Digital Audio Principles and Techniques

Digital Audio Principles and Techniques

This page is just a place to keep some notes about various concepts that appear to be important in the sonic quality of digital audio processing. It's been triggered by the excellent presentation by Rob Watts, Chord Electronics' digital audio consultant responsible for Hugo, Mojo and Dave. He uses lots of terms which I didn't really understand, and it's in the interest of grasping the DAC process that I started this investigation.

Noise Shaping

One of the effects of quantisation is noise i.e. the difference between "reality" and the numeric representation of that reality manifests itself as random noise. Example: Assume allowable values in digital system are 0-9; sample at time t has value 5.4, which is quantised to 5. The difference (0.4) will manifest itself as noise, and clearly varies randomly (or is it random??) across samples.

Reducing bit depth i.e. the number of bits being used to represent a signal [not yet sure why you'd want to do this - seen it referred to as part of DAC construction/design] results in quantisation noise also, however, by using a feedback loop such that the noise value for the preceding re-quantised sample is used to alter the quantisation of the current sample. The way in which the feedback is applied can be used to "shape" the energy spectrum of the noise, such that although the total energy is the same, the visible/audible/perceptible effect is reduced because the energy is lower in the more sensitive areas. Phew. Cool though.

See this Wikipedia entry for more specifics.

Dither

Actually, quantisation error is not random... It generates harmonics i.e. non-random distortion. Adding random noise of some spectrum to the signal prior to sampling makes the noise more random, and reduces the maximum level of the distortion/noise, although again I suspect the overall energy is constant.

1 Bit Conversion (!)

It's easy to understand multi-bit e.g. 16 bit ADC. Conceptually, the analogue signal is a continuously fluctuating voltage. The voltage is measured at the "sample rate" e.g. for Red Book CD 44.1k times/sec, and the resulting measurement is "quantised" to the current bit depth i.e. to fit in the number of possible values. So for 16 bit audio, the value can vary between 0 and 65535 i.e. 0 to 2^16-1. So how would a 1 bit ADC work?! I've always struggled with that...

Apparently, by using a colossal sampling rate e.g. 2.4MHz in the case of DSD, and 1bit (with a dynamic range of 6 dB!), then doing (serious!) noise shaping to push the noise out of the 20-20kHz region into the ultrasonic, you can get > 100dB SNR/dynamic range. However, it is hard (impossible?!) to add reasonable amounts of dither in the feedback loop in the pure 1 bit case, so most realistic systems use more bits to enable better and more effective dither. Sounds like DSD is crap to me... Fundamentally flawed. Especially as it gets turned into PCM anyway...

Decimation

The process of reducing the bit depth or sampling frequency, for whatever reason. Interestingly, this requires two steps

• Reduce high-frequency information so that fmax is < new sample rate; this is to prevent aliasing in the resulting digital output; this can be done with a digital filter, using IIR or FIR techniques
• Resample the data i.e. chuck away all the unwanted bits/samples

Obviously this reduces the effective bandwidth and dynamic range, but you'd expect that. Rob Watts describes using downsampling as part of the DAC process, not sure why yet, maybe it's to simplify the conversion i.e. by requiring fewer steps.

[Infinite|Finite] Impulse Response Filtering

Digitally represented signals can be filtered for frequency response i.e. low/band/high-pass filtered using two approaches

• Infinite Impulse Response
• Finite Impulse Response

Analogue electronic filters are necessarily IIR i.e. their components always retain some trace of an impulse input in their state. Thus capacitors retain some charge, however long you wait (although admittedly vanishingly small) and this necessarily impacts the working of the filter.

The presence of feedback in a digital filter generally creates an IIR filter and its "z domain transfer function" contains a denominator in its sequence of terms. An FFR series contains only a numerator.