When I listen to the output of a delayr/delayw pair with a time-varying
deltapi, I'm hearing major distortion artifacts. Could be a problem in my
code, but I'm not seeing it. Could be a bug in deltapi. Below is the
example. If you switch the output from adel, adel to asig, asig, you'll hear
that the dry signal is free of distortion.

sr = 44100
ksmps = 8
nchnls = 2
0dbfs = 1

giSine	ftgen	0, 0, 8192, 10, 1
giCos	ftgen	0, 0, 8192, 11, 1
giSeq	ftgen	0, 0, 8, -2, 1, 1.5, 1.25, 1.125, 1, 1.375, 1.625, 1.5

instr 1

iamp = 0.5
ibasefreq = 300
kfreq		init	ibasefreq
krawfreq	init	ibasefreq

; create a simple sequence of 8 pitches:
kctr	init	-1
ktrig	metro	2
if (ktrig == 1) then
	kctr = kctr + 1
	if (kctr > 7) then
		kctr = 0
	endif
	kstepval	table	kctr, giSeq
	krawfreq	=		ibasefreq * kstepval
endif
kfreq	portk	krawfreq,	0.005

; play the pitches with an oscillator:
asig	gbuzz 	iamp, kfreq, 15, 1, 0.8, giCos

; delay the sound of the oscillator by a varying time
; interval of 0.5 to 1.5 second:
adel	init	0
adelt	oscil	0.5, 0.1, giSine
adelt	=		adelt + 1
adummy	delayr	2
adel	deltapi	adelt
		delayw	asig

		outs	adel, adel

endin




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I'm not sure I'm understanding you correctly, Justin, but I don't think that
explains it.

First, using deltap3 rather than deltapi does make a small but not, in the
end, very significant difference. Still hearing lots of ring modulation.

Second, the highest overtone is NOT hitting the Nyquist frequency, because I
can get the same result by sending a sine wave (max frequency less than
500Hz) into the delay.

Third, if I'm understanding your formula correctly, the values for (del t+1)
and (del t) would be two adjacent delay times, right? Since the delay time
is being modulated by an oscillator with a maximum amplitude swing of 1.0,
at a frequency of 0.1Hz, in a given sample period (and by the way, I've also
set ksmps = 1) the delay time is changing by 1/441000 second. That would
give a value for sr/((del t+1) - del t)) of more than 19 billion (speaking
American billion here). Not sure what the significance of that number would
be, but I'm pretty sure a sine wave has no overtones at 19,000,000,000Hz.

Can you help me understand a little better what you're suggesting? Maybe I'm
just running the formula upside down or something.



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Still not following you, Justin. If ksmps = 1, you're saying that if the
delay time increases by 2 samples in one k-period, there will be ... what? A
doubling of the output signal in frequency relative to the input?

First of all, I _want_ the output signal to be changing in frequency
relative to the input signal. That's the whole point of sweeping the delay
time with an LFO. So I have to assume you're referring to some _other_
frequency shift, because what I'm hearing is a frequency artifact (which
sounds like aliasing) over and above the expected frequency shift.

If you haven't run the .csd, please do so. You should hear what I'm
describing.

Second, with the delay time changing by a total of 1 second over the course
of a 5-second LFO sweep, in each second the delay time will change, on
average (because I'm using a sine wave as an LFO, not a triangle), by 8820
samples. But during that second, there will be 44100 sample periods
(because, for one thing, ksmps = 1). So in each sample period the delay time
will be changing by 1/5 sample (0.2 sample).

0.2 is less than 2, so I don't see how your statement applies. Am I missing
something?



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Okay, I'm getting similar artifacts while sweeping the delay time with an LFO
in Reason. Reason's control rate is certainly lower than its sampling rate,
but let's ignore that factor.

Assuming that these pitch artifacts are inherent in a change in the delay
time, I don't understand why that's the case. As a thought experiment, let's
compare a delay line to a tape deck.

The tape is whipping through the transport in such a way that 300 complete
cycles of a sine wave pass the playback head in every second. So far, so
good. We then slide the playback head gradually to the left or right.
Assuming the tape is traveling from left to right, as we move the playback
head to the left, slightly more cycles of the sine wave will pass the
playback head per second, so the pitch will rise. (Essentially, this is a
doppler effect.) When the playback head is moving to the right, fewer than
300 cycles of the sine wave will pass over it in each second.

If our digital "playback head" is using zero-order interpolation (that is,
dropping or adding samples), I can see that artifacts would be introduced
into the output signal. But deltapi is supposed to be interpolating. The
manual doesn't say how many adjacent samples are used in the interpolation,
but the manual does caution the user that for delay times that are changing
at a moderate-to-fast rate, an a-rate time-shift signal should be used.

That's exactly what I'm doing. And I'm hearing major artifacts.

One question that occurs to me is, how does the pitch-shifting process that
occurs in the delay line differ from the pitch-shifting process that occurs
within an oscili? Granted, by the time a 300Hz sine wave hits the delay
line, each cycle is only 147 samples long, so dropping a few samples in each
cycle would distort the waveform ... but the interpolation process within
deltapi should smooth out the distortion, shouldn't it?



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One more point: The sound of deltapi is, to my ears, exactly the same as the
sound of deltap (see .csd below). This strongly suggests that in 6.01,
deltapi is not performing any interpolation.

Whether or not artifacts are inevitable in a digital delay that uses a
constant clock rate, I think there may be a problem with the code for
deltapi. That's my guess, anyhow.



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Oops -- forgot the test code. Here 'tis:

sr = 96000
ksmps = 1
nchnls = 2
0dbfs = 1

giSine	ftgen	0, 0, 8192, 10, 1
giCos	ftgen	0, 0, 8192, 11, 1

instr 1

iamp = 0.5
ifreq = 300
asig	oscil	iamp, ifreq, giSine

; delay the sound of the oscillator by a varying time
; interval:
adel	init	0
kdelt	oscil	0.5, 0.1, giSine
kdelt	=		kdelt + 1
adummy	delayr	3
adel	deltapi	kdelt
		delayw	asig

		outs	adel, adel

endin




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