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Sampling, sampling frequency

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Sampling, sampling frequency

Sampling frequency

Discretization (discretization frequency – ing.) – transcoding an analog signal into digital by reading the characteristics of the signal at a given moment and converting it into a digital data matrix (approx. 100010110).

Sample Rate

The sampling rate is a parameter that allows you to know the number of calls to an analog (or digital) signal in a given period of time (usually one second), to record frequencies in digital form or to convert to an analog signal.

If we rely on Kotelnikov’s theorem, then to record a lossless signal, a sample rate is required that is two or more times greater than the maximum sound frequency of the played track. That is, in theory 44,100 Hz will be sufficient for most recordings, which is more than 2 times higher than the threshold for human audible frequencies, but this is not entirely true.

The higher the sampling frequency, the more accurately the sound will be reproduced in an analog or digital signal. However, the more conversions made from analog to digital and vice versa, the more the precision and quality of the original signal recording will be lost.

The maximum sample rate for 2010 was 2,822,400 Hz and was compliant with the Super Audio CD (SACD) standard. Most multimedia centers, home theater systems have DACs (digital-to-analog converters) and ADCs (analog-to-digital converters) with a sample rate of 192,000 Hz.

To convert a signal into analog, special chips are used: DACs (digital to analog converters). To convert the signal to digital, ADCs (analog to digital converters) are used.

These microchips and chipsets have a variety of characteristics other than sample rate, such as THD, the amount of interference introduced by the transformation, the number of possible false errors, no saving a digital signal, and so on.

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Sampling frequency

To convert a so-called analog audio to digital, we use a process called: sampling. Sampling is done on a converter (or sound card). The principle is to take regular snapshots, which are the measurements of the analog signal voltage, and transform them into digital data whose language is numbers (numbers).

Here is a diagram representing the samples included in the amplitude of a sound wave. The number of samples in this wave defines the sampling frequency or sampling frequency.

La frecuencia de muestreo

Sampling frequency

The sampling rate is expressed in hertz (Hz) or (kHz). The following values are commonly found: 44,100 Hz, 48,000 Hz, 96,000 Hz, 192,000 Hz. The CD and the digital world standard are 44,100 Hz. This means that for every second, there are 44,100 samples. (samples) reproduced. The higher the sample rate (number of “snapshots” of the audio taken per second), the more accurate the analysis and coding of the music in digital data. The sampling rate affects the audio frequency range from the lowest to the highest pitch that can be stored.

Sampling frequency
16-bit / 44.1 kHz coding was the best quality available when the CD was released in the early 1980s, but things have changed, and we can now record and distribute music at higher bit-depth levels and sample rates. These formats have been used in studio recordings and for mastering for many years.

High-resolution audio (HRA) matches any recording format above the 16-bit / 44.1 kHz standard for CDs, and HRA recordings usually use 24-bit encoding, providing a greater dynamic range than CD and sampling rates up to 192 kHz . This is the pinnacle of HRA business records. First and foremost, it’s about getting as close as possible to the sound heard in the studio.

Which sampling rates should you choose?

In order to capture the smallest details at high frequencies, we need to try more frequently. The way it works is that a given sampling rate can accurately detect audio frequencies down to just under half its value. For example, a sample rate of 48 kHz can accurately detect audio frequencies as low as just below 24 kHz. This limit for half the sampling frequency is called the Nyquist frequency and is named after one of the engineers who developed the calculation behind the sampling principle.

La frecuencia de muestreo

The human ear can generally hear in the following spectrum: 20 Hz – 20,000 Hz. As we have just seen, for no obvious loss, the sampling rate must be at least twice as high as the maximum frequency contained in the audio when digitizing. The sampling rate must be at least 40,000 Hz for a correct result for our ears.

This is why 44 100 Hz resolution is the most widely used because it allows us to cover the spectrum up to 22 050 Hz. We even benefit from a small margin because we could have rounded up to 40,000 Hz, but it also means that if you export your music at a sampling rate higher than 44,100 Hz, your ear can’t hear the difference.

Anti alias filters

The first thing an analogue to digital converter does to analogue audio before sampling is to filter all frequencies above the Nyquist limit of the desired sampling frequency. If not filtered, all frequencies above Nyquist are injected again into the sample. This is called an alias effect.

Fortunately, almost all converters on the market today have implemented high-quality anti-aliasing filters. As a result, it seems undesirable aliasing effects are not, and all frequencies below the Nyquist recorded accurately. In most cases, as long as you use a good quality converter and a sampling rate of at least 44.1 Khz, you can record all frequencies in the area of human hearing in an orderly manner. Since the analog to digital converter measures each sample, you have to assign a number to that sample, as that is what makes it digital instead of analog.

How about sound cards up to 192,000 Hz?
There are two benefits to working at a very high frequency:

The first is that the drivers for your sound card (especially professional converters) will be optimized for a given sampling rate. In general, the ASIO drivers for your drives are optimized to the maximum sample rate it offers: 96,000 Hz and 192,000 Hz in most cases. This may be surprising, but it will have less delay and more relief for the microprocessor with a higher sample rate.

Sample rate, all about sample rate

For many years it was thought that the sample rate or sampling frequency did not decisively influence the final quality of the digital audio; There are currently several engineers who record in 44.1K or 48K without really knowing why they do it. With the advent of new and better computers, interfaces, ports and protocols, 88.2K, 96K and up to 192K entered the discussion table on the best sample rate to use. It has always been the subject of discussion between engineers and audiophiles; some argued that they did hear the difference between different sample rates and others that did not, and the topic has been subjected to millions of A / B tests with very high quality equipment, causing all kinds of opinions found and uncompromising, fights and friendships of years broken.

While this is a basic issue of digital audio, it is always surrounded by a halo of mystery, mysticism and magic (like every sound theme), which is well worth clarifying.

What is the sample rate?

This topic, although it occurs in the first or second class of digital audio, is not always understood correctly. In scholastic thinking, sample rate is defined as the amount of audio samples transported and taken per second. Since this is a unit of measurement over a second and with events that occur cyclically, the Hertz (1 / Frequency) is used as a unit. Obviously we cannot talk about this subject without referring to the Nyquist sampling theorem, which was tested by Shannon almost twenty years after its publication and in which it is stated that for a limited bandwidth (B) signal (for example, a vibraphone reaches 14.917Hz), the sampling frequency must be twice its bandwidth (2 * B). Then, taking the previous example, we can say that: 2 * B → 2 * 14.917Hz → The sampling frequency for 14.917Hz should be 29.834Hz. This would be equivalent to 29,834 samples per second (1/29, 834) to be able to regenerate the signal of a vibraphone without error. Hence, it is taken that the highest frequency that the human being listens to is 20kHz and if we apply Nyquist it should be 40kHz, but it takes 44.1kHz to meet the demanding ears and for a matter of multiples.

44.1K or 48K to 88.2K or 96K, the correct division

At the dawn of the digital audio era, Nyquist was used to use the sampling resolution of 44.1K, used at that time audio CD format that played at 16bit / 44.1kHz. With the advent of DVD and Blu Ray as video and audio formats, resolutions such as 24Bits / 48K or 24Bits / 96kHz began to be used. Although for many years there were recordings that were made in 24Bits / 88.2kHz or 24Bits / 96kHz, at a certain time of mastering, before sending it to the disk duplicator, the audio suffered a mutilation that reduced it to 16Bits / 44.1kHz as It was ordered by the CD format. This process should be carried out with equipment specially designed for this function and in stages so that the audio did not suffer a very noticeable cut and the bad conversion was evidenced. Although the old and dear Dither was applied since then to compensate for this process (something like “grain” in the cinema. Watch a film without “grain” and it will look like HD even though it was filmed in 1980 on tape and goes to notice until the makeup of the actor and the assembly of the special effects, something otherwise disagreeable).

Generally, to prevent the audio from mutilating or applying several conversions that degrade it, it was decided at what resolution to record before pressing the REC button (we will not mention those that come down directly with your DAW from 24Bits / 96kHz to 16Bits / 44.1kHz in one step to export the audio … there is a place reserved especially for them in hell). If the audio was going to end on CD, a sample rate of 88.2kHz was generally applied, since at the time of mastering, with the symmetrical re-sampling at “half”, it was at 44.1kHz.

Sounds better?

The subjective point of this is that we expect recordings to “sound” better at a higher sample rate. The reality is that if we record in high sample rates, with very good sampling, our sound will not “sound better”, but will be more detailed. Obviously, if our sound source is bad, our microphones and preamps too and so on, no matter how much we record at 192K, the result will not be the best. Now, if we use a good sound source, good audio chain and a good converter, everything will be obviously good. But don’t confuse; We are talking about detail here, not if it will sound more “warm,” “fat,” or “full-bodied.” This translates into a more homogeneous capture of the entire frequency spectrum, both audible and non-audible.