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Will filtering a signal through multiple bandpass filters, where each filter is passed the complete signal, and then combining the output have the same result as a parametric EQ?

What if the signal is passed into a series of bandpass filters?

Are there any performance issues or optimizations that can be made when EQing a signal this way?

Update:

After reading the answer in this question which-filter-for-an-audio-equalizer it seems splitting the signal through a filter bank (in parallel) is the correct way.

The answer explains how the bands need to blend together to avoid audio issues, how is this calculated if each bandpass filter can have a varied bandwidth?

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  • $\begingroup$ That looks more like a graphic equalizer to me (parametric equalizer is something different). $\endgroup$ – keith Jul 4 '16 at 19:04
  • $\begingroup$ I think its the same thing. Where the user uses the UI to control gain, center frequency and bandwidth of each band. $\endgroup$ – jarryd Jul 4 '16 at 19:06
  • $\begingroup$ OK, sure, if you're controlling gain, center frequency and bandwidth you are using a parametric EQ and you want a serial cascade of band shelves in my opinion :-) $\endgroup$ – keith Jul 4 '16 at 19:08
  • $\begingroup$ Thanks Keith. The answer in the other post discusses how each band needs to blend with the previous one, how would this work if bandwidths overlap? Would that matter if its being done in serial? How are the filter responses of each filter combined, to be able to draw the response in the UI? $\endgroup$ – jarryd Jul 4 '16 at 19:10
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    $\begingroup$ If you figure out how to bode plot the cascade of a few of the filters from the cookbook you'll learn a lot about how they work. Then you can make your own mind up as to whether it's the direction you want to head. All the modern parametric EQ plugins that I've used are based on filters similar to the ones in the cookbook. $\endgroup$ – keith Jul 4 '16 at 19:35
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a graphic EQ need not mean cascaded shelves. it could mean cascaded peak/cut bell filters. maybe with shelves as bookends, maybe not.

the bell filters are symmetrical in log freq (or the pitch scale) and are naturally spaced equally in log frequency. you can draw any reasonable shape with a sum dB of these cascaded peak/cut filters. but nothing too wild.

you could also do this more analytically with a sum of FIRs, all time-aligned. make a series of overlapping complementary window functions (like a Hann) but operating on log frequency instead of linear frequency. but that frequency response can be interpolated and sampled in linear frequency and an FIR can be derived from that magnitude response with a delay of some sufficient constant value.

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A parametric equalizer at its crudest is usually a serial cascade of band shelves. I suppose you could make one from a parallel sum of band passes with different gains.

Not sure I can comment on the performance as it would need to be compared to the performance of something else.

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  • $\begingroup$ I'm not sure whether I understand you correctly, but a parametric equalizer is not usually a serial cascade of band shelves. Shelving filters may be used for the lowest and highest bands, but in my eyes the typical building block for a parametric equalizer is the peak filter. $\endgroup$ – applesoup Jul 6 '16 at 11:01
  • $\begingroup$ A peak filter is a band shelf. You're confusing band shelf with high/low shelves. A band shelf is a low shelf transformed using a similar transform as that used to convert a low pass to a band pass. Orfanidis has covered these mappings in depth, his stuff is worth reading. $\endgroup$ – keith Jul 6 '16 at 18:12

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