On 13/08/2015, robert bristow-johnson <r...@audioimagination.com> wrote:
>> Are you *sure* truncating adds extra quantization noise? > > ---->[sigma-delta modulator]---->[decimation filter]---->[quantizer]---> > > adds extra quantization noise to: > > ---->[sigma-delta modulator]---->[decimation filter]----> Okay, this is the VERY LAST time I'll show this demonstration. If you want to understand this, then pay attention VERY closely: Here is a fading out 440 Hz sine wave at 16 bits precision: http://morpheus.spectralhead.com/wav/sine_fadeout16.wav Here is its spectrogram - a single sinusoid at 440 Hz: http://morpheus.spectralhead.com/img/sine_fadeout16_spectrogram.png If you simply truncate it to 8 bits, here is what you get: http://morpheus.spectralhead.com/wav/sine_fadeout8.wav As expected, the spectrogram shows harmonic distortion: http://morpheus.spectralhead.com/img/sine_fadeout8_spectrogram.png This is because the sinewave gets distorted, and starts looking like a square wave, having harmonic spectral artifact, as expected. ...HOWEVER.... *IF* the signal is already noisy, say, from the thermal noise of the converter, *THEN* this will NOT happen!!! To demonstrate this, here is a -36 dB white noise floor: http://morpheus.spectralhead.com/wav/noise_36db.wav If we mix this with the original sine wave, we got this: http://morpheus.spectralhead.com/wav/sine_fadeout16_noise.wav It is a fading out 440 Hz sine wave, buried in a -36 dB white noise floor. If we quantize this to 8 bit, this is what we get: http://morpheus.spectralhead.com/wav/sine_fadeout8_noise.wav Do you hear harmonic distortion in this signal? ABSOLUTELY NOT!!! To prove, here is the spectrogram of this 8-bit noisy signal: http://morpheus.spectralhead.com/img/sine_fadeout8_noise_spectro.png Do you see harmonic distortion on the spectrogram? ABSOLUTELY NOT!!! A/B spectrogram comparison between quantization with no noise floor, and quantization with -36 dB white noise floor: http://morpheus.spectralhead.com/img/sine_fadeout_8_vs_16.png The original, non-noisy sinusoid, quantized to 8 bit, then converted back to 16 bit, subtracted from the original signal, normalized to -16 dB (= the harmonic noise from the quantization, amplified, without the original signal): http://morpheus.spectralhead.com/wav/sine_fadeout_quant_noise.wav The noisy sinusoid, quantized to 8 bit, then converted back to 16 bit, subtracted from the original signal, normalized to -16 dB (= the error from the quantization, amplified, without the original signal): http://morpheus.spectralhead.com/wav/sine_fadeout_noise_quant.wav Conclusion: when there is a loud enough noise floor present in the signal, then there's no harmonic distortion from the quantization!!! Nope, nil, nada, zilch, zero, null!! The white noise floor eliminated it completely!!!!! That's the whole purpose of dithering... The error in the case of a quantized noisy sinusoid is almost like white noise. It would be good if - after multiple demonstrations, and giving you 30 external references - you could finally understand that noise from either dithering or a thermal noise floor eliminates harmonic distortion from the quantization step. Bonus experiment: try to see if you can hear the difference between sine_fadeout16_noise.wav and sine_fadeout8_noise.wav in a blind ABX test. If not, then having extra bits of noise make zero sense. -P _______________________________________________ music-dsp mailing list music-dsp@music.columbia.edu https://lists.columbia.edu/mailman/listinfo/music-dsp
