HiFi Techical stuff
DAC (Digital to Analogue Convertor)
Digital to Analogue Converter (D-to-A or DAC) is the part of the CD replay system that converts the digital signal back into analogue. The job of the DAC is to reconstruct data as a series of numbers that represent the analogue waveform as a series of steps. These steps are spaced by the clock that’s part of the circuit. The data consists of a series of impulses with the gaps between filled in by means of interpolation.
As you can see from Fig. 6 the output at this stage begins to resemble analogue but you wouldn’t want to feed this to your speakers.
The end result of DAC processing, an audio waveform
The next stage can be considered as smoothing out the ragged edges to a more usable form. This is done by using low pass filters set at 20 kHz for example. This frequency is determined by the Nyquist theory, which in essence states that the highest usable frequency must be sampled at least twice to avoid severe distortion of higher frequencies. Ideally we must block everything above 22 kHz. What we’re looking at is a filter that has 0 dB at 20 kHz sloping down to -90 dB at 22 kHz, a steep slope indeed. Filters are not ideal though, they have a finite slope and immediately we have a problem setting the cut off frequency, too high means we’re cutting off audio frequencies, too high and we’re letting digital frequencies through. We can minimise this problem though by using multi stage filters enabling a steep cut off slope, essentially this filter would be a brickwall filter. Ideally a brickwall filter passes all frequencies below 22 kHz, and cuts all above. The problem with a brickwall filter is that it causes phase distortion and other audible distortions. This was the cause of digital recordings sounding harsh.
Oversampling
Many of the problems with using filters are solved by the use of oversampling. What it means in essence is to sample the recorded media (e.g. CD) more times than it was sampled on the original recording. It’s like looking at one point in the recording and saying ‘check the amplitude at this point’ – OK, now check again. – OK, now check again – OK, now check again. This is an example of 4X oversampling and increases the sampling rate to 176.4kHz. We can now set the filter at a much more sensible rate. The audio industry has now settled for 8X oversampling rate which means sampling occurs at 352.8kHz. The filter now can be set for around 158 KHz removing the need for brickwall filters and are now much simpler. We end up with a cheap and simple filter that has none of the phase effects incurred by brickwall filters.
Upsampling is a variation of oversampling, whereas oversampling is done by orders of 2X, 4X, 8X. 16X etc. upsampling is anything greater than 1, for example 5/4.
What we end up with is a neat solution to a problem by using some clever maths.
There is a misconception that since analogue signals use continuous parameters they offer better resolution than digital. Analogue is limited by the same problems as digital such as noise and bandwidth. Just as noise limits amplitude in analogue so does quantisation noise limit amplitude in digital. If an analogue signal contains frequencies from DC to 10 kHz, this will have the same resolution as a digital signal sampling at 20 kHz, this is guaranteed by sampling theorem.
Bit Depth
Bit Depth is a means of expressing the detail to which the amplitude of the audio waveform is sampled. This determines the dynamic range available. It tells how accurate the sound has been scanned. With CD this is 16 bit, or a possible 65,536 levels of amplitude. If you think of it as a ruler with so many markings on it, you can only take so many measurements from it. An error that occurs at this stage is called a quantisation error resulting in quantisation distortion. At loud levels they become noise, at low levels they cause audible distortion. It’s desirable to have accuracy when sampling the music because greater accuracy means better sound. In order to overcome this low level distortion at low sound levels low level white noise is introduced in a process known as Audio Dithering. The end result is more acceptable noise replacing undesirable distortion. It’s a more acceptable compromise between two evils. There are many A to D converters that use dither as an automatic process when sampling.
