January 8, 2021

by Paul McGowan

There sure is a lot of confusion over sample rates. We hear about CD-quality sample rates at 44.1kHz (and its multiples), or another common sample rate, 48kHz (and its multiples), and then there are multiple higher sample rates (176kHz, 192kHz as examples) and of course DSD.

Lots of numbers. All very confusing.

Perhaps a short primer would help.

First, what is a sample rate? Simply put, it’s a snapshot of the audio signal. A slice of time where we capture the voltage level of the music signal. The number of times per second we take that snapshot determines the sample rate. (Bit depth determines the loudness range we can capture within each sample)

First, what’s the difference between 44.1kHz and 48kHz and why do the two exist? The former is what Sony/Philips set as a standard for the Compact disc. When we do higher sample rate versions of this standard we get 88.2kHz, 176kHz and so forth. The latter, 48kHz, is the standard the “pros” use (because, well, they can’t use something as conventional as consumers, now can they?). 48kHz gives us multiples we’re familiar with like 96kHz, and 192kHz.

What’s painful about the above two standards is the difficulty moving between them. When recording studios record at “pro” sample rates of 48kHz they then have to interpolate down a few Hz to 44.1kHz to make something we poor consumers can listen to.

Silliness.

When we nerds talk about sample rates we use different terminology. We base our discussion on how many multiples of the base frequency (44.1kHz) are in play. So, for instance, the CD sample rate is referred to as 1f_{s}. Its multiples are 2f_{s}, 3f_{s}, etc.

The sampling frequency or sampling rate, f_{s}, is the average number of samples obtained in one second (samples per second). Think of 1f_{s} as the minimum baseline to capture 20Hz to 20kHz.

While we might be familiar with all the differing PCM sample rates, DSD brings in a whole other dimension with its far higher sample rates. For example, standard DSD is 64f_{s} while double rate DSD is twice that at 128f_{s}. So what’s that mean? Well, 1f_{s} is running at 44,000 times per second, while 64f_{s} is running at 64 times that frequency, or 2,822,400 times per second! That’s fast, man.

And, while DSD is so much higher of a sample rate as to raise a few eyebrows, it’s instructive to remember it’s a 1-bit system compared to a basic 16-bit system like PCM (remember that the number of bits is needed to measure amplitude). This boils down to something less hair raising if we do a bit of math. 64f_{s} (1xDSD) runs at a very high clock rate of 2,822,400 Hz (2.8mHz). Now, simply divide that by 16 (the number of bits in a PCM word) and guess what you get? A sample rate of 176kHz. Sound familiar? 176kHz is the same as 4f_{s} PCM. So, while PCM requires 16 bits to adequately measure amplitude, and DSD needs 16 single bits to do the same, it all kind of works out in the end. (Don’t take what I just wrote about DSD and 16 bits as literal. I use it only as a means of helping form a picture. DSD is far more complicated, using a Sigma-Delta Modulator, noise shaping, etc.)

Without getting too much more in the weeds, that’ll give you a brief simplistic overview of sampling rates.

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