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# Digital representation of sound in multimedia

Last updated on April 13th, 2019

## Digitization of sound:

**The sound** is a mechanical wave that’s **an oscillation** of pressure transmitted through a solid, liquid, or gas. The perception of sound in any organism is restricted to a particular range of frequencies (20Hz~20000Hz for humans).

The ever-changing atmospheric pressure caused by sound is translated into dynamic voltages. The unsteady pressure can be modeled as ceaselessly ever-changing numbersâ€”a function where time is the input variable and amplitude (of atmospheric pressure or voltage) is the output.

**Principles of digitization:**

When you produce a new audio file in a digital audio processing program, you’re asked to decide on

**Sampling rate**: The rate, sample rate, or frequency defines the number of samples per unit of your time (usually seconds) taken from endless signal to create a distinct signal.

**Bit depth:** Bit depth describes the number of bits of data recorded for every sample.

For CD quality, the rate is 44.1 kHz and therefore the bit depth is 16, that you may be conversant in when you illegally download music for the web

**The Nyquist Theorem:**

The Nyquist Theorem also referred to as the **sampling theorem**, is a standard that engineers follow within the transformation of analog signals. For **analog-to-digital conversion (ADC)** to lead to a trustworthy replica of the signal, slices, known as **samples**, of the analog waveform should be taken off. The number of samples per second is termed the sampling rate or frequency.

An analog signal comprises of elements at varied frequencies. The best case is that the sine wave, within which all the signal energy is focused at one frequency. Analog signals sometimes have advanced waveforms, with elements at several frequencies. The very best frequency element in an analog signal determines the bandwidth of that signal. The higher the rate of recurrence, the greater the bandwidth, if all dynamics are constant.

Suppose the highest frequency element, in **hertz**, for a given analog signal is max. According to the **Nyquist Theorem**, the rate should be a **minimum of 2fmax**, or double the highest analog frequency element. The sampling in an analog-to-digital converter is set in motion by a **clock (pulse generator)**. If the sampling rate is less than 2fmax, a number of the highest frequency elements within the analog input signal won’t be properly represented within the digitized output. Once such a digital signal is regenerate back to analog form by a digital-analog converter, false frequency elements appear that weren’t within the original analog signal. This unfavorable condition may be a type of distortion known as **aliasing**.

**Application of Nyquist Theorem:**

- The Nyquist theorem is employed to calculate the optimum rate so as to get smart audio quality.
- The CD normal rate of 44100 Hertz implies that the waveform is sampled 44100 times per sec.
- Digitally sampled audio contains a bandwidth of (20 cycle per second – 20 KHz). By sampling at double the utmost frequency (40 KHz), we tend to achieve sensible audio quality.
- CD audio slightly exceeds this, leading to an ability to represent a bandwidth of around 22050 cycles/second.