# [PD] Creating a basic oscillator from first principles?

Sun Feb 8 18:29:46 CET 2009

```Thanks for the example patch
I am almost getting perhaps close to understanding  :)
However have a few queries about what is happening.

I have been trying to work out the wrapping a vline patch first as
this seems the most straightforward, as this is all really new to me.

So first off

[r x] object receives a bang from the x subpatch every 200 milliseconds.

This bang then outputs the message [0, 1 10] every 200 millisecond
The message [0,1 10] means go from 0 to 1 in 10 milliseconds

this message then goes into the vline object which creates the ramp
(sawtooth)

i.e. the y=mx equation that you mentioned where the 10 milliseconds
could be the gradient of the sawtooth waveform or the gradient could
be later on.

The output of the vline object is then multiplied by 3 which in
effect multiplies the steepness of the slope by 3
This multiplication could be the m in the equation y=mx and seems
like a more logical place than in the ramp.

This is then wrapped to keep the output cycling to 1.
So in effect we get 3 sawtooth waveforms for each bang sent by x
which occurs every 200milliseconds.

and now I have an oscillator :)

Just a few things I need to clarify
> The frequency of the phasor is determined by the slope of the line,
> by the phase
> increment k.

If y=mx +k and wrapping this produces an oscillator, I understand
that adding k can be the phase increment i.e. what point the waveform
will start from,

Does this mean that in this example the [*~ 3] object represents m
and therefore the frequency of the oscillator and you would add a
[+~ ] to control the phase increment?

> 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.

Am I understanding you correctly in thinking that the integrator and
wrap and combined so that rather than leave the integrator to keep
counting higher and higher (unitl the processor can't cope) the wrap
function is somehow combined with it so that the integrator keeps
reseting itself so that the number it counts up to never gets that big?

Once again thankyou for this example, I don't know if you are a
lecturer and this is an example you use. Its really helped me
visualize things.
cheers
Geoff

On 7 Feb 2009, at 19:07, Andy Farnell wrote:

>
>
> 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.
>
>
> ------snip------------------
>
>
>
> On Sat, 7 Feb 2009 17:31:48 +0000
> Geoff <geoffspuredata at 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;
>
>
> --
> Use the source<oscil-
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