Sample Rate and Bitrate: The Guts of Digital Audio

January 12, 2008 Uncategorized

This post focuses on the basics of digital audio: sample rate, bitrate, and how analog signals are represented digitally.

We use digital audio all the time, but I am surprised on a fairly regular basis how many people are unclear about how digital audio works. Digital audio has two primary qualities that compose the way the audio is described. These two qualities correlate to the qualities of real world sounds more like metaphors than anything else. Real sounds have frequencies and volumes. In order to measure real world sounds and represent them digitally, we have created sample rate and bitrate as digital’s audio qualities. Sample rate determines how analog frequencies are described digitally whereas bitrate determines how analog volume is described digitally. The two qualities need each other in order to describe a sound. You can’t have volume without frequency or frequency without volume.

In order to understand why sample rate and bitrate came about, you need to understand a little bit about how all things digital work. Digital works like a ticking second hand. Whereas time and the world as we know it seems continuous and seamless, digital breaks things like time up into little measurements. When we’re talking about measurements of time, we are talking about ticks just like the ticking of a second hand. If anything is to happen digitally, it has to happen on a tick. The rate of these ticks is measured in hertz. A 2ghz computer has 2,000,000,000,000 ticks a second. That’s a lot of ticks.

Analog Signal (Wikipedia)

What is a Sample Rate?

Sample rate is a rate, just like the ticks we just talked about. Analog signal is smoooooth, just like the image you see to the right here. Like the real world, it just keeps going. In order to get this signal represented in the digital world, we need to measure it into little chunks by defining a rate. On the bottom line of the graph to the right you’ll see time is represented by t.

Digital Signal (Wikipedia)

If we start to split up the smooth analog signal into digital chunks, you will start to see something like the second image. With each tick of the clock we measure what’s happening at each tick ‘t’. That measurement is documented, represented by the balls on the signal graph. How often we do these measurements is called the sample rate. The higher the rate, the closer you’ll get to the smoothness of the first image. Measuring things in bits like this is called quantizing and the measurements are called samples (hence sample rate).

The sample rate can be thought of as how often or how much the sound is described.

CD quality audio has 44,100 of these measurements a second. That’s called 44.1 kilohertz (khz).

What is a Bit Depth?

With what we just learned in mind, consider that in order for these ticks to make any sense at all they need to actually be measuring something. What is it that we’re measuring? Volume. Volume is represented by the height of the balls in the image. With each tick a new measurement of the volume is made. How do we describe the volume? Is it a range from 0 to 100? 0 to 2000? 0 to 1? The range of volumes that can be described is the bit rate. Now, in each of these examples, 0 means totally silent and 100, 2000, or 1, respectively, means as-loud-as-it-can-get. So the only difference between each of these ranges is not how loud the sound can be but how many different volumes can be described. We only have two choices for ‘0 to 1′, ie. is there a sound or not? But from 0 to 2000 we can have half volume (1000), quarter volume (500), or even somewhere in between (829). The higher the bitrate, the more accurately we can communicate exactly how loud the volume of the ‘real’ sound we want to describe is.

The bit rate can be thought of as how well the sound is described.

CD quality audio has 65,536 volumes to choose from for every sample that’s measured. That’s called 16-bit audio (because 2 to the 16th power is 65,536).

Putting Them Together

As mentioned earlier, these things are only useful when used together. With each sample rate and bitrate there’s a limit to how accurately the analog sound to be described can be described. The Nyquist–Shannon sampling theorem states that a sample rate of twice the maximum frequency of the signal being sampled is needed to describe the frequency. Most humans can hear from 20hz to 20khz, so the sampling rate of 44.1khz was chosen to be able to capture frequencies up to 22.05khz.

Speaking in General Terms

In general, the higher bitrate the ‘smoother’ the sound will be. 8-bit sounds rather grainy and harsh whereas 16-bit sound sounds quite a bit better. 24-bit sound is used by most audio professionals these days not because it sounds so much better than 16-bit sound but because the higher accuracy is useful because so much is done to the audio in the recording, mixing, and mastering process. Higher bitrate means that each change that is done to the sound produces a more accurate result. Imagine only being able to describe the sounds you’re recording with two volumes: on or off. It would be impossible to produce any music at all with such a low bitrate.

A couple of years ago there was a lot of buzz going on about high sample rates in pro audio equipment. Higher sample rates are theoretically able to capture higher frequencies that humans may or may not be able to perceive (it’s still being debated whether it makes a difference or not). There are many things to consider when making these claims, including the quality of the microphones used, the sounds being recorded, the delivery medium, and the quality of the speakers to be used to listen to the material. Since then, most people have come to the agreement that high resolution samples rates are not as important as higher bit rates with respect to pro audio. Again, you can’t replace one with the other, so a balance is required, but 44.1khz/24-bit audio is still the standard when producing 44.1khz/16-bit audio CD quality audio. Why the higher sample rate if your ultimate destination is lower? It just sounds better, especially if the final product is dithered (a subject for another post altogether)

When digital audio is played back, the audio processor looks at the information and recreates the waveform from the sample/bit rates. It’s actually creating, as best it can, real continuous sound from the quantized digital data. Remember: you can’t hear digital so it’s up to the audio processor to figure out how to create sounds from the information.

Final Thoughts

As with any choices of this type, one needs to measure what one’s needs are. Why carry around a dozen cups from shot glasses to five gallon jugs when one 12 ounce travel mug suits most of your drinking needs throughout the day? It’s the same way with sample rates and bitrates. If you don’t need super high-res audio, it may not be worthwhile to record it. The higher the bitrate and samplerate, the more data will be recorded, the larger your sessions will be, and the harder your DAW will have to work. See this table for a few examples (taken from tweakheadz.com)…

Bit Depth Sample Rate Bit Rate File Size of one stereo minute File size of a three minute song
16 44,100 1.35 Mbit/sec 10.1 megabytes 30.3 megabytes
16 48,000 1.46 Mbit/sec 11.0 megabytes 33 megabytes
24 96,000 4.39 Mbit/sec 33.0 megabytes 99 megabytes
mp3 file 128 k/bit rate 0.13 Mbit/Sec 0.94 megabytes 2.82 megabytes
Hard disk requirements for a multi-track 3 minute song
Bit depth/sample rate number of mono tracks size per  mono track size per song songs per 20 gigabyte hard disk songs per 200 gigabyte hard disk
16/44.1 8 15.1 megs 121 megs 164 1640
16/48 8 16.5megs 132 megs 150 1500
24/96 8 49.5 megs 396 megs 50 500
16/44.1 16 15.1 megs 242megs 82 820
16/48 16 16.5 megs 264 megs 74 740
24/96 16 49.5 megs 792 megs 24 240

Do some listening, talk with your clients, and get a feel for the capabilities of your gear to decide what suits your needs!

I hope this helps demystify the guts of digital audio for folks!

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25 Comments

  1. Karl VanPelt says:

    I had a quick question that maybe you can help me with. I work at a radio station and we are considering putting files on flash drive back up as apposed to burning each show to a cd. I was wondering how many MB’s a WAV file with a smaple rate of 44,100 hertz and a bit rate of 16 and in mono would take up. To you need a rough time length?

  2. David says:

    Typo at end of second paragraph:

    2,000,000,000,000 = 2THz (terahertz)

    2,000,000,000 = 2GHz (gigahertz)

    (you have one extra block of zeros too many)

  3. Lee Shipton says:

    Why doesn’t a sample rate of 44,100 equate to a BT rate of 1.4112 Mbits/sec as opposed to 1.35?

  4. Kunal says:

    This is very very well explained. Thanks a lot :-) I may include this in my blog in future.

  5. Dan Connor says:

    Cheers Kunal!

  6. Dan Connor says:

    I believe you’re correct, Lee.

  7. NeoN says:

    Confusing.You have not mentioned about Bit rate correctly.What is the meaning of 192/44.1 where 128 is bit rate in units of kbps and 44.1 is sample rate in KHz

  8. lio says:

    This is messed up what an mp.3 bit rate is doing in the sample rate scheme when sample rate is sound frequency range??
    And Mp3’s have a 44,100 sample rate.
    The bite rate of an mp3 is usualy 128 kbps to 320 kbps.
    You’ve just confused the people here more…

  9. Russ P says:

    Thanks for this; good explanation and just what I was looking for. Perhaps to help readers understand the table you could add that
    bit rate = sample rate x bit depth x 2 (for stereo)

  10. Dan Connor says:

    MP3s can actually have non-44.1 sample rates.

  11. Rick404 says:

    I’m about as confused as a Monty Python cat if this isn’t an error : “What is a Bit Rate?” Should that heading in the article say”Bit Depth” instead of “Bit Rate”?

  12. Magantia says:

    Rick404, you are right. Bit Depth, not Bit Rate. Amplitude can be described via depth, not rate. Bit depth is the size of a single sample (in bits), and hence the bit rate can be derived from the sample size, bit depth, and number of channels in uncompressed PCM audio (bit depth x sample size in hertz x channels). Generally, you would be listening to stereo audio (2 channels). The table provided in this post does correctly display the relationship between these values.

  13. Dan Connor says:

    Right you are!

  14. Mr. Heath says:

    GREAT post and fantastic educating description of a rather abstract (for some people) subject, which, still are crucial in today’s digital media world.

    Thanks a lot :-)

  15. ron says:

    There’s really no question that sample rate is most important to sound quality as sample aliasing starts to happen WELL before the Nyquist frequency. On standard 44.1KHz sample rate significant aliasing starts happening in as low of frequencies as 5KHz. Peaks of waves can be significantly truncated at this freqency already. Not only that, but my brother at his job was able to actually benchmark a number of A/D converters and told me thet the very best converters available were only capable of resolving about 17 bits cleanly. Anything beyond that was just noise. Realize that at a 24 bit conversion on a standard 2V peak-peak audio signal every division is approximately 1 ten millionth of a volt.

  16. Ryan says:

    EDIT
    *Finally record digitally-derived audio at sampling rates higher than 48 kHz…

  17. Dan Connor says:

    Hi Ryan. I’m going to assume you’re not trolling here. Digital audio a complex topic full of a) misinformation/mythology b) unintuitive science/ complex math and c) a lot of unknowns that are still not fully understood (like psychoacoustics, how human hearing works, and interactions between equipment). So while I appreciate your taking the time to comment, next time you do don’t come in swinging. I don’t have an editor on this blog, so mistakes can happen.

  18. dorbert says:

    Number of base ten volume levels at bit depth of 8 bits is 256 not 65,536. 8 binary bits can represent a base ten number from 0 through 255 for a total of 256 amplitude levels, including 0.

  19. dorbert says:

    16 bit depth yields 65, 536 sound levels and 24 bit yields 1,048,576. As just a few bits are added to each sample the articulation greatly increases. If you ever A/B compared a 24 vs 16 bit sampling rate, the diff is noticeable.

  20. conner says:

    Why was bit rate not covered? sample rate and bit depth were covered followed by a chart which contained bit rates but never was bit rate discussed.

  21. Dan Connor says:

    The effect of bit rate depends on the codec being used and gets very complicated very quickly. MP3 is touched on briefly here. If you’re curious to learn more about bitrate, I suggest reading some of the wiki articles on hydrogenaudio.org.

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