Bit Depth and Sampling Rate

When talking about digital audio, there are two terms which will come up first: bit depth and sampling rate. You will encounter them often when working with digital audio equipment. But before we can begin to understand them, we need to learn a little bit more about analog audio.

An analog audio signal has a waveform with completely smooth curves, like so:

Analog waveform
Analog waveform

An analog signal is one continuous set of values. By quantizing an analog waveform, you convert it into digital data with values that can be counted in binaries. The problem with this is that, as you may already know, binary data is a string of ones and zeroes. This poses a limitation which can be illustrated below.

quantizedwaveform
Quantized waveform

In the context of the above graphical representations, quantization converts a waveform into a series of horizontal and vertical lines. And as you may have noticed, quantizing did not exactly yield a faithful recreation of the original analog signal. By quantizing, values most be rounded off, which effectively become approximations of. This leads to what is called quantization error. You can imagine how horrible the digital waveform might sound like when compared to the original.

Obviously, the downside or limitation of quantizing must be addressed. This is where working on bit resolution or bit depth comes into play. The previous figure is a rather crude representation of what is called a 2-bit resolution. It has four levels of quantization (going back to your binary mathematics, two bits contain two digits which can have four possible values). In order to have a more faithful reproduction of the analog signal, there needs to be more levels of quantization which can be achieved through a higher bit depth, which can be imagined as such:

Quantized waveform (with a higher bit depth)
Quantized waveform (with a higher bit depth)

With a higher bit depth, you reduce the quantization error and subsequently approach a closer approximation of the analog signal.

When quantizing, the analog signal is not converted in its entirety. It is instead, sampled — meaning little pieces are taken from the signal. The number of times this happens at a given period of time is called the sampling rate. As you may surmise, a highly sampling rate means a closer reproduction of the analog signal. So, let us say that if your digital audio file has a sampling rate of 22 kiloHertz, that means that the analog signal it was converted from was sampled twenty two thousand times per second.

The video below offers an easy to understand explanation of bit depth and sampling rate.

Youtube link: https://youtu.be/BNVVq-iVPy8

But if you need more detailed readings, please check the references at the end of this page.

Whichever you peruse, there are tidbits which I hope you will be able to pick up, namely:

  • What is the Nyquist Theorem and what is its implication over sampling.
  • What are the industry standard bit depths and sampling rates and how they came about.
  • Understanding as to whether or not digital can exactly match analog .

References:

Apple, Inc. (n.d.). Final Cut Pro 7 Manual: Digital Audio. Retrieved from https://documentation.apple.com/en/finalcutpro/usermanual/index.html#chapter=52%26section=7%26tasks=true.

Hass, J. (2013). Digital audio. In Introduction to Computer Music: Volume One. Retrieved from http://www.indiana.edu/~emusic/etext/digital_audio/chapter5_digital.shtml.

Presonus. (n.d.). Digital audio basics: sample rate and bit depth. Retrieved from http://www.presonus.com/news/articles/sample-rate-and-bit-depth.