[sdiy] Fwd: saw vs ramp, audible?

[Ian Fritz]

-------- Forwarded Message --------
Subject: Re: [sdiy] saw vs ramp, audible?
Date: Mon, 9 Dec 2024 12:25:45 -0700
From: Ian Fritz <ijfritz at comcast.net>
To: Tom Wiltshire <tom at electricdruid.net>



On 12/9/2024 9:47 AM, Tom Wiltshire wrote:
> 
> 
>> On 8 Dec 2024, at 22:43, Donald Tillman <don at till.com> wrote:
>>
>> Note that a sawtooth ramping down has all the harmonics in phase with the fundamental.
>>
>> And a sawtooth ramping up has its harmonics alternating in phase (+1, -1/2, +1/3, -1/4,...) from the fundamental.
> 
> That's an odd way to look at it, since it produces a waveform which is half-a-cycle out of phase. In my view, it's the half-cycle-out-of-phase that leads to the harmonics being alternately flipped, not the changed slope.
> 
> If you want to flip the slope without changing the phase, you'd simply invert all the harmonics. E.g. the amounts are *all* negative, not every other one.
> 
> Tom
> _____

Choose your coordinate system so the SAW is symmetrical both 
horizontally and vertically. Then it is zero at the origin and thus 
there are only Sin functions in its Fourier series expansion, Cos 
functions being non-zero at the origin.

Now you should be able to see that inverting the SAW is the same as 
simply reversing the sign of each Sin component's argument. As you 
cannot hear the difference between Sin waves with opposite arguments, 
the two SAWs will sound the same, unless there are nonlinear process 
introduced in the audio pathway or in the ear.

So Tom is, of course, absolutely correct.

Ian



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