Digital Sound: Resolution and Sampling Frequency

Digital Sound, the difference

Every day we use computers that does not look like they are digital and sound that are stored on the hard disk can not be other than digital. On a daily basis, however, do not wonder what the digital audio. Therefore, to avoid confusion arising from ignorance, I urge you to familiarize themselves with it. You will learn about the most important parameters such as sampling frequency and number of bits

To understand the difference in the sound of analog and digital, I will cite two images. The first, which can be seen below, shows the natural sound wave in the shape of sine wave. As you can see it is a perfect sine wave, that is, runs smoothly, has a completely round shape with no corners.

Rys. 1. Sine wave.

This sine wave as a rule, we will hear the monotonous sound except that it will be a sinusoid at a sufficiently low frequencies where the period (around the time of one cycle sine wave – see picture above) will last longer, and then the human ear is able to capture the changes taking place, which will be heard in vibrations. At high frequencies, the period lasts so briefly that we are not able to catch the difference – we can hear the monotonous sound. For example, for a sine wave with a frequency of 1000 Hz the duration of one period will be less than one thousandth of a second. By the way napomnÄ™ that the wave period is shorter, the sound is higher and the period is over, the sound is lower.

Nature nature, but the computer thinks in binary, or in the system of ones and zeros. So how does the machine saves the sine wave, which is perfectly round? If your computer will be paid on a 1-bit memory, then this wave will be so corrupted:
Digital sound – 1 bi

Rys. 2. The same sine wave – this time saved by the computer by sampling 1-bit.

They are here only two possible states: ‘1 ‘, and’ -1 ‘.

For a sine wave or any other sound was recorded on a computer with greater precision, we need to take advantage of higher resolution. It’s just like with the graphics on your computer. We can have colors in 4 bits and the image will be very distorted, and we can set the colors in 16 bits or 32 bits and the picture will look fine.

Consider, as a sine wave would look at the 2-bit resolution. It gives us four possible states (22 = 4):
Bit resolutio

Rys. 3. Sine wave at a resolution of 2 bits.

There is a considerable improvement, but still a lot missing to the chart looks as it is marked with gray dots. If we were enrolled in the sound as an 8-bit, we have 256 possible levels (steps). However, today is a standard 16-bit, which gives us the possibility of up to 65,536 … How, then, look like a sinusoid saved at a resolution of 16 bits, which is commonly saying give us 65,536 “steps”? The human eye does not see the individual ‘steps’, but sees a circular sine wave, and the average human ear will hear a natural sound.

When you attend an amateur recording, audio processing, or music production, entirely 16-bit you need – plates have 16-bit audio. Today is of course possible to use 24-bit audio, with which we meet, for example, on DVD. This high resolution is recommended for professional recording, or professional music production.

Sampling frequency

At the beginning of this article, I wrote that will elucidate the two most important features of a digital audio WAVE format. While we discussed the bits responsible for the dynamics of sound (“steps”), nothing mentioned about the sampling frequency, which allows the computer describes the variation of sound in time. The unit of frequency is 1 Hz and 1 Hz corresponds to one second. 1 Hz means that the computer every one second will collect information about the sound. In other writing, computer every one second, take a sample of the sound wave. Hence the term “sampling rate” – the frequency of sampling.
Sampling frequenc

Rys. 4. Sampled sine wave with a frequency of 1 Hz.

As a result, we obtain the following entry:

Sampling frequency hz
Sampling frequency hz

Rys. 5. The same wave after sampling.

This figure again shows the highly distorted sound wave-like sound a bit (even though we used 16-bit). You can see here the importance of proper selection of the sampling frequency. The higher it is, the better the sound quality. Let us, for example, the frequency of 8 Hz (8 samples per second):
Resolution and sampling frequency of digital sound

Rys. 6. Sine wave – the sound of a 16-bit, sampling frequency of 8 Hz.

We see the improvement in this state is very far from ‘ideal’, which is to fool our ears. It is recommended that sound recording in 16 bit and 44100 Hz – CD quality.
I hope that the resolution [BIT] (vertical axis – growth rate) and the sampling frequency [Hz] (horizontal axis – time) was discussed in a manner understandable to you.
Graphs taken from:
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