Talk:Equalization filter

Graphs

Maybe some example graphs showing the input and output of an equalizer would make it more clear. --Bernard François 10:51, 2 January 2007 (UTC)

Mixing and phase shift

It seems to me that the "problem" with mixing would only occur if one were to mix the equalized and "dry" signal -- a questionable practice at best. Can someone justify this "problem"? -- algocu 20:12, 27 June 2007 (UTC)

Frequencies vs Frequency Ranges

There are several phrases like this:

 "A high Q means that only a few frequencies are affected, whereas a low Q affects many frequencies."

wouldn't it be more accurate to say

"A high Q means that only a narrow frequency range is affected, whereas a low Q affects a wide frequency range?"

Is the implication that a named frequency implies a range strong enough that we don't need to be, well, clear?--Elvey (talk) 18:01, 25 May 2009 (UTC)

Sounds good to me. SpinningSpark 23:49, 25 May 2009 (UTC)

What sounds good? The way it is or the change I'm considering? I'll assume the latter.--Elvey (talk) 20:35, 26 May 2009 (UTC)

Oh sorry, I meant your wording is good (and more accurate) SpinningSpark 21:34, 26 May 2009 (UTC)

The formula relating bandwidth (in octaves) and Q is suspect.

The article says

The formula for conversion from bandwidth in octaves to $Q$ is:

$Q={\frac {\sqrt {2^{N}}}{2^{N}-1}}$, where $N$ is the bandwidth in octaves.

but I am convinced it is:

$Q={\frac {1}{2\sinh \left({\frac {\ln(2)}{2}}N\right)}}$.

Can we check to see that these are the same? I'll work on it, but I am convinced the latter is both correct and likely a better form (it puts N into a single spot so the formula can be inverted to solve for bandwidth in octaves in terms of Q). 70.109.188.83 (talk) 01:29, 16 August 2010 (UTC)

I agree it is the same, but I cannot see that it is enlightening to introduce log and hyperbolic functions. The original form can easily by inverted with the help of a quadratic equation. It would be easier still to give the inverted form specifically if you think the article needs it. SpinningSpark 17:59, 16 August 2010 (UTC)

I got the form with sinh from the so-called "RBJ Audio EQ Cookbook" which has been referenced in Filter design and Digital biquad filter. Personally, I would suggest showing both *and* the inverted form and changing N to something like BW for "bandwidth". Also, as best as I can tell from the Audio EQ Cookbook, this relationship is true for all filters but not precisely true for the regular parametric peaking or "presence" filter. And for the BPF or notch filters, the bandwidth is measured from the lower -3 dB bandedge to the higher -3 dB bandedge.

Also I might suggest breaking this into sections of the different 2nd order filter families, with the same headings as the Audio EQ Cookbook (but combine the lowshelf and highshelf into a single section). There are LPF, HPF, BPF, notch, APF, presence, and shelving filters. Does that make sense, Spinning? Would you like me to do it?

Also, we should get some good pics of typical frequency responses for each filter family. I have Octave but do not have MATLAB so it would be a little difficult to do a freqz() plot, but I might be able to do it. If I do, can you upload the images, because I am just an IP and I have to remain that way. 70.109.188.83 (talk) 22:14, 16 August 2010 (UTC)

I would caution against identifying one single conversion between bandwidth and Q. There are at least two versions of working formulae in professional audio products, differing in the shape of the bell curve vs gain or attenuation. The way forward might be to give a general idea of the conversion, or a complete description of both curves. Binksternet (talk) 05:33, 17 August 2010 (UTC)

For all except the parametric EQ (a.k.a. "peaking EQ" or "presence filter", the bell-shaped thing), the meaning of Q in audio is the same as what they taught us in our electrical engineering curriculum. But for the parametric EQ, it is different. It can't be the -3 dB bandwidth, because if the boost gain was only 2 dB, there are no -3 dB bandedges. I have also seen two versions (at least for boost). One is that the bandwidth is that of the BPF that is in parallel to a wire to make the parametric EQ (which is not symmetrical for cut) and the other is the RBJ Cookbook definition (where the bandedges are at half the dB of the dB boost or cut). But the Q is also messed up in the same way, so the formula relating Q and bandwidth remains the same. But strictly speaking, that formula relates Q and bandwidth for a BPF where the bandwidth are the octaves between the -3 dB points. 70.109.188.83 (talk) 06:13, 17 August 2010 (UTC)

@Binksternet, the IP is not proposing "identifying one single conversion between bandwidth and Q"; that is already in the article, for better or worse. The proposal (which I do not support) is rather, an alternative formula for the same thing. SpinningSpark 17:14, 17 August 2010 (UTC)

Spinning, one issue is that of form. For some reason, you think that using "N" for a symbol for bandwidth is good, I don't. Also you think a form with bandwidth appearing twice, and with a square root is better than a form where it appears once and has a sinh() function. That's fine, but it's not a big deal. One thing, though, is that that formula applies to bandpass filters or notch filters in which the bandwidth is defined to be the spread in log frequency (octaves) between bandedges that are -3 dB from the top level.

But this -3 dB thing doesn't exist in all bell-shaped EQs because sometimes the boost gain is less than 3 dB and there are no -3 dB bandedges. That formula that relates bandwidth to Q is not entirely meaningful for such parametric EQs. It works *only* if you fudge the meaning of Q a little and of bandwidth a little for parametric EQ. It is not necessarily the electrical engineering definition of Q and bandwidth, but a slightly fudged definition from the original EE definition of Q or "quality factor". 70.109.191.39 (talk) 06:53, 19 August 2010 (UTC)

At the risk of this being unappreciated, I'll intersperse comments. Revert it if this offends...

The choice of N as a symbol, or indeed the insertion of this formula in the article, had nothing to do with me. On Q, it is a fudge anyway, whether or not the response drops below 3dB. This is the equivalent Q of the circuit - that is, the Q that a simple second order resonator of the same bandwidth would have.

What resonator? The BPF that is in parallel with a wire? That is one definition. And a result is that a boost of N dB is not symmetric with a cut of N dB if the resonant frequency and Q are the same. But some have fudged the definition of Q for the cut case so that a cut of N dB precisely undoes what a boost of N dB does, given the same Q and resonant frequency. Another definition, is to define the bandwidth in terms of the half-dB gain points. And if bandwidth is defined like that and you relate it to Q with that formula, that Q is not the same the "equivalent Q of the circuit"

The equivalent Q of a complex circuit may well not be related to the energy stored at all and there may be many different resonances. SpinningSpark 19:47, 19 August 2010 (UTC)

That general definition of Q (ratio of stored energy to dissipated energy per cycle gets translated directly to the denominator of the transfer function:

$H_{\mathrm {BP} }(s)={\frac {s/\omega _{0}}{(s/\omega _{0})^{2}+{\frac {1}{Q}}(s/\omega _{0})+1}}\$

From that, you can determine where the half-power (-3.01 dB) bandedges are, relate them together in terms of log frequency measured in octaves, and you have a formula relating bandwidth in octaves to Q. It might be convenient to retain that formula even if there are no -3.01 dB bandedges, but if your definition has symmetrical boost and cut, then Q is not always the Q of the resonant circuit in the parametric EQ. There is not consistency in the definition for these 2nd-order peaking EQ. 72.95.93.187 (talk) 18:14, 20 August 2010 (UTC)