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					Digital Audio

• What is digital Audio? • What are the main differences between a digital and analogue audio signal? • What is the Nyquist Theorem?

Digital Audio
• Digital audio is simply an alternative means of carrying the same air pressure variation information as an analogue audio signal • Numbers are used to represent the changes in air pressure, the numbers are usually handled in binary format

Why use digital audio?

Why use digital?
• Analogue audio is vulnerable to being distorted or picking up stray signals (noise), particularly while travelling through cables or being recorded onto magnetic tape

Why use digital?
• Digital audio is only vulnerable when being converted from analogue: the audio is represented by a steady stream of numbers which are unambiguous and robust • Although digital is usually more expensive than analogue, now it is almost on par and in some cases more cost effective than analogue

Digital Evolution

Digital Evolution
• Digital audio evolved from the telephone industry • Professional digital products first appeared in the late 1970’s: The Sony PCM-F1 recorded onto video cassettes

Digital Evolution
• As technology is developed for computers, this is applied to digital audio so the pace of development is very rapid • In particular, computer storage devices have become so cheap and readily available that they are an appealing candidate for storing digital audio (which consumes a lot of storage) • Faster computing devices and custom chips have made it possible to reduce the space required by audio signals for storage and transmission. This has minimal impact on the quality of the sound

Conversion from analogue to digital

Conversion from analogue to digital
• At present, analogue microphones are the only sources for gathering acoustic sounds • Therefore we have to be able to convert analogue voltage variations into digital form if digital audio is to be stored or processing is to be done

Conversion from analogue to digital
• The sound quality is determined by two things
– the precision of the measurements – the speed at which these are taken

• The measurements are called ‘samples’ and the rate at which these are taken is called the ‘sampling rate’

Conversion from analogue to digital
• A typical precision for audio samples would be 16 bits • A typical sampling rate would be 48kHz or about one sample every 21 millionths of a second • The highest quality realistically possible is a precision of 22 bits (one part in 4,000,000) and a sampling rate of 100kHz

Conversion from analogue to digital
• Sampling at a rate of 40 kHz is enough to convert signals of up to 20kHz, the widely agreed limit of human hearing • The CD sampling rate is 44.1kHz and the standard ‘pro’ sampling rate is 48kHz

• The telephone sampling rate is 8kHz since the most useful intelligibility elements of the human voice reside below 3.4kHz
• Specially designed chips are used to perform the conversion from analouge to a digital number

Digital Audio | Binary representation
• A binary digit is abbreviated to ‘bit’ • Instead of 0 to 9 as in decimal the range of values is 0 to 1 • As in decimal, each digit rises in ‘weight’ as you move from right to left. • in decimal the digit weights rise by multiples of 10’ in binary this rises in multiples of 2.

Binary representation
• Four bits can represent any decimal number from 0 – 15 • Each addition bit doubles the range of numbers that can be represented, so five bits can represent any decimal number from 0to 31

• Eight bits can represent any decimal number from 0 to 255 commonly referred to as ‘bytes’. These are useful for many things including Telephone and multi-media application audio. • However they are insufficient for representing the positions on a microphone diaphragm.

Binary representation
• 16 bits can represent 65,536 possible speaker cone or microphone diaphragm positions. • This is enough for very high quality audio (provided that the samples are taken at a high enough rate) • The current maximum resolution used in analogue to digital conversion is 24 bits. • This equates to 16,777,216 positions. However the last four bits of the converted value are not trustworthy; they are only approximate. nobody has manufactured a converter accurate to more than 20 bits.

Explanation of 44.1 kHz CD sampling rate
• The CD sampling rate has to be larger than about 40 kHz to fulfill the Nyquist criterion • The sampling frequency is chosen somewhat higher than the Nyquist rate since practical filters needed to prevent aliasing have a finite slope. • Digital audio tapes (DATs) use a sampling rate of 48 kHz. It has been claimed that their sampling rate differs from that of CDs to make digital copying from one to the other more difficult. • 48 kHz is, in principle, a better rate since it is a multiple of the other standard sampling rates, namely 8 and 16 kHz for telephone-quality audio. Sampling rate conversion is simplified if rates are integer multiples of each other.

Bit Depth

Binary Numbers
• All digital information is stored as binary numbers. • The numbers of bits used to store the data, will determine the resolution of our data • For sound this means, how accurately we can record minute amplitude changes

Binary Numbers
• A sample is essentially a "snapshot" of the instantaneous amplitude of a sound, and that snapshot is stored as a binary number. • When we talked about sampling, we made the point that the faster you sample, the better the quality (we get a more accurate picture of the sound wave)

• The faster the sampling rate the higher the resolution in time

Bit Width
• The faster our sampling rate, the more media space it consumes and storage space is needed on the computer.

• The more bits you use when sampling the more hard disk you need.

Bit Width
• High sample rates and bits eat up storage space • 64 bit numbers are capable of storing extraordinary details and sampling at a rate of 100khz would give us great resolution in time, but our digitally stored numbers would be huge.

Bit Width
• we have to make some decisions balancing our need for accuracy and sonic quality against our space and storage limitations.

Bit Width
• For example, suppose we only use the values 0, 1, 2, and 3 as sample values. • This would mean that every sample measurement would be "rounded off" to one of these 4 values. • This would be a pretty inaccurate recording

Bit Width
• But on the other hand, each sample would then be encoded using only a 2 bit number. • Leaving lots of storage space!!!!!!!!! • Using only these 4 numbers would probably mean that sample values won't be distinguished all that much and the sound would be extremely poor.

Bit Width
• While speed is important — the more "snapshots" we take of a continuous function, the more accurately we can represent it

• There's another factor which seriously affects resolution, the resolution of the actual number system we use to store the data.

Bit Width
• In the example above, with only four numbers available (say, 0, 1, 2,3), every value we store has got to be one of those three numbers. • We'll basically be storing a bunch of simple square waves. • We'll be turning highly differentiated, continuous data into non-differentiated, overly discrete data.

Bit Width

An example of what a 3 bit sound file might look like (8 possible values).

An example of what a 6 bit sound file might look like (64 possible values).

Bit Width
• In computers, the way we describe numerical resolution is by the size, or number of bits, used for number storage and manipulation.

• The number of bits used to represent a number is referred to as its bit width. • It's also more often referred to as bit depth or word length in audio lingo.

Bit Width
• Bit width (or depth) and sample speed more or less completely describe the resolution and accuracy of our digital recording.

Bit Width
• Common bit widths used for digital sound representation are 8, 16, 24 and 32 bits. • As we said, more is better: 16 bits gives you much more accuracy than 8 bits, but at a cost of twice the storage space.

Bit Width
• • • • • • • 4 bits 8 bits 16 bits 1024 bytes 1000 K 1000 MB 1000 GB 1 nibble 1 byte (2 nibbles) 1 word (2 bytes) 1 kilobyte (K) 1 megabyte (MB) 1 gigabyte (GB) 1 terabyte (TB)

Synthesis
• Audio synthesis is the art and science of generating audio signals. • A synthesiser is an electronic instrument capable of producing musical sounds • A strong understanding of timbre is key to being able to synthesize sounds

Timbre
• In music, timbre, also timber is the quality of a musical note or sound that distinguishes different types of sound production or musical instruments.

• For example, timbre is what, with a little practice, people use to distinguish the saxophone from the trumpet in a jazz group, even if both instruments are playing notes at the same pitch and amplitude.

Timbre
We can look at timbre as being composed of two basic ideas. (This is a simplification but fine for our needs) 1. Spectral Content

2. Amplitude Envelope

Spectral Content
• Spectral Content • What are the different individual frequencies that make up the spectrum of our sound? • How are they related to each other?

Spectral Content
• The sine wave is very simple. It is a fundamental vibration. • Real sounds can be seen as being composed of many different sine waves of different frequencies and amplitudes all added together. • Musical sounds tend to have harmonically related components.

Spectrum. A definition
• The Spectrum of a sound is the FREQUENCY content of a sound or audio SIGNAL • This is often displayed as a graphic representation of amplitude (or INTENSITY LEVEL) against frequency. • Three-dimensional displays of a spectrum add the time variation on the third axis (see below). • The spectrum of a sound is a primary determinant of its perceived TIMBRE.

A harmonic spectrum

Amplitude Envelope
• How does the sound as a whole evolve over time? • A simple envelope we see in synthes is attack, decay, sustain, release

Amplitude Envelope
• Attack, decay, sustain and release • The first part of the envelope is called the attack. • How long it takes to go from silence to the maximum volume. A drum and a piano usually have short attack times. • The next section is called decay. • During the decay section the amplitude would decrease from the maximum level to some constant level. Drums have short decay times, a piano might have a slightly longer decay time and a horn longer still. • The sustain level is a constant level that the sound maintains during the middle part of the sound. • The final part of the envelope is called the release. The release time is the time it takes the sound to fade from the sustain level to silence.

Amplitude Envelope

Amplitude Envelope
• Of particular importance to the timbre of a sound is the attack and the decay. • Experiments where the attack and decay of a recorded sound have been removed have shown listeners have difficulty identifying the instrument.

Synthesis
• Armed with a basic understanding of timbre we are ready to look at synthesising tones • We now know that our task may be broken into two parts 1. Create a dynamically changing spectrum 2. Pay attention to the amplitude envelope

Synthesis type 1 Additive Synthesis
Additive synthesis emulates timbres by: 1. combining numerous waveforms pitched to different harmonics 2. with a different amplitude envelope on each 3. along with inharmonic artifacts.

Synthesis type 1 Additive Synthesis
• Usually, this involves a bank of oscillators (is an
electronic circuit that produces a repetitive electronic signal,
often a sine wave)

tuned to multiples of the base

frequency. • Often, each oscillator has its own customizable volume envelope, creating a realistic, dynamic sound that changes over time.

some examples
• A classic additive synthesizer was the Synclavier. Released 1975 • Developed at Darthmouth College, manufactured by new England Digital • The pipe organ may also qualify as an additive synthesizer because its pipes generate sine waves when blown, which are added to each other to generate tones.

some examples
• More contemporary popular implementations of additive synthesis include the Kawai K5000 series of synthesizers in the 1990s • more recently, software synthesizers such as the Camel Audio Cameleon, the VirSyn Cube, White Noise WNAdditive, and the ConcreteFX softsynth Adder.

Kawai K5000 is a series of digital synthesizers manufactured by Kawai Musical Instruments of Japan. It was introduced in 1996

Additive synthesis

Subtractive/Analog Synthesis
• Subtractive synthesis is a method of subtracting harmonic content from a sound via sound synthesis, characterised by the application of an audio filter to an audio signal.

Subtractive/Analog Synthesis
• For example, taking the output of a sawtooth generator and using a low-pass filter to dampen its higher partials generates a more natural approximation of a bowed string instrument than using a sawtooth generator alone.

Subtractive/Analog Synthesis
• In this type of synthesis we begin with a rich waveform. • We then use filters to remove parts we do not want. • Add dynamics using LFOs (an audio signal usually
below 20 Hz which creates a pulsating rhythm rather than an audible tone) to

modulate filter and oscillator

parameters.

Subtractive/Analog Synthesis
• • • • Typically, the complexity of the source signal the cut-off frequency and resonance of the filter are controlled in order to simulate the natural timbre of a given instrument.

Subtractive/Analog Synthesis
• Subtractive synthesis is historically associated with analogue voltage controlled synthesizers such as the Moog synthesizer due to the simple circuitry required to generate the most common source signals: square waves, pulse waves, sawtooth waves and triangle waves.

Subtractive/Analog Synthesis
• Modern digital and software synthesizers may include other, more complex waveforms or allow the user to upload arbitrary waveforms.

• Some synthesizers may use a form of pulse width modulation which dynamically alters the source for a richer, more interesting, more organic tone.

Subtractive/Analog Synthesis
• • • • • • Key terminology in analog synthesis VCO - Voltage controlled oscillator VCA - Voltage controlled amplifier VCF - Voltage controlled filter LFO - Low frequency oscillator whats with all this voltage control? more later.

Amplitude Modulation/ Ring Modulation
• Amplitude Modulation (AM) Synthesis is performed by combining two signals together. • A source audio signal, the carrier, is multiplied by a modulation signal. • This process is typically used to alter the carrier signal in one of two ways.

AM Synthesis / Ring modulation
• The modulation signal can be used as an envelope which is applied to the carrier signal to determine the audio signals amplitude over time.

• AM synthesis used to apply an amplitude envelope.

AM Synthesis / Ring modulation
• The modulation signal can be also be used to quickly cycle the carrier signal's amplitude to form two additional frequencies known as sidebands, forming harmonic or non-harmonic sounds.

• AM synthesis is used to add sidebands.

FM Synthesis Frequency Modulation
• A very powerful technique. • Very fast vibrato. Creates a theoretically infinite number of sidebands. • Invented by John Chowning in 1967.

FM Synthesis Frequency Modulation
• Frequency Modulation (FM) Synthesis produces an output signal by oscillating the frequency of a source oscillator's signal.

FM Synthesis Frequency Modulation
• This process can generate fairly complex output containing multiple frequencies/sidebands with only two oscillators, requiring minimal computations. • This computational efficiency is the reason for it's invention and great popularity in earlier synthesizers and sound cards.

FM Synthesis Frequency Modulation

FM Synthesis Frequency Modulation
• In FM synthesis we come across the term operator which refers to an oscillator and envelope in one.

• An operator can be a carrier or a modulator depending on how it is used


				
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