Corey Bailey

Audio Engineering

USEFUL INFORMATION SAMPLE FREQUENCY DEFINED

One very noteworthy aspect of digital sample frequency (sample rate) is that it will define the bandwidth of the audio being sampled. This is because the highest frequency that can be sampled is roughly half of the sampling frequency. This upper limit is known as the Nyquist frequency. This discussion requires a minimal understanding of the term bandwidth. So, please use the link if you are at all unsure of it’s meaning. We get an idea of how the sampling frequency can affect fidelity by using some simple math; Using a frequency response of 20Hz to 20,000Hz (bandwidth) and a sample frequency of 48kHz, we can divide the sample rate by a given frequency to determine just how many times per second that particular frequency is actually being sampled. 48,000 ÷ 48Hz (Bass Frequency) = 1,000 samples for each peak-to-peak wave. 48,000 ÷ 480Hz (Lo Midrange) = 100 samples for each peak-to-peak wave. 48,000 ÷ 4,800Hz (Upper Midrange) = 10 samples for each peak-to-peak wave. 48,000 ÷ 9,600Hz (High Frequency) = 5 samples for each peak-to-peak wave. 48,000 ÷ 16,000Hz (The upper limit of most quality cassette recorders) = 2.5 samples for each peak-to-peak wave. 48,000 ÷ 20,000Hz (The upper limit of most professional reel-to-reel tape recorders and human hearing) = 2.4 samples for each peak-to-peak wave. It becomes readily apparent that the higher the analog audio frequency, the less it gets sampled. So, what happens to the higher piano notes, cymbals and the like when lower sample frequencies are used? Obviously, they get sampled very little. What can happen is that important things like some of the harmonics, which make up timbre and such, are lost in the sampling process. The resulting digital audio can sound strident and brittle. The rest of the un-sampled waveform is made up by the electronics doing the conversion back to analog. Much has been done in the world of electronic design to counter the problem with playback hardware that samples the audio signal at much higher sample frequencies than the original recorded file (over-sampling) so that the re-creation of the higher frequency content of the audio is more accurate. However, the best of over-sampling techniques cannot accurately recreate information that wasn’t there in the first place. So, the higher the sampling frequency during the digitization process, the more accurate the representation of the analog source will be. Very low sample frequencies (lower than 32kHz) can result in noticeably poor fidelity, which is why some answering machines sound as bad as they do. (Not to mention the “monotonic” voice programmed into them!) Because we humans can sense frequencies that are out of our normal hearing range, there are those, particularly in the music industry, who argue in favor of the higher sample frequencies (96kHz and above). The higher sampling frequencies provide considerably more bandwidth. This means that the frequency limiting (Low Pass) filters are well above anything that humans can perceive. Common sample frequencies for digital audio: 44.1kHz. The audio sample frequency originally specified for the Compact Disk format. The 44.1kHz sample frequency was chosen because it was the sample frequency that that worked mathematically with NTSC analog video recorders which, were the most available device for recording and storing digital audio at the time. When using a PAL video recorder, (The video standard in the EU) the sampling frequency is 44.056 kHz. 48kHz. The sample frequency originally specified for audio playback on audio CD’s and DVD’s. 48kHz is the standard adopted by the feature film industry for all of the digital sound played in theaters. 88.2kHz. Used as an archival format by many who tailor their product for Compact Disk. In the early days of digital recording, math algorithms were rudimentary. It is the opinion of some that, when sample-rate converting to 44.1kHz, the math is simpler and therefore less data is compromised. 96kHz. The sample frequency adopted by most institutions worldwide as the archival standard. 192kHz. The mother of all sample frequencies? We’re talking about being able to sample a bandwidth up to 96kHz. Now we’re getting into the commercial broadcast range! But seriously folks, this does get used by those who want to squeeze every possible sample out of that analog waveform. In fact, some are going beyond 192kHz and sampling at 384kHz! There is even research that suggests that analog audio should be sampled at 384kHz because we humans can perceive the difference, peculiarly when it comes to the direction of the source. Who knows, within 10 years or so, as hardware and storage space becomes faster and cheaper, it may become the new archival standard. So, when it comes to creating the digital audio archive file of your family history, what is the best thing to do? 96kHz is the archival standard that has been adopted by the likes of the Library of Congress, the European Union, the Audio Engineering Society, and several other institutions and organizations. The feature film industry uses 48kHz as it’s archival standard sample frequency. Why the deviation? The prime concern is the fact that 48kHz files take up half as much storage space as 96kHz files. Today’s lavish film sound mixes contain hundreds of source files that get archived and it all ads up quickly. Of the home recordings that I have had the opportunity to work with, the average frequency response (bandwidth) of instantaneous discs has been from around 50Hz to about 5kHz, with the best audio tape recordings having a measured upper limit of 7 to 12kHz. The truth is that the consumer tape recorders, working with their supplied microphones and running at much slower speeds than professional recorders, were rarely capable of producing a bandwidth that exceeded 12kHz or so. Thus, a sample frequency of 48kHz will be adequate for the vast majority of home audio recordings, particularly if storage space is a concern. As stated above: the higher the sampling frequency, the more accurate the representation of the analog source will be (storage space considerations aside). So, in the end, the choice of the archival sample frequency is yours. You can go with a 48kHz sample frequency and stay within the audio band, or use 96kHz which, is the archival standard, for a bandwidth out to about 48kHz, consuming twice the storage space. All of the sample frequency standards currently in use will be around for the same amount of time, so playability in the future should not be an issue. The other half of the digital audio equation is bit depth. I’ve written an article that will hopefully demystify this very important, often misunderstood aspect of digital audio recording. In the glossaries section, there is a simple definition of bit depth. Return to TOP of page © Corey Bailey Audio Engineering

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