Re: [PD] Creating a basic oscillator from first principles?

Here's some notes and an example patch on exactly this subject hope it helps.

a.

----------------snip-------------------------- The first principles of generative DSP can be broken into three concepts which follow easily from one another.

The first and most fundamental is that of the accumulator. This just means something like

x = x + 1

Or more correctly x[t_n] = x[t_n-1] + k

It just makes a line. The line increases without bound. From high school maths you will know the line equation y = mx + c, the slope m determines how fast the line rises from an origin c on the y axis for a given interval on the x axis. In DSP we make the x axis be time, t, and the discrete time values n and n-1 represent contiguous samples along the time line.

In a simple sense of programming the accumulator/incrementor/integrator can be considered an endless loop, a do-while(1) or for(;;;) loop, in which a variable is incremented by a small amount on each step. In a more advanced interpretation the accumulator/incrementor can be thought of as a filter, an IIR filter in which the current output depends on the last output plus input k, so it integrates k over time. Thus by changing k we can change the slope (slew or phase increment) of the line.

Shown in part one of the example patch is a couple of ways of doing this. The first uses [vline~] to make a line that will rise steadily over a long period of time. The second is more arcane, it uses a [biquad~] object as an integrator.

This isn't much use until we combine it with the second fundamental concept, the idea of wrapping. Wrapping creates a discontinuous periodic function by making any input value x greater than N become 0 < x < N, wrapping the output back into the range between zero and N. If x is a float then it's the fractional part of x, or x - floor(x), like the modulo operator is to integers. In Pure Data it is defined for the range 0 to 1.0. What we get by combining an accumulator with a wrap is called a phasor, a line that cycles up from 0.0 to 1.0 over and over. The frequency of the phasor is determined by the slope of the line, by the phase increment k.

In practice, in code, we combine the integrator and wrap into a single unit so that the line does not increase without bound. If it does then the oscillator will work for a while, but then the line will exceed the representation range of the CPU.

A wrapped line is shown in the second part of the patch along with an example of how it is like the built-in [phasor~] object.

The final part of the picture is a new periodic function that sets the waveform of our oscillator. It is defined over the domain 0.0 to 1.0 so the phasor drives the input nicely, but it normally has a bipolar range defined between -1.0 and 1.0 to give a symmetrical waveform without a DC component. This can be in the form of a lookup table, for which the domain is mapped to the table size, or a trigonometric function like cos(x) for which the domain is mapped to 2 time PI. In other words the periodic function takes a phasor that cycles up to 1.0 and maps it onto a waveform that cycles backwards and forwards around zero.

In the last part of the example patch we see a wrapped line and periodic function behave as an oscillator alongside the built-in [osc~] object which does more or less the same thing.

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On Sat, 7 Feb 2009 17:31:48 +0000 Geoff geoffspuredata@googlemail.com wrote:

Hi I am very new to PD and DSP concepts. So this will be hopelessly, awfully, basic :)

I have just started chapter 3 of 'The theory and technique of
electronic music' which is excellent

However it raises a million questions in my head...... one of which
is how do I create an oscillator myself?

Its really bugging me everytime I create an example from the book. I
feel I need to understand the fundamentals of how the basic objects
are created too.

It seems too easy for me to just use the phasor object provided,

So I thought I would struggle through it and try to work it out.

This is how I am thinking about it. If I want to create a sawtooth oscillator then this is just a ramp
function i.e. a number that increases by 1 each time. therefore if I use a simple float that, that adds 1 each time and a
modulus % object to cap it, then I will have my repeating ramp wave :)

However I am triggering it by the metro object which is way too slow,
how can I send a bang to the float object say every sample? or alot
quicker than one millisecond?

My thinking is if I could speed up the bangs to a sample level I
would then have more scope to then actually tune it, and create the
shape I want. However I am sure to do this well would require working
at a higher sample rate, but I am not really sure how to proceed.

Below is my appalling attempt :) I use the number box to change pitch.

Any guidance appreciated Cheers Geoff

#N canvas 325 62 681 388 10; #X obj 119 69 bng 15 250 50 0 empty empty empty 17 7 0 10 -262144 -1 -1; #X obj 121 96 f; #X obj 181 116 + 1; #X obj 115 17 bng 15 250 50 0 empty empty empty 17 7 0 10 -262144 -1 -1; #X obj 127 238 dac~; #X obj 118 46 metro 1; #X floatatom 187 163 5 0 0 0 - - -; #X obj 115 160 %; #X obj 114 199 /; #X connect 0 0 1 0; #X connect 1 0 2 0; #X connect 1 0 7 0; #X connect 2 0 1 1; #X connect 3 0 5 0; #X connect 5 0 0 0; #X connect 6 0 7 1; #X connect 6 0 8 1; #X connect 7 0 8 0; #X connect 8 0 4 0;