signal.
The delay in your case is induced by an analog filter. They are linked automatically.
Signal processing exposes several techniques for extracting information and mitigating delay.
See also this address:
http://documents.irevues.inist.fr/bitstream/handle/2042/9907/AR1_1.pdf
From τp(ω)=−ϕ(ω)/ω,ω≠0 (see definition from the link posted by Usman Rashid, additionally it's worth to make the observation that if the phase response it's linear (τp(ω)=k*ω) then the filter system (not the signal) have a time delay =k.
Thanks for your helpful answers (Marcel Nicola , Messaoud Mokhtari ,Hugh Lachlan Kennedy , Usman Rashid and Aparna Sathya Murthy ).
- Badges
- Science topic