I have a multichannel array that I need to bandpass before feeding into my time-difference-of-arrival localisation (TDOA) routine.
I remember hearing somewhere that I should be vary careful about performing any filtering. I know some filters can alter the offset of high/low frequency components.
How large are the offsets really, and would it be large enough to mess with the actual TDOAs? My audio is noisy, how do I perform filtering then?
I'm not sure what you mean by "offset", but I'm assuming you mean the time alignment of the waveforms. Yes, filters generally introduce a time delay in their outputs due to their phase response, such that the output waveform is a filtered AND delayed version of the input:
[From Mathworks Help Center - Compensate for Delay and Distortion Introduced by Filters ]
For digital filters, the offset will depend on your sampling frequency, filter type (FIR/IIR), and order, amongst other things, with higher order filters intoducing longer delays.
This delay should not matter too much for TDOA applications, as long as you apply the exact same filter to all your channels. Thus they would all be delayed by the same amount, and the relative TDOA information would be preserved across the channels.
Having said that, one option to remove the time delays in offline processing (i.e. for pre-recorded signals only, not for real-time analysis) is to perform the so-called forward-backward filtering: you apply your filter to your recorded signal, time-reverse the filtered signal, apply the same filter again to the time-reversed signal, and bring the signal back to non-reverse-time. The first filtering step introduces its time-delay, and the 2nd filtering step introduces a "negative delay" that compensate for the first one. Programming languages such as Matlab and Python/Scipy have this function available with the name filtfilt. See the link directly under the image for a short tutorial on this method using Matlab.
There is no worry with filtering when you apply the filter on all channels as then the TDOA is unchanged. If you wanted to overlay the filtered data with the original data and you use an FIR filter, then you can exploit the fact that for FIR filters the delay is half the filter size
Example in Matlab:
yy= fftfilt(fir1(128,0.5),[xx;zeros(64,1)]);
yy(1:64)=[];
For IIR filters, this does not work as group delay of IIR filters are frequency dependent. But there are routines implemented in signal processing tool-boxes that provide the group delay and one could correct time delay for a given frequency.
