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What is the sample rate and bit rate?

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What is the sample rate?

Sample Rate

Frequency is defined as the number of cycles of periodic motion per unit of time. The SI unit of frequency is called hertz (Hz, after its inventor Heinrich Hertz). One hertz corresponds to one cycle (or complete oscillation) per second.

Sample Rate

Example. Sound waves have a frequency in the range of approximately 20 to 20,000 Hz. This means that at any point along the path of the sound wave, the pressure will fluctuate from high to low, 20 to 20,000 times per second.

In digital audio, the maximum frequency that can be successfully recreated is half the sample rate. Therefore, with a sample rate of 44.1 kHz, frequencies up to 22.05 kHz can be recreated. Wave frequency refers to how many times per second a wave moves from its highest point to its lowest point and vice versa. It is usually measured in hertz (Hz) or cycles per second. The frequency of the wave determines its height. High-frequency waves have a high pitch, while lower frequencies have a lower pitch. The average person can hear frequencies from 15 or 20 Hz to about 20,000 Hz (20 kHz).

Analog wave The wave amplitude refers to half the distance between the highest point of the wave and the lowest point. The greater the amplitude of the wave, the greater its volume, which is generally measured in decibels (dB). The decibel range for human hearing is complex and depends on the frequency of the sound in question, the age of the person and the listening environment, but varies from approximately 0 to 120 dB, with each 10 dB change corresponding to a doubling of the perceived volume.

Absolute Threshold: ATH is the volume level at which a certain sound can be detected 50% of the time.

What is the bit rate?

Bit rate refers to the data transfer rate (that is, how many bits are transmitted in a given time), generally expressed in bits per second. Common units of bit rate are kilobits per second (Kbps) and megabits per second (Mbps). The term is also commonly used when talking about digital sampling and sample rates. For example, the MP3 audio compression algorithm is often configured to output files at a bit rate of 128 kbps. This means that the file contains an average of 128 kilobits for every second of audio (960 KB per minute). This is in contrast to CD audio, which is encoded as 44,100 16-bit stereo samples per second: 1411.2 kbps (16-bit x 44100 Hz x 2ch).

Often times, bytes are written in uppercase and are multipliers (for example, “KB” for kilobytes) and lowercase factors are bits (for example, “kb” for kilobytes). All modern computers use 8-bit bytes.

MP3 bit rate
The MP3 bit rate can be misleading. For example, an MP3 “constant bit rate” (CBR) of 128 kbps will use approximately 128 kilobits for every second of encoded audio (so the file size in bits divided by the length of the audio is approximately 128,000), and Your frame headers will appear at regular intervals, but internally, frame-by-frame, you can encode audio at bit rates higher or lower than 128 kbps by using a bit pool (the ability of a frame to use spare bits from a previous block). However, the size of this bucket, and thus the amount of variability, is limited, so 128 kbps will be very close to the effective bit rate throughout the file.

See also: 8D surround sound and how to do it
As another example, “128 kbps VBR MP3” is often incorrect, as the purpose of VBR is to allow each of the internal MP3 sectors to have its own bit rate. When people refer to the VBR MP3 bit rate, they are generally referring to the actual average bit rate of their frames. If the length of the encoded audio is known, then the “bit rate” can be the data size of the file divided by its duration, which will be fairly close to the same number. However, the length of an MP3 VBR cannot be accurately determined without scanning all the frames.

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Digital Sound and Sample Rate

Digital Sound and Sample Rate

Sample Rate

Given the wide availability of inexpensive digital audio equipment, we invite you to take a closer look at digital audio.

Sample Rate

Acoustic sound is a continuous process in time and in amplitude, that is, the air pressure changes smoothly with time and does not jump from one value to another. Acoustic sound can be converted into an electrical signal using a microphone that, depending on the change in air pressure, changes the electrical voltage it generates at the output. After the conversion of an acoustic sound into an electrical signal, continuity is maintained in time and in amplitude: the signal voltage changes in the same way that the air pressure changes, which is why this sound is called analog. We can record an electrical signal on magnetic tape and convert it back to sound using a loudspeaker that functions as a “reverse microphone”: it moves air in response to changes in voltage. Respectively,

Despite the fact that the analog electrical signal has regularly served humanity for decades, over time some of its representatives (of humanity) became clear that the analog signal and magnetic recording are not the best ways to transmit and store audio information, since both during transmission and during storage occur. unavoidable losses, i.e. sound degradation. At the same time, the transmission and storage of data on computers that operate exclusively on digital data can be done without any loss. The only question is how to convert analog audio to digital and vice versa.

To solve the first problem, there are special devices known as analog-to-digital converters (ADCs). These devices are capable of converting a continuous analog signal into a sequence of separate numbers, that is, making it discrete (English discrete – separate, consisting of separate parts). The conversion takes place as follows: the device measures the amplitude of the analog signal many times per second and outputs the measurement results in the form of numbers.

Analog signal
Sampling
Sampled signal
As seen in the figure, the measurement result is not an exact analog of a continuous electrical signal. How much does digital sound compare to analog? Obviously, this correspondence will be more complete the more often the measurements are made and the more accurate they are. The frequency at which measurements are taken is called the sample rate. And the precision of amplitude measurements is indicated by the number of bits used to represent the measurement result. This parameter is called the bit depth.

Sampling rate
So, the conversion of an analog signal to digital consists of two stages: sampling in time and quantization in amplitude. Time sampling means that the signal is represented by a number of its samples (samples) taken at regular intervals. For example, when we say that the sample rate is 44.1 kHz, it means that the signal is measured 44,100 times per second (in MO, the more intelligible term “sample rate” is usually used, however, “sample rate “is more correct.).

The main issue in the first stage of converting an analog to digital signal (digitizing) is to choose the sampling frequency of the analog signal. As already mentioned, the higher the frequency, the closer the digital signal is to the analog. However, in proportion to the increase in frequency, the following increases: a) the intensity of the digital data stream and the bandwidth capabilities of the interfaces are not unlimited, especially if several channels are recorded / played simultaneously; b) the computational load of digital effects processors and their computational capabilities are also limited; c) the amount of memory required to store the digital signal. Obviously a compromise is needed.

The choice of the sampling frequency affects the frequency range of the received digital sound or the maximum frequency of an analog signal, correctly represented in digital. The range of frequencies a person hears is believed to be 20 to 20,000 Hz. According to the well-known Nyquist theorem, in order for an analog (continuous in time) signal to be accurately reconstructed from its samples, the sampling frequency it must be at least twice the maximum audio frequency. An audio frequency equal to half the sampling frequency is called the Nyquist frequency and is the maximum frequency that a given digital system can store and reproduce correctly. Thus, if the real analog signal that we are going to digitize contains frequency components from 0 Hz to 20 kHz.

Sample Rate

The seconds are defined by taking as a time sample the period of oscillation of the light waves emitted by a cesium 133 atom in a particular atomic transition.

As we have already observed in the dedicated paragraph, sound is generated by small variations in atmospheric pressure that propagate in space and time and until the end of the 40s of the last century it could only be transduced by the human auditory system or by the microphone devices used. for the transmission of signals by radio but it cannot be stored in any type of support dedicated to mass cultural diffusion. In fact, there were already several technologies dedicated to the memorization of sound waves but they were either of poor quality and diffusion such as phonographs and gramophones or were used only experimentally or were dedicated to communications between military devices.

The only vehicle to transmit sound events for musical purposes was still the score that had to be interpreted by a human interpreter and, if someone wanted to listen to a certain piece of music, they had to go to a theater or concert hall that had it on the bill. We emphasize that the performance (as well as the listening) was unique and non-repeatable and the only memory capable of preserving the sounds was the human. All this until 1948, when in the United States Columbia patented the first 33 rpm vinyl record in the 25 and 30 cm formats and where the waveform (as previously happened with 78 rpm records) was printed in micro-grooves that were They developed in a spiral along the surface of the disk and were read by one of the giradichi heads.

The following year (1949) another type of media dedicated to the preservation and reproduction of sound was also introduced on the market: the first magnetic tape recorders wound on reels and later in 1964 Philips commercialized the four-track cassette in Europe. The era of massive musical (and cultural) enjoyment has begun, which after hundreds of years has profoundly and definitely changed our relationship with the world of sounds.

All the means and systems for storing sound waves that we have just exposed (in addition to others that I have not considered appropriate to mention here) belong to the world of analog audio since the information or rather the representation of the sound wave is produced in a continuous and analogous to the original changes in atmospheric pressure. This is because analog recording devices (transducers or microphones) transform changes in atmospheric pressure into changes in the voltage of an electrical signal, which can be stored on mechanical (vinyl records) or electromagnetic (magnetic tapes) media. to be eventually reproduced one or more times at later times. This, in addition to being a transcendental technological revolution, has also greatly influenced the diffusion of music in society, the role of music within it and the development of languages closely linked to the sound or musical arts.

In 1971 a new revolution began which, however, this time is strictly technical (from the cultural and social point of view it only amplifies and accelerates the process of global dissemination of information already underway): the birth of digital audio. In fact, in that year the research laboratories of NHK (Japanese public television radio) created the first digital audio recorder that, using the PCM (Pulse Code Modulation) technique patented by the British A.

Sampled signal

We have said that sampling a signal means measuring its amplitude (y) in each sampling period, obtaining a discrete signal in time and continuous in amplitude:

Sample rate

At this point, however, we are faced with a question: how often to sample the signal? Theoretically we can say that the shorter the sampling period, the less information will be lost between one sample and the next, obtaining a digital signal more similar to the original up to the ideal limit (infinitely small period) in which the analog signal and the sampled.

Sample rate

In practice, however, there are technological limits in the construction of ADC converters that do not allow us to achieve such short periods. Therefore, we must start from the assumption that the samples must be taken with a speed dependent on the variation of the signal and this speed depends on the harmonic component of higher frequency that will determine the sampling period.