Basics of Digital Audio

Outline  Introduction  Digitization of Sound  MIDI: Musical Instrument Digital Interface

Introduction  What is Sound?  Sound is a wave phenomenon like light, but is macroscopic and involves molecules of air being compressed and expanded under the action of some physical device.  Is a form of energy produced & transmitted by vibrating matter  Travels in waves  Travels more quickly through solids than liquids or gases

Introduction  For example, a speaker in an audio system vibrates back and forth and produces a longitudinal pressure wave that we perceive as sound.  Since sound is a pressure wave, it takes on continuous values, as opposed to digitized ones  Even though such pressure waves are longitudinal, they still have ordinary wave properties and behaviors, such as reflection (bouncing),refraction (change of angle when entering a medium with a different density) and diffraction (bending around an obstacle).  If we wish to use a digital version of sound waves we must form digitized representations of audio information.

Vibration  Back and forth movement of molecules of matter

Compression - Where molecules are being pressed together as the sound waves move through matter - For example, - a wave travels through the springs just like sound waves travel through the air - the places where the springs are close together are like compressions in the air.

Sound Waves - Alternating areas of high & low pressure in the air - ALL sound is carried through matter as sound waves - Sound waves move out in ALL directions from a vibrating object

Wavelength & Frequency - Wavelength is the distance between one part of a wave and the same part of the next wave - Frequency is the number of waves moving past a point in one second

Pitch  A measure of how high or low a sound is.  Pitch depends on the frequency of a sound wave  For example, - Low pitch - Low frequency - Longer wavelength - High pitch - High frequency - Shorter wavelength

Volume  Amount of sound energy reaching your ears  Depends on:  How far the vibrating object is moving as it goes back and forth  How far you are from the source of a sound Volume Control

Sound and Instruments - Instruments can be played at different pitches by changing lengths of different parts. - For example, - Another way to make different pitches is to change the thickness of the material that vibrates.

Digitization  Digitization means conversion to a stream of numbers, and preferably these numbers should be integers for efficiency.  Fig. 6.1 shows the 1-dimensional nature of sound: amplitude values depend on a 1D variable, time. (And note that images depend instead on a 2D set of variables, x and y).  Values change over time in amplitude: the pressure increases or decreases with time.

Digitization

 The graph in Fig. 6.1 has to be made digital in both time and amplitude. To digitize, the signal must be sampled in each dimension: in time, and in amplitude.  To represent waveforms on digital computers, we need to digitize or sample the waveform side effects of digitization: introduces some noise

Digitization

Sampling Rate  The sampling rate (SR) is the rate at which amplitude values are digitized from the original waveform.(sample per cycle)  CD sampling rate (high-quality): SR = 44,100 samples/second  medium-quality sampling rate: SR = 22,050 samples/second  phone sampling rate (low-quality): SR = 8,192 samples/second  For audio, typical sampling rates are from 8 kHz (8,000 samples per second) to 48 kHz. This range is determined by the Nyquist theorem, discussed later.

Sampling Rate  The human ear can hear from about 20 Hz (a very deep rumble) to as much as 20 KHz; above this level, we enter the range of ultrasound.  The human voice can reach approximately 4 KHz and we need to bound our sampling rate from at least double this frequency. Thus we arrive at the useful range about 8 to 40 or so KHz.

Sampling Rate  Higher sampling rates allow the waveform to be more accurately represented

Nyquist Theorem and Aliasing  Nyquist Theorem: We can digitally represent only frequencies up to half the sampling rate.  Example: CD: SR=44,100 Hz Nyquist Frequency = SR/2 = 22,050 Hz  Example: SR=22,050 Hz Nyquist Frequency = SR/2 = 11,025 Hz

Nyquist Theorem and Aliasing  Frequencies above Nyquist frequency "fold over" to sound like lower frequencies.  This foldover is called aliasing.  Aliased frequency f in range [SR/2, SR] becomes f': f' = |f - SR|

Nyquist Theorem and Aliasing f' = |f - SR|  Example:  SR = 20,000 Hz  Nyquist Frequency = 10,000 Hz  f = 12,000 Hz --> f' = 8,000 Hz  f = 18,000 Hz --> f' = 2,000 Hz  f = 20,000 Hz --> f' = 0 Hz

Nyquist Theorem and Aliasing  Graphical Example 1a:  SR = 20,000 Hz  Nyquist Frequency = 10,000 Hz  f = 2,500 Hz (no aliasing)

Nyquist Theorem and Aliasing  Graphical Example 1b:  SR = 20,000 Hz  Nyquist Frequency = 10,000 Hz  f = 5,000 Hz (no aliasing)

Nyquist Theorem and Aliasing  Graphical Example 2:  SR = 20,000 Hz  Nyquist Frequency = 10,000 Hz  f = 10,000 Hz (no aliasing)

Nyquist Theorem and Aliasing  Graphical Example 2:  BUT, if sample points fall on zero-crossings the sound is completely cancelled out

Nyquist Theorem and Aliasing  Graphical Example 3:  SR = 20,000 Hz  Nyquist Frequency = 10,000 Hz  f = 12,500 Hz, f' = 7,500