From Benchmark

Sample-rate for Digital Audio

Definition

Sample-rate describes the number of times a signal is sampled each second. In a digital audio recording configuration, the analog signal is fed to an analog-to-digital converter (A-to-D), such as those made by Benchmark. The A-to-D will take multiple digital word coded 'snapshots' of the analog audio signal it is receiving, and store them as samples. The number of samples the converter takes every second is determined by the sample-rate chosen for the A-to-D. For example, an audio signal that is converted at a sample-rate of 44.1 kHz will have 44,100 samples recorded every second.

These samples, when played back successively at the specified sample-rate through a digital-to-analog converter (D-to-A), i.e. the Benchmark DAC1, will recreate an analog audio signal that is an estimation of the original audio signal. The accuracy of this estimation is directly related to the resolution of the sampling (sample-rate and word-length), as well as the quality of the electronic implimentation of the A-to-D and D-to-A being used.

What does it mean for audio quality?

The sample-rate limits the bandwidth of the audio being sampled. Mathematically, an analog signal must be sampled more then 2x its highest frequency (this is called Nyquists Theorem). Therefore, since human hearing goes up to near 20 kHz, the original CD sample-rate is 44.1 kHz. For this to work though, everything in the audio signal above 22.05 kHz (1/2 of 44.1 kHz) needs to be filtered out completely. Since perfect filters don't exist, the filter will attenuate some of the frequencies lower then 22.05 kHz, and actually well below 20kHz as well.

As digital audio progressed, a natural progression was to move to higher sampling rates. This would allow the filter to start filtering higher on the frequency scale, with the intent of overshooting and not affecting the audible range at all. Therefore, most professional recording is done at sample-rates higher then 44.1 kHz to maintain a 'flat' frequency response in the audible range.

Standard Audio Sample-Rates

• 8 kHz - Telephone
• 22.05 kHz - Radio
• 44.1 kHz - CD, and other computer audio
• 48.0 kHz - Professional audio applications
• 88.2 kHz, 96.0 kHz, 176.4 kHz, 192.0 kHz - DVD audio, other High Definition audio

Sample-rate Conversion

What is sample-rate conversion?

Stated simply, sample-rate conversion is a function to convert an audio file or signal from one sample-rate to a new sample-rate. One common scenario in which it is implimented is to match the sample-rate of audio to the sample-rate of the destination of the audio signal.

Digital audio equipment must run at a specified sample-rate in order to properly re-construct the audio. If an audio signal with a sample-rate of 48 kHz, for example, was played with equipment running at a sample-rate of 96 kHz, all of the audio would be twice as high in pitch and twice as high in speed - similar to a tape playing back at the wrong speed. Also, mis-matched sample-rates usually cause 'ticks' and 'pops' in the audio as well.

The sample-rate of the destination can usually be changed to match that of the audio that is being sent to it. This is much more desirable, as explained in the following section.

How does sample-rate conversion affect my audio?

In short, it is ALWAYS best to avoid sample-rate conversion of the audio, when possible. Sample-rate conversion can have anywhere from disasterous effects to minimal effects on the audio, depending on the quality of the converter design.

Example of Distortion caused by Sample-Rate Conversion (using iTunes with Mac OSX 10.4.6)

A 16-bit 10k sine wave played through iTunes on OSX 10.4.6, without any sample-rate conversion.	A 16-bit 10k sine wave played through iTunes on OSX 10.4.6, with sample-rate conversion from 48kHz to 44.1kHz.
This is the ideal, bit-transparent results. A properly-designed sample-rate conversion program should always have conversion results with a THD+N floor similar to this (~-129dBFS for 16-bit).	The distortion seen in this graph is solely caused by sample-rate converting from 48kHz to 44.1kHz. As seen in the graph, the signal-to-noise ratio went from 130dB to less then 80dB!