Hello, at the moment, I'm trying to implement a parametric equalizer using a gaussian curve. It actually works fine so far, but one thing isn't really perfect: The width of the curve should grow by increasing frequency, which it doesn't at the moment. I'm programming with Java and my formula looks like this: y = Math.pow(Math.E, -q * Math.pow(frq, 2)) * gain * (1 / 2 * PI) for maybe better reading: y = e^(-q * frq^2) * gain * (1/2 * PI) The width of the curve is controlled by the factor q. The x value is represented by frq, which has a range from 0 to 20.0 When I use linear values for q and a linear coordinate system, of course the curve's width stays the same when the frequency gets higher. But I want it to become wider the higher the frequency gets. Then I modified q, so that when you change the q value, it gets replaced by e^(q/2), which is actually much better than before. But I don't know if this is the correct approach. When I view it with a logarithmic coordinate system, it looks more correct, but still it becomes a little thinner when moving to the right. On the other hand, I don't even know if my coordinate system has the correct scale, compared to how I modified the q value. As you might have already guessed, I'm not the world's best mathematican ;) and especially logarithmic and exponential stuff is a bit hard for me to understand and visualize. So my questions would be: 1) How should I calculate the logarithmic coordinate system? I know that it can be scaled differently, but what would be the best approach? 2) How can I affect the q value for the curve, so that its width always stays the same, in relation to the coordinate system I use? Thanks in advance Rock Lobster

# Gaussian curve, logarithmic width

Started by ●July 5, 2007

Reply by ●July 5, 20072007-07-05

Rock Lobster schrieb:> at the moment, I'm trying to implement a parametric equalizer using a > gaussian curve.I wonder a bit. Usually this is better done by IIR filters. If you place zeros in the negative s-plane then you can compensate for the group delay too.> It actually works fine so far, but one thing isn't really perfect: The > width of the curve should grow by increasing frequency, which it doesn't > at the moment.You have to use a ->log-normal distribution rather than a normal distribution for this purpose.. But I would prefer biquads for a parametric EQ. And if you are going to generate the amplitude response of an FIR kernel this way, I would prefer a single sine lobe as shape. Define this shape in the double logarithmic space, i.e. log(|H|)/log(f) or H in dB vs. log(f). This gives reasonable results for frequency equalization. Marcel

Reply by ●July 5, 20072007-07-05

>Rock Lobster schrieb: >> at the moment, I'm trying to implement a parametric equalizer using a >> gaussian curve. > >I wonder a bit. >Usually this is better done by IIR filters. >If you place zeros in the negative s-plane then you can compensate for >the group delay too. > >> It actually works fine so far, but one thing isn't really perfect: The >> width of the curve should grow by increasing frequency, which itdoesn't>> at the moment. > >You have to use a ->log-normal distribution rather than a normal >distribution for this purpose.. > >But I would prefer biquads for a parametric EQ. > >And if you are going to generate the amplitude response of an FIR kernel>this way, I would prefer a single sine lobe as shape. Define this shape >in the double logarithmic space, i.e. log(|H|)/log(f) or H in dB vs. >log(f). This gives reasonable results for frequency equalization. > > >Marcel >Ahh okay, thanks, I looked for log-normal distribution now and it actually could serve my needs :) (haven't tested it yet) But what are biquads? I didn't find reasonable stuff with google, at least nothing that would fit. Is there also a formula for this?

Reply by ●July 5, 20072007-07-05

I now checked the log-normal curve, and it has the correct shape, but its width still doesn't grow depending on the x value (which means, in a linear coordinate system, the curve still has the same width for e.g. x = 0 and x = 3000).

Reply by ●July 5, 20072007-07-05

Rock Lobster schrieb:> I now checked the log-normal curve, and it has the correct shape, but its > width still doesn't grow depending on the x value (which means, in a > linear coordinate system, the curve still has the same width for e.g. x = > 0 and x = 3000).You are free to multiply the width by x before you start. Marcel