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cristian_vogel Member posted 19 July 2006 06:28 I was checking out the FIR filter sound, and set me wondering about how to generate the co-efficients -I don't really understand what they are , or how they change the way a sound is filtered? how do filter co-efficients work, and how to go about generating them from the filter characteristics of an impulse response?

and how to think about co-efficients in Waveshaping? Are they points on an input->output map or what?

there isn't really anything about co-efficients in the book, so a little guide would be useful ot help grasp what is audibly a very powerful and unique way of shaping sound

-- CristianVogel - 19 Jul 2006


Hi Cristian You can think of it as a multi tap delay line but where all the taps are right next to each other. The coefficients are like the levels of each tap. So if you had 1 1 1 1 1 it would be like playing the signal 5 times each time delayed by one sample. In this case you would probably over load and clip the signal as a low frequency signal could become amplified five times. A hi frequency signal would be smeared and the plus and minus would tend to cancel a bit and hence get attenuated. This would be a very basic lo pass filter. If instead you put in {1/5} {1/5} {1/5} {1/5} {1/5} then you would get the same thing but without the clipping. If you now put in 1 {-1/4} {-1/4} {-1/4} {-1/4} you can see that a lo frequency will tend to average out to zero and hence get cut quite a lot, but a hi frequency is more likely to get through. This is a very basic hi pass filter.

This is a very basic description of a huge subject and I'm sure there are plenty of filter design experts that will tell you all the flaws and disadvantages of using the figures I've given, but it might give you a taste of something the you could end up reading about for years.

hope this helps


-- PeteJohnston - 19 Jul 2006

Yes! thanks! ..that really helped.... All we need to do now is work out how to generate these co-efficients by analysing an analogue filter .. Any takers? (is that even a sensible suggestion?)

-- CharlieNorton - 02 Dec 2010

For the FIR, the coefficients are the amplitudes of the taps. Think of each coefficient as a fader on a delayed signal. The order number of the coefficient is the number of samples delay at that tap.

For the Waveshaper, a rule of thumb is that even numbered coefficients control the amplitude of even-numbered harmonics in the distortion and odd-numbered coefficients control the amplitude of odd-numbered harmonics in the distortion.

In this case the coefficients are like faders on increasing powers of the Input signal that are all mixed together to form the output. For example, using ^ to mean raised-to-the-power-of, we have:

(a0 * Input^0) + (a1 * Input^1) + (a2 * Input^2) + .. + (an * Input^n)

Anything raised to the zeroeth power is 1, so the first fader, a0, controls DCOffset. Anything raised to the first power is just itself, so the second fader a1 controls the Input. A signal multiplied by itself is ring modulated so a2 is a fader on the difference frequency (0) and the sum frequency (2f or one octave higher), etc.

-- CarlaScaletti - 19 Jul 2006

Question: What do the coefficients mean in the FIR and WaveShaper? Sounds?
Keywords: coefficients filter FIR waveshaper polynomial

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