Mark is right, it would be rare to need more than 5-6 filters to smooth response. I’ve only seen a few instances where more were needed, where response was extremely ragged and uneven. Your unequalized response has only a few, broad problems, certainly not a situation where 12 filters would be needed – maybe not even six.
Perhaps a rudimentary explanation of bandwidth and filters would be helpful. Brucek recently offered an excellent technical elucidation about bandwidth and Q – perhaps he can provide a link to it for your edification. Being mathematically challenged and a musician to boot I find it easier to deal with bandwidth as octaves.
Basically, any doubling or halving of the frequency spectrum is an octave. Thus starting at a reference point of say, 100Hz, an octave down would be 50Hz and an octave up would be 200Hz. Likewise, from a reference point of 4kHz, one octave down would be 2kHz, one octave up would be 8kHz. And so on.
With that in mind, let’s take a look at your graph. Notice the end-to-end points of the 50Hz hump. You can see it starts at 31.5 Hz. Take a look one octave above that point, which is 63Hz, and you can see the hump has not fully “resolved” – it is still pretty high. Looking further “upstream” you can see the hump has pretty much “bottomed out” at about 80Hz. So to keep it simple let’s say our hump begins at 31.5Hz and ends at 80Hz. Thus:
From 31.5Hz to 63Hz = one octave.
From 63Hz to 80Hz = 1/3 octave.
Conclusion: your 50Hz response peak is 1-1/3-octaves wide.
So all you need to do is set a 1-1/3-octave filter for the BFD to eliminate this problem, right? Uh... no.
The tricky thing about bandwidth and filters is that a filter will affect its set (or so-named) bandwidth value by a like amount in both directions from the center frequency. So if you dial in a 1-1/3 octave filter centered at 50Hz, it will actually be moving frequencies from 25Hz (1-1/3 octave below 50Hz) to 125Hz (1-1/3 octave above 50Hz).
Of course, this is not what we want. We only want to effect changes for the 1-1/3-octave bandwidth between 31Hz and 80Hz. Thus to find the correct filter value you need to divide the total bandwidth by 2. So to address our 1-1/3-octave problem all we need is a 2/3-octave filter.
The next tricky thing about filters: The bandwidth they affect is not “set in stone,” but varies with amplitude (that is, the amount of boost or cut applied). For instance, let’s say you have a 1/2-octave filter that has been boosted 6dB, and let’s say it is affecting a true 1/2-octave above and below the center frequency. Let’s also say you have a spectrum analyzer so you can see what actually happens when you adjust the filter. If you raise the filter’s amplitude from +6dB to +12dB you will see on the analyzer that the outer fringes “drag up” wider and wider as boost increases. So at +12dB the total affected bandwidth is noticeably wider than it was at +6dB.
The inverse happens when you cut the filter from zero down to -6dB and lower.
Thus you have to keep in mind that after you analyze your response graph and determine how wide the area is that you want to equalize, that bandwidth is “theoretical” when it comes to actual action from the equalizer. You have to keep an eye on the beginning and ending points on your chart and see if they have changed after you use the filter.
For example, let’s go back to your 1-1/3-octave problem between 31.5Hz and 80Hz. If you use a 1/2-octave filter and cut 15dB as Mark suggested, you will probably see that 31.5 and 80Hz have also been “dragged down” considerably, perhaps as much as 4-5dB. This may or may not be a desirable effect, depending on one’s specific EQ situation; in your case it is not good. So to keep the values at 31.5Hz and 80Hz at the same pre-EQ levels, you would want to “tighten up” the filter’s bandwidth as much as needed to accomplish this goal. That’s the nice thing about parametric equalizers - the ability to dial in the exact bandwidth you need.
The next thing to keep in mind: Don’t be obsessed with perfect response. Deviations that are ±2-4dB are usually difficult to hear (depending on how broad they are). For instance, if you effect major improvements with only 3-4 filters, then “burn” another 4-5 filters chasing every last ripple in response, chances are if you switch between the 3-4 filters and the 8-9 filters you won’t hear any difference. It’s always best to use as few filters as possible to get the job done.
Regarding your specific situation, Dan, I think there are two ways you could approach it: You could smooth response while simultaneously dialing in a “guess” at a house curve (as you did with your first chart), or shoot for flat response (Mark’s recommendations should send you in that direction) and then use an overlay filter to dial in a precise house curve, as brucek did in the link I provided previously. Either way it should take only a few properly set-up filters.
Wayne A. Pflughaupt