# [sdiy] PM vs FM was: Re: Buchla 295 10-band comb filter topology

Donald Tillman don at till.com
Fri Dec 2 08:29:04 CET 2022

```> On Nov 29, 2022, at 5:29 PM, Ian Fritz <ijfritz at comcast.net> wrote:
>
> Thanks for the discussion! (Inline)
>
>> On Nov 29, 2022, at 10:12 AM, Donald Tillman <don at till.com> wrote:
>>
>> ﻿Phase Modulation is:
>> out = sin(kwt + f(w_m t))
>>
>> Frequency Modulation would be:
>> out = sin((kw + f(w_m t)) t)
>
> Ooopsy. You have to integrate the oscillating part, not just multiply it by t.
> Int(cos wt) = (1/w)sin wt.
> (Oh and how many times have I done the same thing!)
> It’s the (1/w_m factor that makes the FM waveshape (ideally) invariant over pitch.

Did I screw up there?

Lessee, f(w_m t) is intended to be the modulator output, an enveloped sin() at frequency w_m.   Which would be:

Mod = env_m(sin(w_m t))

In the PM case I added it to the phase.  In the FM case, I added it to the carrier frequency.

Perhaps I should have written it:

PM = sin(kwt + env_m(sin(w_m t))
FM = sin((kw + env_m(sin(w_m t)))t)

Isn't that right?

---

The confusion started with the first equation in Chowning's article:

I can't help but think that the guy really, really likes calling it frequency modulation.

-- Don
--
Donald Tillman, Palo Alto, California
https://www.till.com

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