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I was wondering this for quite some time but couldnt find a satisfied answer. Seems like not a lot worry about phase response in general. But maybe I'm thinking about it in a wrong way...

I want to apply a high pass filter to my microphone pressure signals to cut away the low frequency garbage before beamforming. So I was wondering about using filters (low, high, band) on your time signals before beamforming.

How do you guys correct for the phase response? And is it actually needed? If not, is only applying (e.g.) a butterworth filter adequate enough to perform correct beamforming afterwards (outside the frequency for which it is filtered)? Or is some correction in phase needed?

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  • $\begingroup$ Welcome to SE.DSP! Why do you need to do the high pass filtering before the beamforming? Can you do it afterwards? What sort of beamforming? More details would help us answer the question. $\endgroup$ – Peter K. Jun 16 '17 at 15:54
  • $\begingroup$ Thanks! I wanted to remove some signal introduced for a truck passing by. It was a simple time-delay beamforming. The frequency range of interest was around and above 1000 Hz (I assume outside the range of the truck for which I assume is low frequency). I got a satisfied answer already from Stanley below. $\endgroup$ – Anwar M Jun 19 '17 at 12:11
  • $\begingroup$ No worries! Stan's answer came up and he went into more detail, so I left it there. $\endgroup$ – Peter K. Jun 19 '17 at 13:12
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An ideal delay and sum beamformer is Linear, which implies that filtering before beam forming is equivalent to filtering after beam-forming. If you filter each sensor, the filters have to be matched very closely, so for a pure analog system, do you want to use one or N nearly identical filters. Given temperature sensitivity and parameter drift, filtering after is much cheaper. No implemented beam former is perfectly Linear. Filtering prior has a number of advantages, such as reducing dynamic range requirements. Also for a digital beamformer, you need an antialiasing filter prior to the A/D converter so you filter before anyway. 30 years ago, switched capacitor filters were very useful. Today, for audio, over sampled delta sigma converters are not expensive and have huge dynamic ranges but you still have to do some signal conditioning between the mechanical sensor and the converter. The trade off for RADAR is more complicated. If your converters have enough dynamic range.

So the answer is that filtering prior to beamforming needs nearly identical characteristics. Some deviation is ok but you need to make that determination for your self . Ceramic and moving coils are not ideally Linear phase devices either and sensor location uncertainty has an effect. You also need to consider that you might have nonacoustic paths between the source and your array, Element coupling is another problem that can emerge.

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  • $\begingroup$ Thank you for your answer. I was indeed talking about digital filtering in the post processing part (after capturing the signal and hardware anti-alias filter, but before doing beamforming by software). I knew I was forgetting something. Like the filters have to be matched closely between microphones (which is the case when filtering using software). Then the possible phase change introduced doesnt matter as the relative phases between microphones stays the same. So in short, I was forgetting the filters have identical characteristics. $\endgroup$ – Anwar M Jun 19 '17 at 12:08

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