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I have a small team project: use Matlab implement a Gui 5-band digital equalizer using FIR and IIR filters (2 cases) - The sample rate of all audio files is standard audio 44.1kHz. Coding is not my concern, however, I have 2 questions

(1) What are 5 center frequencies that I should choose ? I saw a homework problems select 500Hz, 1.5Hz, 4Kz, 10kHZ, and 16KHz but I am not sure how the author came up with these number.

(2) Should I use 5 bandpass filters? Or should I use 1 lowpass, 3 bandpass, and 1 highpass filter?

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The answer may depend on your application. I suggest you look at some commercial audio equipments with EQs to decide for those band frequencies. For example the old analog philips casette-type stereo system in my room has 5 band graph equalizers with the frequencies: [100-300-1000-4000-10000] Hz respectively. I use it as an amplifier for my laptop :)

If you design the first and last bands as Bass/treble shelve types, be careful to limit their cutoffs so that mid bands will have enough spectral intervals.

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  • $\begingroup$ Thank for your answer. I will look into some commercial ones. So, it is normal to have 5 band filters to be all bandpass filters? $\endgroup$
    – user7226
    Jan 23, 2015 at 21:27
  • $\begingroup$ I cannot say it is "normal" since I dont know an objective "norm" for a commercial audio equalizer. However, I guess it should be easier to design the first band as a lowpass filter instead of a bandpass, due to its steep transient region at 20 hz cutoff frequency. Besides the audio itself will already ideally be bandlimited to [20 20k] Hz range, so effectively a bandpass or lowpass filter should be the same, with lowpass being easier to realize. $\endgroup$
    – Fat32
    Jan 23, 2015 at 21:34
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5 bands ain't alot for a graphic equalizer. there are 10 octaves in our hearing range, so they might be spaced apart by two octaves, if their resonant frequencies were fixed. maybe by one octave with the three middle bands as peak/cut EQ and the top and bottom band as shelf EQ, both covering over 3 octaves. it would be 5 controls.

if all EQs were parametric, that is their resonant frequency (or "significant frequency") were adjustable, then 5 bands is plenty sufficient. the top and bottom bands would, again, be shelving EQ, and the middle 3 are peak/cut EQ. if you include adjustable Q, that would be 15 knobs.

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  • $\begingroup$ Thanks - yes, I go with options 1 - just 5 fixed bandwidth. $\endgroup$
    – user7226
    Jan 25, 2015 at 4:37
  • $\begingroup$ pretty wide bands. are all 5 equal bandwidths? or are the top and bottom much bigger than the 3 bands in the middle? $\endgroup$
    – robert bristow-johnson
    Jan 26, 2015 at 2:58
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If you need to cover 10 octaves by 5 band parametric EQs, then 10/5 = 2 octaves should be covered by each band. So my recommended EQ centers (averaged) would be 60, 240, 950 Hz and their corresponding Mid-High frequencies: 900000/60 = 15K, 900000/240 = 3.75K.

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