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You seem to be asking how DSP filters work and I confess that I have no idea how they work. Even so I would not describe them as you suggest because modifying the phase of a signal does not attenuate it. Filters that attenuate signals generally do also modify the phases of the signals but it is quite easy to build a filter that does phase shifting without attenuating. I'm not sure how deep your filter explanation needs to go, perhaps you could just say that "filters are used to modify the phase or amplitude response of the synthesizer output".
Filter - 1) A device that removes signals with frequencies above or below a certain point called the cut-off frequency. 2) An equalizer section, used in this sense because filters are used with other components to give an equalizer its frequency response characteristics. 3) The action of removing signals of some frequencies and leaving the rest. 4) A mechanical device to smooth out speed variations in tape machines called a Scrape Flutter Filter- more usually called a Scrape Flutter Idler
The biggest thing to mention is of course that a filter attenuates certain freqiencies while leaving others. I'd say next is filter order; how steep the rolloff is. A tie-in for this is that there is no 'brick-wall' filter so there will always be some response from the stopband.
Filter type is also important. Lowpass and highpass are the basics, bandpass and bandstop are pretty powerful shaping tools. Perhaps a little bit about notch filters and their surgical accuracy.
For synth work, topology is probably an important topic. The first that comes to mind is the Moog ladder, you can barely start to talk about subtractive synthesis before hearing about Moog. Sallen-Key is also a classic common topology and is used often by Korg. The other big one is state-variable. This would be a good place to mention 'Q' and resonance. Perhaps a bit about which filters can double as oscillators.
Phase response, I'd say, should get only a passing mention. One: there's not much we can do about it and two: it isn't a big deal unless you're mixing it with dry or another filter with the same cutoff.
Envelope control could be a good topic too. A bit about how the harmonic content/frequency response of instruments evolves as the note decays. Perhaps a bit on how to imitate it.
Wow, that was longer than I thought it'd be. :what: Hope this helps.
"I'm writing a piece on programming subtractive synthesizers"
that is really just it...its called subtractive synthesis because of the filter. The filter is removing or subtracting certain frequencies.
so when you see the word "pass" its pretty much those frequencies are being allowed to pass, and the others are being removed or subtracted.
there you go subtractive synthesis
so a low pass is allowing the lows to pass and everything else above the cutoff point is being subtracted.
likewise a high pass allows highs to pass everything below the cutoff is being subtracted.
so your real basic filter types would be low pass, high pass and bandpass. pretty common with early subtractive synths like basic moogs or what not. then there are many from there
so the big thing with synthesizers is having a filter where you can sweep the cutoff point or basically change the cutoff frequency manually. usually in radio and some audio applications a filter is preset its always the same the cutoff never changes.
But the cool things for synthesis would be the basic Variable State Filter which is simple a filter where the cutoff can be changed. Usually can be done by hand with a knob or with a voltage control and in a software synth would use a continues controller.
So once you can control the cutoff point with a voltage control.
you get the other wonderful thing in synthesis.....Modulation.
Modulation is .....oh wait this is just filters right, anyhoo
Well, are you talking about in digital, or electronically at the component level? If it's the latter, read up on resonant circuits. Either capacitors, inductors, or a combination of the two (sometimes with resistors thrown in just for fun) are used to block certain frequencies, pass certain frequencies, or even allow only one certain frequency through. It's a bit complicated and the math can get heavy. It's not a fun read. But it's all there for the Googling if you feel like diving in.
Let's not forget things like all-pass filters, filters that do not alter the amplitude content of the signal, but affect the phase content of the signal.
Depending on the order of the filter, a small portion of the signal will always "rotated" so it's 180° out-of-phase with the original signal. With higher-order filters it'll cross that point multiple times. So, if you were to sum the original and all-pass-filtered signal, the amplitude would get affected at those 180°-crossings. Signals that are rotated by 180° against each other (i.e. one has a value of +1.0, the other -1.0) will cancel each other out and you will get what is known as a notch filter at the 180°-crossing frequency.