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Bit Depth, and Bit Rate Version 1.0

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Understanding Sample Rate, Bit Depth, and Bit Rate

Introduction

Sample rate, Bit depth, and Bit rate are the base of the digital audio-making process. To produce, it is necessary to know what makes up an audio file and what factors must be taken care of when opting for music for personal experience.

In the article below, I’ve tried to explain the sampling rate and how it determines the frequency range of the recording, its base, and what factors have to be considered for distortions while sampling audio.

Further, in bit depth, it is explained how a computer perceives and encodes instructions into binary digits, forming an amplitude waveform controlling its dynamic range and how bit rate determines the quality of the music and different types of files offering varying audio quality with altered information.

Sample rate

What is a sample rate?

Sample rate, also known as sample frequency, is the measurement of the tiny frames or slices of digital samples received from a computer by an analog signal, i.e., a continuously varying signal per second.

A high sampling rate or sampling frequency means that more analog changes are recorded per second, leading to better audio quality. When represented graphically, by the frequency, points are marked on the graph, and a line is drawn through it according to the constructed sample rate, which, when joined, resembles a waveform.

The more points marked, the more will be the waveform. Those points marked by the samples represent the signals that the computer collects. With more samples being collected by the computer, more frequencies are recorded, resulting in better audio quality.

However, in the case of a very low sampling rate, there isn’t enough information to represent frequencies after a certain point. This point is called Nyquist frequency.

What is a Nyquist frequency in the Sampling rate?

The concept of Nyquist frequency is given in the Nyquist Sampling theorem, which states that the sampling rate should be twice as high as the frequency to record the frequency. For instance, if the frequency is up to 4,000 Hz, it should be sampled at a frequency rate of 8,000 Hz, and the sound bytes will be taken 8000 times per second to reproduce the sound accurately.

Nyquist sampling theorem – fn = 1/2dt Where: fn= Nyquist frequency dt = sample rate (average number of factors obtained in one second) 1/2dt= represents half the sampling rate because it takes at least two samples to oscillate.

Sometimes, when the sampling rate is too low to sample any particular signal, or the present frequencies are too high for a specific sample rate, the situation forming is called aliason. You can also say that aliason occurs when the highest frequency of a signal is less than the Nyquist frequency of a signal. How do we measure the sample rate?

You can measure sample rate by knowing how often samples are taken. It is measured in hertz (Hz). The most common sample rate is 44.1 kHz, which means that 44,100 samples of audio per second are being taken. This sample rate was chosen back in the 1970s by Sony, due to two reasons: Firstly, the rate is associated with the characteristics of human hearing. For example, human hearing is between 20 Hz- 20,000 Hz. So, the sampling rate, according to the Nyquist theorem, had to be greater than 40 kHz. Secondly, the frequency was set at 44.1 kHz due to the limitations of early recording systems. The early digital audio capacity tools like VCRs were the only way with sufficient capacity for storage of meaningful lengths of audio. 44.1kHz was the highest working frequency rate that could’ve worked efficiently with those tools.

For most music applications, 44.1 kHz is the frequency commonly used as it is the industry standard. Other than this, some more sampling rates are used for professional music or audio production work like 48.1 kHz, 88.2 kHz (nowadays used as a gold standard for high-resolution recordings producing less aliason and allowing greater freedom for mixing and mastering), 96 kHz, and 192 kHz. Though human ears cannot hear above 20,000 kHz, these audios are recorded only to pitch it down later at 44.1 kHz, which makes many inaudible frequencies audible. Meanwhile, many frequencies are lost if any audios are recorded at a sample rate lesser than 44.1 kHz.

Considerations for Sample Rate

Some considerations need to be taken while determining a sample rate:

  • Aliason is the most common error due to a very high frequency or a low sampling rate. An anti-aliasing filter looks at the user-specified sampling frequency and removes any under-sampled frequencies appearing in the signal.
  • Slew rate limit error- is the distortion that occurs when the ADC cannot convert signals rapidly. ADC is the analog-to-digital converter that converts analog signals into digital signals. For instance, sound recorded by condenser microphone or light entering a digital camera.
  • When this conversion doesn't take solace instantly, or any error occurs, that situation is known as a slew rate limit error.
  • Aperture error is the difference between the actual value of the input signal and the flat-topped sample error. Due to the lengthening of the sample, amplitude delay and distortion occurs.
  • Jitter is the deviation error from the precise sampling timing intervals.
  • Noise created from the analog circuit noise or any other source might cause an error.

Does a higher sample rate mean a better-quality recording?

Yes, a higher sampling rate means a better-quality recording. A higher sample rate will receive more slices or samples of the digital signal in a second, resulting in better audio quality. A higher audio resolution will also result in a bigger file, acquiring more space for the same audio length.

Bit depth

What is a bit depth?

In digital music, bit depth determines the signal’s dynamic range as bytes store the information on the amplitude of the sound waves. In easy to understand terms you can say that the higher the depth of bit, the more data it will be able capture ore data; and the result of sound re-creation will be even more accurate.

Some of the common bit depth examples are 16 bit, 24 bit and 32 bit. You can say that these are binary terms and they represent number of possible values. What is Amplitude in Bit Depth? Amplitude is the signal strength perceived as volume or loudness. Every wave a sample forms has a negative and a positive amplitude value.

How bit-depth impacts audio resolution?

During the ADC( Analog to Digital) process, each wave is sampled twice, and thus, thousands of snapshots are taken to reproduce the sound digitally in an accurate manner.

When sampling occurs, the amplitude received is matched to the closest digital value. No matter how many values are available, the amplitude’s digital value will not fall on any particular value but might fall between two values.

In this case, the signal’s value is rounded to the closest value. This is known as quantization error, leading to signal quantization noise. It is also known as low-level white noise or noise floor. The higher the bit depth, the more data will be stored to reproduce the sound. If the bit depth is higher, the data stored to reproduce the sound will either be very less or lost, or the resulting sound will be poor in quality. The higher the bit depth, the lower the level of the noise floor, providing a greater dynamic range and vice-versa.

The most common bit depths used are 16-bit, 24-bit, and 32-bit. Each of these bits has a certain capacity for storing information and a dynamic signal range.

For instance:

A 16-bit can store up to 65,536 levels of information with a maximum dynamic range of 96 dB A 24-bit can store up to 16,777,216 levels of information with a maximum dynamic range of 144 dB. A 32-bit can store up to 4,295,967,296 levels of information with a maximum dynamic range of 1528 dB. In these examples, it is seen that a 16-bit depth provides a dynamic range of 96 dB, whereas a 32 bit-depth provides a dynamic range of 1528 dB. The standard format is 16-bit at a sample rate of 44.1 kHz, with an audible frequency and dynamic range for general purposes. However, for professional use, a 24 bit-depth is mainly used.

Bit rate

When you talk about the digital network, the bit rate is the number of bits that can be transferred or received per second. In any file format, bit rate encodes the number of bits required to be transferred relating to the storage and size of the files. It is measured in kilobits per second (kbps) and is commonly used to describe audio stream quality for music streaming services. A higher bit rate means higher audio quality.

When you download or listen to music, you come across files with kbps written at the end. This is bitrate, for instance, 320 kbps means 320 kilobits are stored per second of audio in that file. There are three types of files in reference to audio bitrate: Uncompressed files are large files that take up a lot of space on a device with all the original information available. Examples are Wavelength Audio Format (WAV), which offers 1,411 kbps at 16-bit, and Broadcast Wave Format (BWF).

Lossy compressed files- in these files, some of the data, while converting from the original file, is permanently lost. You cannot restore this data, and further conversion leads to a degradation in the quality of the file, deteriorating the clarity and causing permanent loss of information.

Lossless files-in these files, during and after conversion from the original file, no data is lost. Examples are CDs and MP3 which are more widely available, offering a bitrate of 320 kbps at 16-bit. They can be encoded till 96kbps.

Conclusion

To sum up, these concepts of sample rate, bit depth, and bit rate are like the pillars of digital music. All three of them are equally important for a good quality output. Where the sample rate is responsible for determining the accurate frequency of the audio, the bit depth is important for the precise dynamic range. And finally, however precise the sample rate and the bit depth are, if the bit rate is low or not accurate enough, the audio quality will be lacking.

Hopefully, the explanation of the sample rate, bit depth, and bit rate helped clarify the concept of digital music.

References

https://www.headphonesty.com/2019/07/sample-rate-bit-depth-bit-rate/ https://www.adobe.com/creativecloud/video/discover/audio-bitrate.html