Sunday, May 3, 2009

Weaver Modulation

...about sins of omission there is one particularly painful lack of beauty,

Namely, it isn't as though it had been a riotous red letter day or night every time you neglected to do your duty;

You didn't get a wicked forbidden thrill

Every time you let a policy lapse or forgot to pay a bill;

You didn't slap the lads in the tavern on the back and loudly cry Whee,

Let's all fail to write just one more letter before we go home, and this round of unwritten letters is on me.
(From Portrait of the Artist as a Prematurely Old Man by Ogden Nash)

The frenzied finish to inFamous has subsided and I've just finished up a week of vacation. A large part of the week was spent atoning for sins of omission: visiting the dentist, renewing my driver's license, returning clothes to stores, mopping floors, and so forth. I have been reading and thinking, too, though, and finally put fingers to keyboard in the last couple of days.

The earpiece is one of videogames' hoariest clich├ęs. Generally there's a sexy-voiced female operative on the other end dispensing instruction, exposition, and exhortation. Infamous has it; Sly Cooper has it in nerdy-turtle form. In Psi Ops we mixed things up by using telepathy (can't tell you how many times I had to listen to what's-her-name say “I'm speaking to you in your mind, via telepathy”), but generally it's assumed to be some sort of magic radio that never fails unless the story requires it. Anyone who has used a cell phone knows this is a major simplification.

One of my childhood memories is of listening to amateur radio in the HF band. Radios in this band use single-sideband amplitude modulation because of its efficient use of both power and bandwidth. As you tune across a signal with an SSB radio you get some really interesting effects on the voice. Here's an example of a sexy-voiced female spy transmitting her report as a series of spoken numbers:

(Borrowed from this site. You may need to use Firefox or Chrome to see the embedded players; I had a lot of trouble even getting them to appear in Firefox. If they don't, you can always click on the links to the MP3 files and play them yourself.)

A lot of what you hear in this recording is noise, but the reason for the odd effects on the voices is that AM radio consists fundamentally of frequency shifting. A signal in the audible range of frequencies (20-2000 Hz, say) is shifted up by a whole lot (e.g. to 2 MHz) and then broadcast using radio waves. After receiving the signal, it is shifted back down to audible range to drive a speaker. If it isn't upshifted and downshifted by the same amount all the harmonics in the signal become misaligned with respect to each other. Human voices and our understanding of them are all about harmonics (which is why linear predictive coding works so well) so they sound pretty strange when they are out of alignment.

I'm interested in simulating what this round-trip transmission/reception does to an audio signal in the presence of noise and/or mistuning. The core part is the frequency shifting. I found an article that describes beautifully how to do digital frequency shifting using Weaver modulation. Since it is nicely illustrated and I'm still learning this stuff I refer you to it.

My three-year-old daughter supplies the audio clip for today's demonstration. (I've awakened a monster; ever since, it's been a never-ending litany of “Can we sit in front of Mommy's computer and say ‘Weaver modulation’ again?” Stage Dad, here I come!) First the original, and then a series of shifts upward and downward from there.


Here are the results of shifting this audio by a variety of frequency offsets:

Shifted down 10000 Hz:

Shifted down 5000 Hz:

Shifted down 1000 Hz:

Shifted down 500 Hz:

Shifted down 100 Hz:

Shifted down 50 Hz:


Shifted up 50 Hz:

Shifted up 100 Hz:

Shifted up 500 Hz:

Shifted up 1000 Hz:

Shifted up 5000 Hz:

Shifted up 10000 Hz:

Shifted up 22050 Hz:

The recording was made using the Zoom H2 Handy Recorder, which lives up the “handy recorder” part of its name. It was a birthday gift from my wife, who researched the various options and found the one that delivers the best bang for the buck. It is also popular with music teachers in eastern Washington (my mother tells me) and my brother said he wished he'd bought one instead of whatever he did buy for field-recording classroom instruction. Highly recommended!