posted 23 April 2001 01:59            

blkffteq.zip

The IQ RingMod performs broadband In-phase (I) and Quadrature (Q) ring modulation to produce a one-sided spectrum that can be shifted up or down anywhere over the entire sampled frequency domain, from DC to Nyquist.

It does this by using FFT's in lieu of phase shifting filters, to produce a more true pair of signals that are in phase quadrature over the entire spectrum, instead of being restricted to some smaller frequency interval. In effect, I'm forming the Hilbert transform of the input signal using FFT's.

[For those that follow this sort of thing, I'm actually rotating the real and imaginary planes by +/- 45 degrees with respect to their original orientations, when viewed as crossed planes in 3-D. The net result is a pair of signals 90 degrees apart in phase, but neither one has any direct relationship to the original real and imaginary axes. Which one is I and which one is Q is merely a matter of preference.]

After the I and Q signals are generated by reconstruction from the inverse FFT, they are independently modulated by Cosine and Sine oscillators, respectively, and these results are combined to produce the resulting shifted spectrum.

There is a spectrum analyzer display provided to let you watch what happens. Whereas, normal product modulation (Ring Modulation) causes double sidebands to arise, this technique produces only one -- an accurate copy of the original spectrum is simply shifted up or down in frequency.

Note that the !FreqMod modulation frequency can be made either positive or negative. The input spectrum is shifted by this amount.

The second sound, IQ RingMod Filter, does double duty within the Fourier domain by first filtering the incoming signal and then converting to I and Q channels. It uses the windowed, thresholded, ramp technique, to create a smoothed frequency window on the incoming spectrum.

The example VCS shows how I can use this to produce a very narrow band (200 Hz) filter at 15.7 KHz, and ring-mod shifting to allow me to listen to the 15.7 KHz tape bias signal on old recordings by shifting it down to audible frequencies and applying heavy amplification. (Sounds like shortwave radio... but otherwise not very interesting).

- DM

posted 23 April 2001 10:18            

Kyma works only with real valued signals, and their FFT presents only the positive frequency components of the real and imaginary parts of the transforms. They implicitly force Hermitian symmetry in the frequency domain, no matter what you intend - in an effort to preserve real valued signals in the time domain.

Hence, Kyma actually ends up providing Hartley transforms instead of Fourier transforms.

I had never seen a direct application of Hartley transforms until now. In the past I always worked with complex valued signals.

Kyma never ceases being interesting!

FWIW

- DM

posted 23 April 2001 14:09            

I set up the IQ RingMod with an oscilloscope display, used a sine wave oscillator Sound generating 250 Hz, and translated it by ring mod with a modulation carrier of 5750 Hz (nice odd number WRT 48 KHz sample rate). The result is a 6 KHz sine wave that's nice and coarse with 8 samples per cycle.

By sitting here and watching the oscilloscope display (cheapo phase detector), I see the waveform very slowly changing with an effective period of around 45 sec for 1/8 cycle change. I did this for three cases: with internal clocking, external Word Clock, and external sync to digital input running at 48 KHz.

All of these methods give about the same drift rate of around 6 minutes/cycle. This is consistent with the statement in the manual about the smallest carried phase increment being equivalent to 0.0026 Hz. My numbers give about 0.0028 Hz - which is close enough, taking account of experimental error. The discrepancy amounts to a Kyma claimed drift rate of 48 sec per 1/8 cycle, versus my measured 45 sec.

Given the slowness of the change, I could easily have been off by 3 seconds in my perception of when a phase subcycle had started or completed. I would only need to be about 1.5 seconds off in my starting and ending times with the stopwatch to account for the difference in my measurements versus the SSC statement.

Since the system is software driven, not analog, I would have to defer to their statement as being the "truth".

- DM