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Sampling rate

The sample rate is an index for converting analog data such as speech into a digital signal and indicates how many times a sample of information is measured per second.

The unit is Hertz (Hz). Also called “sample rate” or “sample rate.” In most security cameras and surveillance camera systems, recording is done using the linear PCM method. The quality of recorded audio is highly dependent on the sample rate (Hz) and bit rate (bps / bit), but the amount of data is overwhelmingly less than that of motion pictures, so if you are concerned about the balance between quality and quantity of data It can be said that there is no such thing.

On the other hand, the standard for general music CDs was decided in the early 1980s, and the sample rate is 44.1 kHz and the bit depth is 16 bits. In other words, 1,411,200 bits of information are recorded per second. If this is converted to 60 minutes, it will be converted to 5,080,320,000 bit data ≒ 635 MB (megabytes). This is called uncompressed linear PCM recording, but of course the data capacity is too large in the uncompressed state, so when recording with a security camera or surveillance camera, this data is compressed and they record. The amount of data is compressed to approximately 1/10 to 1/30 by processing such as lossy compression that removes data that is outside the human audible range.

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This is the only analog term you should know

Sampling rate

The sampling rate is the number of sampling processes performed per second in an A / D converter that converts an analog signal into a digital signal. Also called sample rate, sample rate, or sample rate. The unit is sample / second (sps) or Hz.

A / D converters have two crucial functions. One is resolution. The other is this sample rate. The resolution represents the precision of the conversion in the direction of the voltage axis (vertical axis) and the sample rate represents the precision of the conversion in the direction of the time axis (horizontal axis). Therefore, the higher the performance (the higher the performance), the better the performance.

Input signals of fs / 2 or less can be sampled
Higher sample rates allow faster analog input signals to be converted to digital values. However, there is a limit to the frequency of the analog input signal that can be converted. If the sampling frequency is fs, the frequency that can be sampled is fs / 2. Below this frequency, it is possible to restore the original analog input signal after sampling. This relationship is called the sampling theorem (sampling theorem) and the frequency of fs / 2 is called the Nyquist frequency.

What sample rate do you need? It depends on the application the A / D converter is applied to. For example, tens of k to several M samples / sec (Hz) for audio equipment, tens to hundreds of M samples / sec (Hz) for audio processing equipment. pictures and tens to several G samples for communication equipment. The A / D converter is used for / sec (Hz), several k to several M samples / sec (Hz) for high precision measuring instruments, and several tens of M to several G samples / sec (Hz) for measuring instruments. Of high speed.

Currently, as a high-speed A / D converter, an IC with a high sampling rate of several Gsample / sec is marketed. For example, Texas Instruments (TI) “ADC12D1800RF”. The resolution is 12 bits. It integrates two A / D converters with a high sampling frequency of 1.8 Gsample / sec. By interleaving (time division) operation, it can be used as a 3.6 Gsample / sec A / D converter, and also as a dual A / D converter operating at 1.8 Gsample / sec. For broadband communication equipment, radar equipment, test / measurement equipment, etc.

The problem of finding the length of recordable audio

Audio is sampled 11,000 times per second, and each sampled value is recorded as 8-bit data.

At this time, what is the maximum length of audio that can be recorded in flash memory with a capacity of 512 x 10 6 bytes?

A 77 B 96 C 775 D 969

Next is the question of finding the length of audio that can be recorded. With the knowledge acquired so far, you can easily find a calculation method. The way of thinking when calculating is shown below.

Since 11000 samples are taken per second and each one is recorded as 8 bits = 1 byte of data, the amount of data per second is 11000 x 1 = 11000 bytes.
Since the capacity of the flash memory is 512 x 10 6 bytes, data of 512 x 10 6 ÷ 11000 = 46545.45 … seconds can be recorded.
Since the answer is obtained in minutes, 46545.45 … ÷ 60 = 775.75 … minutes.
Since the question says “maximum number of minutes”, the maximum is 775 minutes rounding down the fraction of 775.75 …, and option c is the correct answer.

correct answer hare

Problem finding the sampling interval
Question 4 (Fall 2016)
When the audio was sampled using the PCM method, converted to 8-bit digital data and transferred in real time without compression, the transfer rate was 64,000 bits / sec. How many microseconds is the sampling interval at this time?

A 15.6 B 46.8 C 125 D 128

Now the question is to find the sampling interval (how many seconds to sample).

The “transfer rate” is involved, but since the audio was transferred in real time, 64000 bits / second is the same as the encoded capacity per second. Once you know that, you will be able to find a calculation method with the knowledge you have gained so far.

The way of thinking when calculating is shown below.

Since there are 64000 bits per second and the size of the encoded data is 8 bits, the number of samples taken per second is 64000 ÷ 8 = 8000 times.
Since 8000 samples were taken per second, the time interval is 1 ÷ 8000 = 0.000125 seconds.
Since the question is “how many microseconds?”, The correct answer is 125 microseconds, which is 0.000125 seconds in microseconds.

correct answer hare

Problem finding buffering time
Q31 (Fall 2014)
To play 2.4 Mbytes of audio data at 192 kbit / s encoding speed without interruption during downloading using a network with 128 kbit / s communication speed, buffering the data before the start of playback How many seconds do you need in less?

A 50 B 100 C 150 D 250

Finally, let’s fix an issue with a slightly different coat color. Finding the buffering time when downloading digitized audio data is a problem.

Buffering is downloading some data before starting to play. This allows you to play the audio without interruptions, even if the download speed is slow.

The idea when calculating is shown below, so please check each one carefully. Here, M = 1000 k.

A code rate of 192 kbits / s means that the amount of digitized data is 192 kbits per second.
The total amount of data is 2.4 Mbytes = 2.4 M x 8 = 19.2 M bits, which is expressed in seconds as 19.2 M ÷ 192 k = 19200 k ÷ 192 k = 100 seconds.
Since the communication speed is 128 kbit / s, data of 128 k x 100 = 12800 kbit can be transferred in 100 seconds.
However, since the total data capacity is 19.2 Mbit = 19200 kbit, the difference of 19200 kbit – 12800 kbit = 6400 kbit of data must be buffered beforehand.
Since the communication speed is 128 kbit / s, it takes 6400 k ÷ 128 k = 50 seconds to buffer the 6400 kbit data.
From the above, the buffering time is 50 seconds and option A is the correct answer.

Sampling, quantification, coding

The computational problem of voice sampling is to convert analog data (smooth and continuous data), such as raw speech and music, into digital data (discontinuous and discontinuous data) that can be processed by a computer.

In a familiar example, music recorded on a CD (compact disc) is analog data converted to digital data.
Aim to solve speech sampling computational problems, to understand the term “sampling”, “quantization”, “encoding”. Let’s use a general CD as an example to explain the meaning of each term.

What is “sampling”?
It consists of collecting data from analog signals by dividing them at regular time intervals. This time interval is called the “sample rate” and is expressed in units of Hz (Hertz). Once per second is 1 Hz.
The sampling frequency of the CD is 44.1 kHz (kilohertz) and the data is collected 44.1 x 1000 = 44100 times per second.
What is “quantification”?
It consists of converting the data collected by sampling into numerical values. The magnitude of this number is called the “quantization bit number”.
The number of quantization bits on a CD is 16 bits (16 digits in binary).
What is “encode”?
It consists of putting the numerical value obtained by quantification in a specific format. The “PCM (Pulse Code Modulation)” format encodes 16-bit quantized data in its original form.
Once you understand the meaning of the terms, as an example of the calculation, the amount of data when digitizing music with a 5-minute playback time at 44.1 kHz sample rate, 16-bit quantization bit number, PCM format, stereo (2ch), Let’s find it in units of M-byte (megabyte). Here, 1 Mbyte = 1,000,000 bytes. The way of thinking when calculating is shown below.

It is just a multiplication, but understand the method of calculation by associating it with the meaning of the term.

Five minutes of playing time is 5 x 60 = 300 seconds.
Since the sample rate is 44.1 kHz, the data is collected 44.1 x 1000 = 44100 times per second.
Therefore, the data is collected 300 x 44,100 = 13230,000 times in 5 minutes.
The number of 16-bit quantization bits is 8 bits = 1 byte, so 16 bits = 2 bytes.
Since it is in PCM format, this 2-byte data is converted to the code as is.
Since a data collection is a 2-byte code, 13230,000 data collections have a capacity of 2 x 13230000 = 26460000 bytes.
Since it is stereo (2 channels), there are two data of the same capacity (one for the left channel and one for the right channel), and the total capacity is 26460000 x 2 = 52920000 bytes.
Since 1 Mbyte = 1,000,000 bytes, 5,292,000 bytes = 52.92 Mbytes.
PR
The problem of finding the amount of data
Q26 (Spring 2012)
If a 60-minute (monaural) audio signal is digitized using the PCM method with a 44.1 kHz sample rate and 16-bit quantization bit rate, how many Mbytes of data are there? Here, the data is assumed to be uncompressed.
A 80 B 160 C 320 D 640

Let us now solve the above problem of speech sampling. The first is a problem that can be solved with the same procedure as in the calculation example shown above. The way of thinking when calculating is shown below.

M (mega) can be 1000 x 1000 = 1000000 or 1024 x 1024 = 1048576, which is not shown in this number. Here, it is calculated as 1,000 x 1,000 = 1,000,000.

The audio signal for 60 minutes is 60 x 60 = 3600 seconds.
Since the sample rate (sample rate) is 44.1 kHz, the data is collected 44.1 x 1000 = 44100 times per second.
Therefore, 3600 x 44100 = 158760000 times of data collection in 60 minutes.
The number of quantization bits is 16 bits, which is 8 bits = 1 byte, so 16 bits = 2 bytes.
Since it is in PCM format, this 2-byte data is converted to the code as is.
Since a data collection is a 2-byte code, data collections 158760000 have a capacity of 2 x 158760000 = 317520000 bytes.
Being monaural (not stereo), the total capacity is 317520000 bytes.
Given that 1 Mbyte = 1,000,000 bytes, 317520000 = 317.52 Mbytes.
Since the question says “how many Mbytes?”, The correct answer is 320 Mbytes, which is close to 317.52 Mbytes.

Sampling rate

In the separate article “Bit rate and bus width” and “Notes on reducing the bit rate”, we presented the history of the “bit rate”, which is the vertical axis of graph paper during PCM sampling.

This section considers the “sample rate” of the horizontal axis.

Maximum frequency that can be sampled (Nyquist frequency)

With the PCM method, exactly half the sample rate is the maximum recordable rate. This value is also called the “Nyquist frequency”.
For CDs recorded at a sampling frequency of 44.1 kHz, half, 22.05 kHz, is the theoretical maximum recordable frequency.

Now half the sample rate is the maximum recordable rate, and the reason is … Seeing is believing, see the figure to the right.
To represent a cycle of a sine wave, you must draw up and down round trips using at least two samples.

Alias ​​noise: frequencies higher than recordable

But what if a signal with a frequency higher than the Nyquist frequency enters the A / D converter?

See the graphic to the right.

While the input signal performs “3 round trips with 4 samples”, the resolution of the horizontal axis (measurement frequency) of the A / D converter is too low to correctly follow the movement of the signal. The sampled values ​​draw a “one round trip with four samples” waveform, which is significantly lower than the input frequency. Once again, the original signal is “manufactured” in the digital domain.

In this way, an input signal with a frequency higher than the Nyquist frequency is the source of a signal with a lower frequency than it should be, called “alias noise.”

Alias ​​noise is also called “envelope noise” because it occurs at a frequency lower than the Nyquist frequency by the amount that the original signal exceeds the Nyquist frequency, as shown in the graph to the right. The alias noise that wraps around and reaches 0Hz continues to be wrapped between 0Hz and the Nyquist frequency so that it is reflected back.

Actually, the A / D converter contains a low pass filter to prevent such alias noise, so alias noise is not a problem when recording analog signals.

However, handling alias noise can be important when using plugins. The next section explains this point.

Do you need a high sample rate?
When starting to record or compose with a DAW, how to set the sample rate of the project is a difficult place. Unlike the bitrate above, once the sample rate is set, it is difficult to change it later.
It is generally said that the higher the sample rate, the higher the quality of the master that can be produced without damaging the original sound, but the PC specs required during work will also improve dramatically.
But is there any merit in editing at a high sample rate, like when the final medium is a 44.1 kHz CD? Also, can you ignore the difference in sample rate based on the trend of the sound you are looking for, such as the genre you are dealing with?

The bottom line is that when you use harmonic effects like saturators and compressors in your DAW, the sample rate setting can have a significant effect.

Next, we’ll use an ultrasound to consider how the project’s sample rate will change.

The first is a single scan signal sonogram. You can see that the frequency of the sine wave gradually increases from 0 to 22 kHz.

Let’s add a distortion effect to this.
In each case, the signal with the effect applied is exported in projects with different sample rates, and then the file is converted to 44.1 kHz.
All effects use the same preset.
Note that the files themselves that are comparing sonograms are all 44.1 kHz.

Sample, sample rate, sample format, and bit rate

The main function of the audio interface is to convert the signal between analog and digital formats.

As mentioned above, real sounds have endless possibilities for pitch, volume, and duration. Computers cannot process infinite information, so audio signals must be converted before they can be used.
Computer approximated waveform
Source: pcm.svg http://commons.wikimedia.org/wiki/File:Pcm.svg Retrieved from.
Figure 1.1 Computer approximated waveform

The figure in Figure 1.1, “Computer approximated waveforms” illustrates the situation. The red waveform shows the sound waves produced by the singer or acoustic instrument. The computer cannot handle the gradual change of the red waves. The computer should use the approximation shown in the gray shaded area of ​​the figure. This figure is an exaggerated example and does not represent the actual recording.
Converting between analog and digital signals reveals the difference between low-quality and high-quality audio interfaces. The sample rate and sample format control the amount of audio information stored by the computer. The more information that is stored, the better the audio interface can approximate the original microphone signal. The possible sample rates and sample formats determine only a part of the quality of the sound produced or obtained by the audio interface. For example, an audio interface built into the motherboard can support 24-bit sample formats and 192 kHz sample rates. On the other hand, a professional-grade FireWire-connected audio interface with a 16-bit sample format and 44.1 kHz sample rate may sound better.
1.3.1. Shows
A sample is a unit of audio data. The computer stores video data as a series of still images (each called a “frame”) and displays them one at a time at a specified speed (called a “frame rate”). The computer stores audio data as a series of still sound images (each called a “sample”) and plays them back one at a time at a specified frequency (called a “sample rate”).
There are not many types of frame formats and frame rates that are used to store video data. There are many types of sample formats and sample rates that are used to store audio data.

Frequency used for audio (sample rate, PCM, DSD, etc.)

On this occasion, I would like to explain the frequencies used in digital audio and their meanings.

 

 

Recently, the high-resolution sound source has increased, such as 192KHz Toka, 11.2MHz, as the frequency has been written or will, what frequency?

I would like to explain the frequency used for said audio taking as an example the Combo384 installed in the USB-DAC used in LV2.0.

1. 1. What is the sampling frequency?

Music distribution is becoming mainstream these days, but audio was first digitized on CDs, which are still on the market.

You often hear that the sample rate of a CD is 44.1KHz. Since digital signals are basically 0 or 1, to reproduce up to the 20 KHz limit that can be heard by the human ear, a resolution of twice that frequency is required. Furthermore, the frequency was decided to be 44.1 KHz taking into account the digital signal processing margin. Since a musical signal is a set of sine waves, it is 44.1 KHz that can fluctuate at a maximum frequency of 20 KHz.

2. What are 16 bits and 24 bits?

As you may hear often, CDs are sometimes described as 44.1KHz / 16bit. This 16 bit is the volume of the sound. Since 16 bits can express the size of 2 raised to 16, there are 65536 different sizes.

Converting this to dB is 20LOG (65536), which is approximately 96 dB. The dynamic range of a CD (the difference between low and loud sounds) is 96 dB.

For DVD and Hi-Res, it can be 24-bit, but in this case, it’s 16.77 million steps of 144 dB.

3. 3. PCM format

So what is the actual signal? In the case of the PCM format, the standard called I2S, which can support up to 32 bits in sample rate, is common. In the case of a CD, being stereo, the data has a frequency of 44.1 KHz with 2 channels (L, R) alternately 32 bits (although in reality 16 bits are used).

Therefore, to process this digitally, a processing capacity of 44.1KHz x 2CH x 32bit = 2.8224MHz is required.

Bitrate

In communication, it indicates how many bits of data are transferred per hour and is generally expressed in bps (bit / s) of how many bits are transferred (processed) per second.

If it is low, the size when saving as a file is small and there is space on the transmission line for communication. For example, when an audio (1 channel) is compressed to 1/3, the 3 channel audio can be sent at the same bit rate. Excuse the old story, but considering the age of analog communication (analog cell phones), digitizing + compression will support multiple calls with the same radio waves.

Finally
I often hear what is called Hi-Res Audio. The sampling frequency is said to be 96 kHz or 192 kHz, which is above 48 kHz, the number of quantization bits is 24 bits, and the limit (high range) of human hearing is about 20 kHz, but it expresses frequencies higher than that. It will be. It is the same bit rate as the image from a long time ago. .. ..
By the way, it seems that dogs can hear up to 60 kHz and cats up to about 64 kHz.

Hi-Res Example (Hi-Res Audio)
Sampling frequency Number of quantization bits Number of channels bit rate Frequency that can be expressed
192 kHz twenty-four 2 9.216 kbps 96 kHz
192 kHz 16 16 2 6,144 kbps 96 kHz
96 kHz twenty-four 2 4.608 kbps 48 kHz
96 kHz 16 16 2 3,072 kbps 48 kHz
48 kHz twenty-four 2 2,304 kbps 24 kHz
Considering the limit of human hearing (around 20 kHz), according to the sampling theorem, 48 kHz or 44.1 kHz is a sufficient frequency, but what about all of them? .. ..
In my case, I cannot distinguish the high resolution range, but it should be able to reproduce the discarded frequency at 48 kHz to 96 kHz, and when the number of quantization bits is in the 24-bit range, the sound pressure (dB) is a bit. Feels like I’m going up (?) (It’s just my ears).
I’d like to make a comparison if I get a chance, but I feel like I can’t say by ear that I don’t have a proper regenerator (like an expensive analog amp).

Is it finally time for cats and dogs to get verified in the acoustics industry? .. ..

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Sample rate and bit rate

I wrote over audio files last time, but if you reduce the file size (code at a lower bitrate), the sound quality tends to deteriorate. How much should it really be? .. ..

When compressing using audio encoding (AAC, MP3, etc.), the compression rate is determined by the bit rate at the time of encoding. Specifically, if you set a low bitrate, the compression rate will be higher and the file size when saved will be smaller, but first, what is the bitrate for the uncompressed original sound source (PCM) ?
If you save it as PCM, the sound quality will be the original sound, but it may be a little inconvenience to save it without worrying about the file size. Also, depending on the application, I think the memory capacity is sufficient even for the size of the original sound, and the communication speed is good. Therefore, I would like to write about the sample rate and bit rate that are often heard in digital audio.

The bit rate of digital audio is determined by the sampling frequency, the number of bits assigned to a sample (number of quantization bits), and the number of channels (stereo, monaural, etc.).

PCM bit rate (uncompressed) = sample rate x number of quantization bits x number of channels
As I wrote a bit last time, for example in file containers like wav and mp4 format, this information is attached as a header, so that the application can see the header and play it. The compression rate of the encoding is determined by the bit rate specified at the time of encoding for this PCM (uncompressed) bit rate.
For example, as many of you know about music CDs, with 44.1 kHz stereo, this is the next bit rate.

Music CD bit rate: 44100Hz x 16bit x 2ch (stereo) = 1411.2kbps
When encoding this with MP3, AAC, etc., it is natural to specify a bitrate lower than 1411.2 kbps. For example, when encoding at 256 kbps, the compression rate is approximately 18% when the original sound is 100% and the file size is 1/5 or less.

Encode Music CDs at 256 kbps: 256 kbps / 1,411.2 kbps = approximately 18%
Generally, the sample rates of audio devices actually connected to PCs are 48 kHz and 44.1 kHz for music, 16 kHz and 8 kHz for audio such as microphones and headphones, and 32 kHz, 24 kHz, 22.05 kHz. , etc.

The bit rate of PCM (uncompressed sound source) with 16-bit quantization bits is as follows.

Stereo (for music) PCM 16-bit bit rate (example)
Sampling frequency Number of quantization bits Number of channels Bit rate Comments
48 kHz 16 16 2 1,536 kbps
44.1 kHz 16 16 2 1,411.2 kbps Music CD
32 kHz 16 16 2 1,024 kbps
24 kHz 16 16 2 768 kbps
22.05 kHz 16 16 2 705.6 kbps
16-bit monaural PCM bit rate (for audio) (example)
Sampling frequency Number of quantization bits Number of channels Bit rate Comments
32 kHz 16 16 1 512 kbps Super Wide Band
24 kHz 16 16 1 384 kbps
16 kHz 16 16 1 256 kbps Broadband
8 kHz 16 16 1 128 kbps Narrowband

Sampling rate
If you check the web, there are explanations like the sampling required to convert analog waveforms to digital conversion. For example, it shows how many samples of an audio signal input from a microphone are taken per second and digitized. The larger the sample, the greater the range that can be recorded. When an analog waveform is digitized, the frequency that can be expressed is half the sampling frequency (sampling theorem). For example, with a sampling frequency of 48 kHz, it is possible to express up to 24 kHz. At 8 kHz (narrow band) and 16 kHz (wide band), which are often used for audio, you can only hear up to 4 kHz and 8 kHz, respectively. The higher the sample rate, the higher the bit rate.

Sampling theorem
It is a very simple explanation, but it can express up to half the sample rate. When sampling a signal, if the interval is small, it can be restored close to the original signal, but if it is too thick, it cannot be restored (I would like to write a little more detail when talking about signal processing or other time).

44.1 kHz
Why is the rate of 44.1 adopted, which is not well separated? .. ..
Isn’t the technician deliberately wearing a pesky watch to prevent music CDs from being easily copied? I heard something like that. When I searched, it seems this happened (?) Due to the convenience of an old PCM recorder. In this age, it is difficult to know what 44.1 kHz is in development. 44.1 kHz sampling conversion

Sampling theorem

It is a very simple explanation, but it can express up to half the sample rate.

 

When sampling a signal, if the interval is small, it can be restored close to the original signal, but if it is too thick, it cannot be restored (I would like to write a little more detail when talking about signal processing or other time).

44.1 kHz
Why is the rate of 44.1 adopted, which is not well separated? .. ..
Isn’t the technician deliberately wearing a pesky watch to prevent music CDs from being easily copied? I heard something like that. When I searched, it seems this happened (?) Due to the convenience of an old PCM recorder. In this age, it is difficult to know what 44.1 kHz is in development. The 44.1 kHz ↔ 48 kHz sampling conversion is a headache. For example, USB audio (USB audio device class) exchanges data at 1 ms intervals. In the case of 48kHz, the data is 48 samples, but when considering 44.1kHz, it will be 44 samples (x9) and 45 samples (x1) in 10ms. If you cheat on a sample when there are 45 samples (tentatively), it will be 44.0kHz. I think it’s more like that with voice and music, and I think the human ear is mostly misleading (it’s just my personal opinion).
However, with an objective evaluation method, it will soon come to light. For example, you can see that you were clearly fooled by a sine wave (sine wave) (maybe you are unexpectedly on the market).

Number of quantization bits
The sampling had to take a value in the direction of time (discretization), but the quantization had to take a value in the direction of amplitude. The range that it is possible to display the volume of the sound, which is often heard, “96 dB dynamic range” means that the number of quantization bits is 16 bits, and the music signal is played in the range of 0 to 65535. I can do it. The number of quantization bits is also called the bit depth or bit depth.

Bitrate
In communication, it indicates how many bits of data are transferred per hour and is generally expressed in bps (bit / s) of how many bits are transferred (processed) per second. If it is low, the size when saving as a file is small and there is space on the transmission line for communication. For example, when an audio (1 channel) is compressed to 1/3, the 3 channel audio can be sent at the same bit rate. Excuse the old story, but considering the age of analog communication (analog cell phones), digitizing + compression will support multiple calls with the same radio waves.

Finally
I often hear what is called Hi-Res Audio. The sampling frequency is said to be 96 kHz or 192 kHz, which is above 48 kHz, the number of quantization bits is 24 bits, and the limit (high range) of human hearing is about 20 kHz, but it expresses frequencies higher than that. It will be. It is the same bit rate as the image from a long time ago. .. ..
By the way, it seems that dogs can hear up to 60 kHz and cats up to about 64 kHz.