FREQUENCY MODULATION (FM):

The modulating frequency is always sinusoidal, regardless of whether you set the carrier Wave to Sine, Ramp, Square, or Triangle.

With a sample rate of 20 kHz, if you set the center Freq to 500 Hz, FM Hz to 1, and delta-F Hz to 39.062, the sine wave will look like a big spring attached to the left side of the screen being pushed and pulled from the right side. Now set the center Freq to mid-scale or 5000 Hz, and delta-F to 2500 Hz: The waveform display becomes a blur of activity. Flip to the FFT via the F-key and you will see the spectral line slowly sweep back and forth from 3750 Hz to 6250 Hz... just what we expect.

Now hit ALT-S to flip to the Spectrogram and you can actually see the modulating sine wave as it moves the overall frequency up and down in the vertical frequency direction while time progresses in the horizontal. (You may notice that the length of one modulation cycle isn't actually one second, despite having set FM Hz to 1. This is an artifact of the signal generation method, which ignores the fact that there is finite processing time between sampling sweeps. The modulator "goes to sleep" at the end of N samples, then "wakes up" for the next N samples, without realizing that there was missing time during which processing and possible alien abductions took place. This is only noticeable at slow modulations that take longer than a sweep.)

FM TRIGGERING:

The same "stationary" effect is seen back in normal FFT spectrum mode: Where we formerly saw the spectral line sweeping back and forth, we now see a fatter peak slightly above the center frequency. Essentially, this is the same thing as when a stoboscope appears to "freeze" a rotating wheel: The wheel is still spinning, but we are only looking at it during a brief time that is exactly synchronized with the spin.

The waveform display is something else. Since it is triggering on the modulator and not the wave itself, the trace appears very unsynchronized under these conditions, but gives a sense of "flowing". Now kick up the modulation rate and the action becomes downright mesmerizing. With the same setup as above, try slowly tuning the modulator up from the original 1 Hz. You can see strange synchronicities and hypnotic patterns. Check out 6 Hz, and 17, and 76, and... well, you may need to have meals sent in to you. And don't forget that you can adjust the center frequency and delta-F as well!

Try setting the center Freq to 5013, FM Hz to 40 (one cycle per trace with N = 512 at 10 kHz), and delta-F Hz = 156.25.

After you check out from the FM Waveform Addiction 12-step Recovery Clinic with a clean bill of health, try FFT mode again, but with high modulating frequencies... a significant fraction of the center frequency. You will find a stationary spectral line at the center frequency, surrounded by symmetrical arrays of peaks. The math that is used to describe these "sidebands" is based upon Bessel functions... heavy stuff. But it turns out that this sort of modulation is very useful for the synthesis of many complex musical sounds (like brass instruments), and it put Yamaha synthesizers on the map.

Spectrogram mode can also produce some pretty addictive displays.

WARNING: Interstellar Research shall not be held liable for lost productivity, loss of employment, failing grades, or weight loss due to excessive viewing of FM displays.

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