Waveform horror! Is a 44.1 kHz sampling rate sufficient? 

If it is really is a 19kHz tone few can hear it. The second harmonic would be 38kHz and third, 57 kHz. Nobody hears these components so the waveform is immaterial. In otherwords the audio channel plus the ear filters out the higher harmonics. Some people may claim they can hear the difference but likely they would be keying off level differences or noise and not on the actual waveform purity.

You mentioned an FFT centered around 19 kHz? A periodic waveform no matter what it's shape should have components at the fundamental frequency, 19 kHz and above, 38 kHz, etc. There should be no components centered around the fundamental. If there are, it means the waveform is being modulated by something else, it has intermodulation distortion. If this spray of modulation products gets down into the audio band, say 10kHz or lower, the signal will definitely be audible. Furthermore the spray of non-harmonic garbage will make a tone sound bad or weird.

The 44.1 kHz sampling rate is, in effect a modulating, signal on the audio input. Modulation creates sum and difference frequencies and their multiples. 44.1 was picked so that no sum or difference products or their multiples fall into the audio band. With over sampling and proper filtering these products called aliasing should not appear in the audio stream.

The strange sampling rate has to do with the early use of VCRs as a digital recorder. The PCM adapters packed three samples from the left and three samples of the right channel into a single video line and added perfect vertical and horizontal waveforms, so that it could be recorded on any standard video recorder.

Since usable data could not be recorded on the invisible field synch lines, some buffering was needed to get the audio data into visible lines only. Thus the sample rate is not three times the horizontal line frequency, but slightly below that.

Paul

The problem is that Audacity seems to use first order interpolation ("connect the dots with lines") to display some waveform, while in the real world, the values are only defined at the sample points (dots). Feeding a pulse train consisting of the actual sample values at the sample points into an analog or digital 20 kHz low pass filter will produce quite different results than the first order interpolation used by the Audacity display.

Only with the audio signal which has simple harmonic relation to the sampling frequency, you will get FFT display with all energy concentrated into a single FFT bin.

Paul

As an experiment, I just genned a 19 KHz tone with CoolEdit 96, and it draws the waveform "splined" correctly.

-- Les Cargill

But that's the most interesting part of this thread!

This shows what a difference a display algorithm makes. If you zoom in so only a few dozen sample points are displayed, Cool Edit correctly brick-wall filters the waveform at 1/2 the sampling rate, and uses the resulting values (in this case a 19kHz sine wave) to lterally "connect the dots" between the sample points. It looks like a drawing right out of a DSP text.

The 19k tone (at 44.1k sampling rate) I just generated in Cool Edit

Pick some "good" windowing for the FFT and it should be pretty close to a single bin.

And just for fun, here's someone who doesn't have a clue what he's talking about: