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What is optimization audio for DAC



Here considered issues of digital analog conversion audio and ways for improving quality of conversion.

Optimization audio for DAC

Bases of analog signal restoring from digital form

Simplest PCM digital analog converter (DAC) contains:

1. Circuit conversion of digital sample (number, value of electrical voltage) to electrical voltage

2. Analog low frequency filter.

Still no robust proofs that we hear ultrasound. By Naquist theorem enough 40 kHz sample rate + band reserve for transient band of the low frequency filter.

So we have 44 kHz sample rate standard. However real implementation of restoring audio stuff (especially low resolution) rise some issues of quality.

Spectrum of audio sample sequence converted to voltage (stairs) have:

1. useful spectrum in low half of spectrum.

2. mirrored useful spectrum an high half of spectrum.

In this article is not real scales in graphs, but scales for more clear explanation.

PCM coded analog signal

Analog signal restored from digital form


Ideal analog filter should:
1. fully pass by useful spectrum {0 … 20 kHz}
2. fully eliminate mirrored spectrum {20 kHz…[sample rate]}.

Ideal analog filter should provide transient band (area between pass and stop frequency bands).

Ideal analog filter in DAC

Analog filter’s frequency response showed as grey line.


Issue of restoring to real analog signal

The DAC’s analog filter have enough sloping transient between pass and stop band.

And it can’t deep suppress mirrored spectrum.

Real analog filtering in DAC


For ideal analog part of playback apparatus mirrored spectrum is harmless.

But real apparatus have non-linear distortions in analog parts of DAC, amplifiers, speakers, etc.
It lead to shifting of mirrored spectrum to audible range.
Therefore audible distortions appear because apparatus have non-linear distortions.

Audible distortions by ultrasound aliases for digital analog converter


How to decrease the distortions in audible range?

Level of the mirrored distortions in audible range depend on amplitude/power of mirrored spectrum. All that placed at upper half of the spectrum of restored digital signal.

Therefore we should decrease the power of mirrored spectrum.

We can’t significantly improve the real analog low frequency filter of DAC. It will slope for modern hi-fi demands.

However we can apply oversampling

Oversampling into DAC

and steep digital filter before analog.

Analog filter vs. digital filter

Oversampling create additional periodical mirroring of {0…[sample rate]} area at frequencies above original sample rate.

But digital filter better (than analog) can suppress artifacts about higher limit of audible range.

Oversampled signal after digital filtration


Now analog filter should suppress area of highest frequencies in oversampled spectrum.
Where analog filter have maximal suppression in band {0 … [new (oversampled) sample rate]}.

Analog signal after digital oversampling-filtration and analog filtration


Hardware vs. software oversampling-filtration

Realtime-hardware-digital-oversampling filter can have computing limitation due restricted resources on chip.

So there may be slope transient band issues too.

As alternative can be used additional offline or inline oversampling filter released in personal computer software.
Computer have big calculation power, including floating point precision.

Analog vs. digital hard vs. digital soft


There DAC’s digital-oversampling and analog filters applied to preliminarily filtered spectrum.

Pre-filtration oversampled audio stuff allow to decrease the mirrored spectrum level even more.