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Background: What is sampling rate/sampling frequency/ sample rate

This is a Background article that will explain that what is sampling rate/sampling frequency/ sample rate.

The result of the digitization is so-called samples – discrete, digitized “extract samples” of the analog original signal. From these, the original analog signals can be reconstructed using digital-to-analog conversion. This reconstruction is subject to the influence of the sampling frequency (sample rate) and the “resolution” of the samples, also called bit depth .

The sampling frequency of audio signals, i.e. the frequency of samples per unit of time (usually specified per second), is comparable to the frame rate per second of a film camera. The number of pixels for each image could, in turn, be equated with the bit depth: HD films “look better” than Super 8 films. The larger the number of pixels in the sensor and the more frequently a picture is taken, the more precisely the “light to be recorded,” the scenery, can be digitally reproduced.

The well-known Nyquist theorem states that an audio signal must be sampled evenly at least twice the frequency to reconstruct the original signal adequately. In practice, the bandwidth limitation takes away from our hearing, which can only consciously perceive frequencies between a maximum of 20 Hz and 20,000 Hz, which means that a sampling frequency of 40 kHz should be sufficient in practice.

The 44.1 kHz sampling frequency/rate usual for CD quality comes from the 1970s or Sony’s “Pulse Code Modulation Process” (PCM) for storing digital signals on videotapes. Aliasing occurs at all frequencies above 22.05 kHz (Nyquist frequency = half the sampling rate), unless appropriate filters are used before recording.

Sony later developed the Red Book standard for audio CDs from this with Philips. The additional 4,000 Hz slightly wider frequency than twice that which is audible to humans, has its origin in the simplest possible filters, which are intended to remove so-called aliasing effects from the audible range of the reconstructed analog signal when digitizing – the wider this “corridor,” the simpler the filter technology.

It became exactly 44.1 kHz because sampling rate converters can be designed more easily (used for studio technology or data carrier transfers) if the sampling frequency is an integer multiple of the output frequency. The output frequency here was the 60 Hz mains frequency used in video digitization with 525 lines for the TV signal to be digitized. Changing the 60 Hz would have been time-consuming, but they kept it. It is no coincidence, however, that by multiplying 525 by an integer factor, one achieves a frequency higher than 44,000 Hz, which is supposed to be achieved to keep the anti-aliasing filters simple: The next larger integer that is divisible by 525 is 44,100. The multiplication factor is then 84, which is an integer as desired.