Why do CDs use a sampling rate of 44.1 kHz?

Howdy Pierce

During a recent conference call discussing audio sampling rates, the question came up: Why do CDs use a sampling rate of 44.1 kHz?

First, a little background: When you sample an audio waveform, you have a choice as to how many samples you take per second. Over the years, a number of standards have developed; in digital media used for entertainment purposes, the two most common sampling frequencies are 44.1 kHz and 48 kHz.

As a video guy, I think of 48 kHz as the “natural” choice for audio sampling. It is the frequency used in most digital television applications, including DVD and HDTV. It’s an even multiple of the sampling rate used in telephony—8 kHz—so conversions are relatively straightforward.

But most music is sampled at 44.1 kHz, because this is the standard used for CD audio. The question we were asking in my conference call was: Why were CDs standardized around this sampling frequency?

Although we think of 44.1 kHz as an audio standard, the great Internet Oracle says that this magic number was actually derived from the early use of video recorders to record audio. Evidently creating a recorder capable of recording at around 1.4 Mbps—the data rate of uncompressed digital audio—was a difficult feat back in the day, so engineers of that time repurposed analog video recorders in order to record digital audio. If you modulate a digital audio stream in such a manner that you encode three samples of audio on every visible line of video, then you can record audio in real time on a VCR if you sample at exactly 44.1 kHz—or so the story goes.

The math from the FAQ linked above works, with some caveats. Take this excerpt from Digital Interface Handbook (Francis Rumsey and John Watkinson, Third Edition, p. 53):

In 60 Hz video, there are 35 blanked lines, leaving 490 lines per frame, or 245 lines per field for samples. If three samples are stored per line, the sampling rate becomes 60 × 245 × 3 = 44.1 kHz.…

The sampling rate of 44.1 kHz came to be that of the Compact Disc. Even though CD has no video circuitry, the equipment used to make CD masters was originally video based and determined the sampling rate.

This sounds good, except that NTSC video actually runs at 29.97 frames per second, which makes the field rate come out to 59.94 instead of 60. And the sampling rate of 59.94 × 245 × 3 = 44,055.9, so it’s off by just a little. (The math works exactly for PAL video.) But I’m willing to assume that there was a way for engineers to jury rig the VCR to run at exactly 30 fps, and not 29.97, and then the math would come out correctly. (If you can shed more light on this discrepancy, please leave a comment to this post. I’d love to get to the bottom of it.)

Incidentally, this math suggests that three samples were stored as black-and-white pixels. We’re talking about stereo audio here, and presumably even in the 1970s people were sampling at 16 bits per sample, which implies that 12 bytes or 96 bits would have been encoded per line of video.

The whole story reminds me of that email—possibly apocryphal—about how the width of the space shuttle rocket booster is related to Roman war chariots.

But maybe the interesting question isn’t why CDs use a 44.1 kHz sampling rate, but rather why digital video uses 48 kHz. The reason this seems like an interesting question is that there’s less data to compress at lower sampling frequencies. Specifically, 44.1 kHz sampling leads to about 8 percent fewer bytes before compression than 48 kHz does. So you’d expect 44.1 kHz audio to be more widely used in digital video, because it should be able to deliver the “CD experience” at a lower overall data rate.

Because of the Nyquist theorem, we know that the maximum frequency that can be represented at any given sampling rate is half the sampling rate; thus a 44.1 kHz CD can capture tones up to 22.05 kHz, while a 48 kHz DVD can capture tones up to 24 kHz. The limit of human hearing is roughly 20 kHz, so in a theoretical, spherical-cow world, it seems like both capture standards would meet the requirement of fully capturing the entire audible spectrum.

In the real world, of course, cows aren’t spherical. In practice there are aliasing artifacts near the limit of the filter, with less computationally complex filters having worse aliasing. So the point of the 48 kHz sampling rate used in digital video is to buy enough headroom for simple filters to operate without introducing audible artifacts.

Still, these standards were written a relatively long time ago. Today we’ve had several more turns of Moore’s law. So maybe a capacity-constrained network operator might want to consider jumping to 44.1 kHz audio sampling, at the cost of a little more filtering logic in the decoder.

Howdy Pierce, managing partner and Cardinal Peak co-founder, is a “video guy” whose technical background is in multimedia systems, software engineering and operating systems. Read more about Cardinal Peak’s digital video expertise.

Categories: Audio, Howdy

Cardinal Peak
Learn more about our Audio & Video capabilities.

Dive deeper into our IoT portfolio

Take a look at the clients we have helped.

We’re always looking for top talent, check out our current openings. 

Contact Us

Please fill out the contact form below and our engineering services team will be in touch soon.

We rely on Cardinal Peak for their ability to bolster our patent licensing efforts with in-depth technical guidance. They have deep expertise and they’re easy to work with.
Diego deGarrido Sr. Manager, LSI
Cardinal Peak has a strong technology portfolio that has complemented our own expertise well. They are communicative, drive toward results quickly, and understand the appropriate level of documentation it takes to effectively convey their work. In…
Jason Damori Director of Engineering, Biamp Systems
We asked Cardinal Peak to take ownership for an important subsystem, and they completed a very high quality deliverable on time.
Matt Cowan Chief Scientific Officer, RealD
Cardinal Peak’s personnel worked side-by-side with our own engineers and engineers from other companies on several of our key projects. The Cardinal Peak staff has consistently provided a level of professionalism and technical expertise that we…
Sherisse Hawkins VP Software Development, Time Warner Cable
Cardinal Peak was a natural choice for us. They were able to develop a high-quality product, based in part on open source, and in part on intellectual property they had already developed, all for a very effective price.
Bruce Webber VP Engineering, VBrick
We completely trust Cardinal Peak to advise us on technology strategy, as well as to implement it. They are a dependable partner that ultimately makes us more competitive in the marketplace.
Brian Brown President and CEO, Decatur Electronics
The Cardinal Peak team started quickly and delivered high-quality results, and they worked really well with our own engineering team.
Charles Corbalis VP Engineering, RGB Networks
We found Cardinal Peak’s team to be very knowledgeable about embedded video delivery systems. Their ability to deliver working solutions on time—combined with excellent project management skills—helped bring success not only to the product…
Ralph Schmitt VP, Product Marketing and Engineering, Kustom Signals
Cardinal Peak has provided deep technical insights, and they’ve allowed us to complete some really hard projects quickly. We are big fans of their team.
Scott Garlington VP Engineering, xG Technology
We’ve used Cardinal Peak on several projects. They have a very capable engineering team. They’re a great resource.
Greg Read Senior Program Manager, Symmetricom
Cardinal Peak has proven to be a trusted and flexible partner who has helped Harmonic to deliver reliably on our commitments to our own customers. The team at Cardinal Peak was responsive to our needs and delivered high quality results.
Alex Derecho VP Professional Services, Harmonic
Yonder Music was an excellent collaboration with Cardinal Peak. Combining our experience with the music industry and target music market, with Cardinal Peak’s technical expertise, the product has made the mobile experience of Yonder as powerful as…
Adam Kidron founder and CEO, Yonder Music
The Cardinal Peak team played an invaluable role in helping us get our first Internet of Things product to market quickly. They were up to speed in no time and provided all of the technical expertise we lacked. They interfaced seamlessly with our i…
Kevin Leadford Vice President of Innovation, Acuity Brands Lighting
We asked Cardinal Peak to help us address a number of open items related to programming our systems in production. Their engineers have a wealth of experience in IoT and embedded fields, and they helped us quickly and diligently. I’d definitely…
Ryan Margoles Founder and CTO, notion