The AM / FM category is a bit strange for effects - true, you can get some interesting effects by modulating the amplitude of an input signal ; but what does "frequency modulation" mean for a complex input signal for which you don't even have an accurate frequency representation? You could very well say that every effect is an amplitude modulation, by the $\frac{out(t)}{in(t)}$ signal, but this is not going to help you implement it!

There is no magic single-purpose engine at the heart of all the audio effects provided by music production software. But if you look at the source code of a large suite of audio effects from a DSP developer, here are some "building" blocks that will have been factored out in their own classes and which are shared by many different effects. I don't imply that this forms a good basis to categorize effect ; but from an implementation point of view, those blocks are essential:

• Biquad filters.
• Fractional delay lines.
• Convolution engine, for fast convolution of an input signal with arbitrary-sized impulse responses.
• Waveshaper (application of a non-linear function to the input signal in the time-domaine).
• Synthesizer building blocks: oscillators, LFOs, ADSR envelopes.
• Signal detectors: envelope follower, f0 extractor.

With those blocks you could build:

• Synth-like filters or wah-wah: one or two biquads
• Auto-wah: envelope follower + envelope + biquad
• Flanger / Phaser: LFO + delay line
• Chorus: LFO + delay lines
• Algorithmic reverb: delay lines (array of parallel and serial comb filters)
• Convolution reverb: convolution
• Spatializer: convolution (with HRTFs impulse responses)
• Guitar amp simulation: convolution, waveshappers
• Distortion, Fuzz: gain + waveshapper
• Bitcrusher (quantizer): a particular case of waveshapper
• Ring modulator with a sine carrier: oscillator
• Noise Gate and other dynamics effects: envelope follower
• Tape simulation: convolution, waveshapper, envelope follower (for the dynamics processing)
• EQ: biquads
• Tremolo: LFO
• Leslie emulation: convolution + LFO
• Vocoder: biquads + envelope follower

While some of these effects are just a matter of patching the different blocks (a flanger truly is a LFO modulating a delay line), some other effects need more complex glue between the parts, that is specific enough not to be factored into a building block of its own.

This is, overall, an interesting set of effects that will cover a lot of ground for music production, but it's not exhaustive and there are indeed some effects which do not fit this framework... Some examples:

• Dirty sample rate reducer (in a bitcrusher): true, it's a multiplication by a dirac comb and then a convolution by a rectangular window... but it's easier to write it as something that duplicate the value of one sample over the N following samples instead of patching an amplitude modulation and a convolution!
• Pitch alteration effects (pitch-shifting, auto-tune) do not fit this framework well. They need a more complex representation of the audio signal to be performed (phase vocoder for frequency-domain methods ; pitch detection and pitch marks for time-domain methods).

I suggest you to play with "modular style" software tools like Pd, Reaktor, Plogue, SyntheEdit... - and try implement effects from the basic building blocks they provide you.

The AM / FM category is a bit strange for effects - true, you can get some interesting effects by modulating the amplitude of an input signal ; but what does "frequency modulation" mean for a complex input signal for which you don't even have an accurate frequency representation? You could very well say that every effect is an amplitude modulation, by the $\frac{out(t)}{in(t)}$ signal, but this is not going to help you implement it!

There is no magic single-purpose engine at the heart of all the audio effects provided by music production software. But if you look at the source code of a large suite of audio effects from a DSP developer, here are some "building blocks" that will have been factored out in their own classes and which are shared by many different effects. I don't imply that this forms a good basis to categorize effects ; but from an implementation point of view, those blocks are essential:

• Biquad filters.
• Fractional delay lines.
• Convolution engine, for fast convolution of an input signal with arbitrary-sized impulse responses.
• Waveshaper (application of a non-linear function to the input signal in the time-domaine).
• Synthesizer building blocks: oscillators, LFOs, ADSR envelopes.
• Signal detectors: envelope follower, f0 extractor.

With those blocks you could build:

• Synth-like filters or wah-wah: one or two biquads
• Auto-wah: envelope follower + envelope + biquad
• Flanger / Phaser: LFO + delay line
• Chorus: LFO + delay lines
• Algorithmic reverb: delay lines (array of parallel and serial comb filters)
• Convolution reverb: convolution
• Spatializer: convolution (with HRTFs impulse responses)
• Guitar amp simulation: convolution, waveshappers
• Distortion, Fuzz: gain + waveshapper
• Bitcrusher (quantizer): a particular case of waveshapper
• Ring modulator with a sine carrier: oscillator
• Noise Gate and other dynamics effects: envelope follower
• Tape simulation: convolution, waveshapper, envelope follower (for the dynamics processing)
• EQ: biquads
• Tremolo: LFO
• Leslie emulation: convolution + LFO
• Vocoder: biquads + envelope follower

While some of these effects are just a matter of patching the different blocks (a flanger truly is a LFO modulating a delay line), some other effects need more complex glue between the parts, that is specific enough not to be factored into a building block of its own.

This is, overall, an interesting set of effects that will cover a lot of ground for music production, but it's not exhaustive and there are indeed some effects which do not fit this framework... Some examples:

• Dirty sample rate reducer (in a bitcrusher): true, it's a multiplication by a dirac comb and then a convolution by a rectangular window... but it's easier to write it as something that duplicate the value of one sample over the N following samples instead of patching an amplitude modulation and a convolution!
• Pitch alteration effects (pitch-shifting, auto-tune) do not fit this framework well. They need a more complex representation of the audio signal to be performed (phase vocoder for frequency-domain methods ; pitch detection and pitch marks for time-domain methods).

I suggest you to play with "modular style" software tools like Pd, Reaktor, Plogue, SyntheEdit... - and try implement effects from the basic building blocks they provide you.

Are you talking about synthesis (creating sounds from scratch) or effects (taking a sound as an input and producing a new sound)?

The AM / FM category is a bit strange for effects - you can get some interesting effects by modulating the amplitude of an input signal ; but what does "frequency modulation" mean for a complex input signal for which you don't even have an accurate frequency representation? You could very well say that every effect is an amplitude modulation, by the $\frac{out(t)}{in(t)}$ signal!

To me, here is a list of important "building blocks" for audio effects. This doesn't intend to be a classification, but more the answer to the following question: "if you look at the source code of a large suite of audio effects from a DSP developer, which building blocks will they have factored out?":

• Biquad filters.
• Fractional delay lines.
• Convolution engine, for fast convolution with arbitrary-sized impulse response.
• Waveshapper (application of a non-linear function to the input signal in the time-domaine).
• Synthesizer building blocks: oscillators, LFOs, ADSR envelopes.
• Signal detectors: envelope follower, f0 extractor.

• Synth-like filters or wah-wah: one or two biquads
• Auto-wah: envelope follower + envelope + biquad
• Flanger / Phaser: LFO + delay line
• Chorus: LFO + delay lines
• Algorithmic reverb: delay lines (array of parallel and serial comb filters)
• Convolution reverb: convolution
• Spatializer: convolution (with HRTFs impulse responses)
• Guitar amp simulation: convolution, waveshappers
• Distortion: gain + waveshapper
• Bitcrusher (quantizer): a particular case of waveshapper
• Ring modulator with a sine carrier: oscillator
• Noise Gate and other dynamics effects: envelope follower
• Tape simulation: convolution, waveshapper, envelope follower (for the dynamics processing)
• EQ: biquads
• Tremolo: LFO
• Leslie emulation: convolution + LFO
• Vocoder: biquads + envelope follower

While some of these effects are just a matter of patching the different blocks (a flanger truely is a LFO modulating a delay line), some other effects need more complex glue between the parts, that is specific enough not to be factored into a building block of its own.

This is, overall, an interesting set of effects that will cover a lot of ground for music production, but it's not exhaustive and there are indeed some effects which do not fit well this framework... Some examples:

• Dirty sample rate reducer (in a bitcrusher): true, it's a multiplication by a dirac comb and then a convolution by a rectangular window, but it's easier to write it as something that duplicate the value of one sample over the N following samples.
• Pitch alteration effects (pitch-shifting, auto-tune) do not fit this framework well. They need a more complex representation of the audio signal to be performed (phase vocoder for frequency-domain methods ; pitch detection and pitch marks for time-domain methods).

I suggest you to play with "modular style" software tools like Pd, Reaktor, Plogue, SyntheEdit... - and try implement effects from the basic building blocks they offer you.

The AM / FM category is a bit strange for effects - true, you can get some interesting effects by modulating the amplitude of an input signal ; but what does "frequency modulation" mean for a complex input signal for which you don't even have an accurate frequency representation? You could very well say that every effect is an amplitude modulation, by the $\frac{out(t)}{in(t)}$ signal, but this is not going to help you implement it!

There is no magic single-purpose engine at the heart of all the audio effects provided by music production software. But if you look at the source code of a large suite of audio effects from a DSP developer, here are some "building" blocks that will have been factored out in their own classes and which are shared by many different effects. I don't imply that this forms a good basis to categorize effect ; but from an implementation point of view, those blocks are essential:

• Biquad filters.
• Fractional delay lines.
• Convolution engine, for fast convolution of an input signal with arbitrary-sized impulse responses.
• Waveshaper (application of a non-linear function to the input signal in the time-domaine).
• Synthesizer building blocks: oscillators, LFOs, ADSR envelopes.
• Signal detectors: envelope follower, f0 extractor.

• Synth-like filters or wah-wah: one or two biquads
• Auto-wah: envelope follower + envelope + biquad
• Flanger / Phaser: LFO + delay line
• Chorus: LFO + delay lines
• Algorithmic reverb: delay lines (array of parallel and serial comb filters)
• Convolution reverb: convolution
• Spatializer: convolution (with HRTFs impulse responses)
• Guitar amp simulation: convolution, waveshappers
• Distortion, Fuzz: gain + waveshapper
• Bitcrusher (quantizer): a particular case of waveshapper
• Ring modulator with a sine carrier: oscillator
• Noise Gate and other dynamics effects: envelope follower
• Tape simulation: convolution, waveshapper, envelope follower (for the dynamics processing)
• EQ: biquads
• Tremolo: LFO
• Leslie emulation: convolution + LFO
• Vocoder: biquads + envelope follower

While some of these effects are just a matter of patching the different blocks (a flanger truly is a LFO modulating a delay line), some other effects need more complex glue between the parts, that is specific enough not to be factored into a building block of its own.

This is, overall, an interesting set of effects that will cover a lot of ground for music production, but it's not exhaustive and there are indeed some effects which do not fit this framework... Some examples:

• Dirty sample rate reducer (in a bitcrusher): true, it's a multiplication by a dirac comb and then a convolution by a rectangular window... but it's easier to write it as something that duplicate the value of one sample over the N following samples instead of patching an amplitude modulation and a convolution!
• Pitch alteration effects (pitch-shifting, auto-tune) do not fit this framework well. They need a more complex representation of the audio signal to be performed (phase vocoder for frequency-domain methods ; pitch detection and pitch marks for time-domain methods).

I suggest you to play with "modular style" software tools like Pd, Reaktor, Plogue, SyntheEdit... - and try implement effects from the basic building blocks they provide you.