I want to create a k-rate signal that is roughly sinusoidal, but
asymmetrical, so that it is below zero for some multiple of the time
it is above zero. For example, where t is some arbitrary time unit:

t=0 value=0
t=1 value=1
t=2 value=0
t=4 value=-1
t=6 value=0

In this case it is above zero for 2 time units and below zero for 4,
making the below-zero duration exactly twice the above-zero duration.
I'd like for this curve to be as smooth as possible.

If I understood more about Fourier analysis, I could maybe come up
with the appropriate harmonics to use GEN10. (Assuming that it could
be accomplished using a reasonable number of harmonics.)

Another possibility would be for me to generate the values myself -- I
think I can get a good one using a weighted average of sinusoids of
different periods -- in some programming language of my choice,. then
load these values into a csound table, uh, somehow that I'm not really
clear about.

I'm sure there are probably other ways too, that I'm not thinking about.

I would be most grateful for any assistance in this matter.

Hi Forrest,

One possibility might be to use two ftables, one with a sine wave, the
other with two linear segments.  The second table could be read with
an oscili or oscil3 and the value used with one of the table opcodes
to index into the sine wave table. Maybe using:

f1 0 10 65536 1
f2 0 -7 65536 0 21845 .5 43691 1

as tables, then something like:

kndx oscili 1, 6, 2
ksig tablei kndx, 1

Haven't tested the above code, but imagine something along these lines
would work.

Hope that helps!
steven

On Fri, Jul 27, 2012 at 8:56 PM, Forrest Cahoon
 wrote:
> I want to create a k-rate signal that is roughly sinusoidal, but
> asymmetrical, so that it is below zero for some multiple of the time
> it is above zero. For example, where t is some arbitrary time unit:
>
> t=0 value=0
> t=1 value=1
> t=2 value=0
> t=4 value=-1
> t=6 value=0
>
> In this case it is above zero for 2 time units and below zero for 4,
> making the below-zero duration exactly twice the above-zero duration.
> I'd like for this curve to be as smooth as possible.
>
> If I understood more about Fourier analysis, I could maybe come up
> with the appropriate harmonics to use GEN10. (Assuming that it could
> be accomplished using a reasonable number of harmonics.)
>
> Another possibility would be for me to generate the values myself -- I
> think I can get a good one using a weighted average of sinusoids of
> different periods -- in some programming language of my choice,. then
> load these values into a csound table, uh, somehow that I'm not really
> clear about.
>
> I'm sure there are probably other ways too, that I'm not thinking about.
>
> I would be most grateful for any assistance in this matter.
>
>
> Send bugs reports to the Sourceforge bug tracker
>             https://sourceforge.net/tracker/?group_id=81968&atid=564599
> Discussions of bugs and features can be posted here
> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
>

I am not sure what the math would be, but a frequency modulated sine
wave, where the modulator and modulated frequencies are the same,
would do this. The trick would be finding the right index of
modulation so you always get one full cycle and get the ratios you
want. To have the smoothest possible curve as you asked, the
modulating and modulated waveforms should both be a sine wave, so
foscili would work perfectly here.

Or maybe the carrier should be desired frequency - (index/2)?

On Fri, Jul 27, 2012 at 5:56 PM, Forrest Cahoon
 wrote:
> I want to create a k-rate signal that is roughly sinusoidal, but
> asymmetrical, so that it is below zero for some multiple of the time
> it is above zero. For example, where t is some arbitrary time unit:
>
> t=0 value=0
> t=1 value=1
> t=2 value=0
> t=4 value=-1
> t=6 value=0
>
> In this case it is above zero for 2 time units and below zero for 4,
> making the below-zero duration exactly twice the above-zero duration.
> I'd like for this curve to be as smooth as possible.
>
> If I understood more about Fourier analysis, I could maybe come up
> with the appropriate harmonics to use GEN10. (Assuming that it could
> be accomplished using a reasonable number of harmonics.)
>
> Another possibility would be for me to generate the values myself -- I
> think I can get a good one using a weighted average of sinusoids of
> different periods -- in some programming language of my choice,. then
> load these values into a csound table, uh, somehow that I'm not really
> clear about.
>
> I'm sure there are probably other ways too, that I'm not thinking about.
>
> I would be most grateful for any assistance in this matter.
>
>
> Send bugs reports to the Sourceforge bug tracker
>             https://sourceforge.net/tracker/?group_id=81968&atid=564599
> Discussions of bugs and features can be posted here
> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
>

Unless I am mistaken, the option you are suggesting Steven is
effectively phase modulation?

On Fri, Jul 27, 2012 at 6:11 PM, Steven Yi  wrote:
> Hi Forrest,
>
> One possibility might be to use two ftables, one with a sine wave, the
> other with two linear segments.  The second table could be read with
> an oscili or oscil3 and the value used with one of the table opcodes
> to index into the sine wave table. Maybe using:
>
> f1 0 10 65536 1
> f2 0 -7 65536 0 21845 .5 43691 1
>
> as tables, then something like:
>
> kndx oscili 1, 6, 2
> ksig tablei kndx, 1
>
> Haven't tested the above code, but imagine something along these lines
> would work.
>
> Hope that helps!
> steven
>
> On Fri, Jul 27, 2012 at 8:56 PM, Forrest Cahoon
>  wrote:
>> I want to create a k-rate signal that is roughly sinusoidal, but
>> asymmetrical, so that it is below zero for some multiple of the time
>> it is above zero. For example, where t is some arbitrary time unit:
>>
>> t=0 value=0
>> t=1 value=1
>> t=2 value=0
>> t=4 value=-1
>> t=6 value=0
>>
>> In this case it is above zero for 2 time units and below zero for 4,
>> making the below-zero duration exactly twice the above-zero duration.
>> I'd like for this curve to be as smooth as possible.
>>
>> If I understood more about Fourier analysis, I could maybe come up
>> with the appropriate harmonics to use GEN10. (Assuming that it could
>> be accomplished using a reasonable number of harmonics.)
>>
>> Another possibility would be for me to generate the values myself -- I
>> think I can get a good one using a weighted average of sinusoids of
>> different periods -- in some programming language of my choice,. then
>> load these values into a csound table, uh, somehow that I'm not really
>> clear about.
>>
>> I'm sure there are probably other ways too, that I'm not thinking about.
>>
>> I would be most grateful for any assistance in this matter.
>>
>>
>> Send bugs reports to the Sourceforge bug tracker
>>             https://sourceforge.net/tracker/?group_id=81968&atid=564599
>> Discussions of bugs and features can be posted here
>> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
>>
>
>
> Send bugs reports to the Sourceforge bug tracker
>             https://sourceforge.net/tracker/?group_id=81968&atid=564599
> Discussions of bugs and features can be posted here
> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
>

Look up pdhalf and pdhalfy. By using one of these, a table with a sine wave,
and a phasor, you should be able to get exactly what you're looking for.

--JA



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Am Fri, 27 Jul 2012 19:56:50 -0500
schrieb Forrest Cahoon :

> I want to create a k-rate signal that is roughly sinusoidal, but
> asymmetrical, so that it is below zero for some multiple of the time
> it is above zero. 

Maybe the pdhalf/pdhalfy opcodes do what you want?

Hi Justin,

Yes, it's pretty much phase distortion.  I'd also join the chorus to
mention pdhalf (great opcode!).

steven

On Fri, Jul 27, 2012 at 9:14 PM, Justin Smith  wrote:
> Unless I am mistaken, the option you are suggesting Steven is
> effectively phase modulation?
>
> On Fri, Jul 27, 2012 at 6:11 PM, Steven Yi  wrote:
>> Hi Forrest,
>>
>> One possibility might be to use two ftables, one with a sine wave, the
>> other with two linear segments.  The second table could be read with
>> an oscili or oscil3 and the value used with one of the table opcodes
>> to index into the sine wave table. Maybe using:
>>
>> f1 0 10 65536 1
>> f2 0 -7 65536 0 21845 .5 43691 1
>>
>> as tables, then something like:
>>
>> kndx oscili 1, 6, 2
>> ksig tablei kndx, 1
>>
>> Haven't tested the above code, but imagine something along these lines
>> would work.
>>
>> Hope that helps!
>> steven
>>
>> On Fri, Jul 27, 2012 at 8:56 PM, Forrest Cahoon
>>  wrote:
>>> I want to create a k-rate signal that is roughly sinusoidal, but
>>> asymmetrical, so that it is below zero for some multiple of the time
>>> it is above zero. For example, where t is some arbitrary time unit:
>>>
>>> t=0 value=0
>>> t=1 value=1
>>> t=2 value=0
>>> t=4 value=-1
>>> t=6 value=0
>>>
>>> In this case it is above zero for 2 time units and below zero for 4,
>>> making the below-zero duration exactly twice the above-zero duration.
>>> I'd like for this curve to be as smooth as possible.
>>>
>>> If I understood more about Fourier analysis, I could maybe come up
>>> with the appropriate harmonics to use GEN10. (Assuming that it could
>>> be accomplished using a reasonable number of harmonics.)
>>>
>>> Another possibility would be for me to generate the values myself -- I
>>> think I can get a good one using a weighted average of sinusoids of
>>> different periods -- in some programming language of my choice,. then
>>> load these values into a csound table, uh, somehow that I'm not really
>>> clear about.
>>>
>>> I'm sure there are probably other ways too, that I'm not thinking about.
>>>
>>> I would be most grateful for any assistance in this matter.
>>>
>>>
>>> Send bugs reports to the Sourceforge bug tracker
>>>             https://sourceforge.net/tracker/?group_id=81968&atid=564599
>>> Discussions of bugs and features can be posted here
>>> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
>>>
>>
>>
>> Send bugs reports to the Sourceforge bug tracker
>>             https://sourceforge.net/tracker/?group_id=81968&atid=564599
>> Discussions of bugs and features can be posted here
>> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
>>
>
>
> Send bugs reports to the Sourceforge bug tracker
>             https://sourceforge.net/tracker/?group_id=81968&atid=564599
> Discussions of bugs and features can be posted here
> To unsubscribe, send email sympa@lists.bath.ac.uk with body "unsubscribe csound"
>