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Principles of Digital Audio

Analog Audio

3 Characteristics of analog audio signals:

1. Continuous signal – single repetitive waveform

2. Infinite – sound propagates as long as oscillator is activated

3. Measured in voltage

Digital Audio

3 Characteristics of digital audio:

1. Discrete – made up of numerous samples taken from a continuous analog signal

2. Finite – has a defined start and end point in time

3. Measured in binary digits (0 and 1)

Binary System

Binary code is a coding system using messages made up of strings of the digits 0 and 1

1 binary digit (or a single instance of 0 or 1) is referred to as 1 bit (or binary digit)

8 bits = 1 byte

Digital Conversion

Analog signals can be converted to digital signals using an analog to digital converter (ADC) Takes numerous measurements of a signal at regular

time points

In order to hear a digital signal it must be converted back into an analog signal, using an analog to digital converter (DAC) Take the sampled digital audio and converts it into a

continuous signal to be output through loudspeakers, headphones, etc.

Digital Conversion

What is the benefit of converting analog signals into digital signals?

Eliminates the need for physical oscillators and large cumbersome electronic equipment

Allows for more accurate timing in processing

Allows for more refined processing methods without the need for external hardware (such as a physical delay module, flanger, phaser, pitch shifter, etc.)

Sampling

The digital conversion process makes use of the process of sampling, or taking measurements of a signal at regular points in time (see analog to digital converter on previous slide)

In the sampling process, a continuous signal is divided into equal segments. Segments are then reassembled inside various digital platforms (computer programs, audio recorders, sampling units, etc.) and create a recorded representation of the original signal.

Sampling

INSERT PITCURE OF SAMPLED AUDIO SIGNAL

Characteristics of Digital Audio

2 measurements characterize digital audio signals:1. Sampling rate/sample frequency

2. Quantization (also known as bit depth)

Sampling rate – how often an audio signal is sampled Measured in samples per second, the more samples per

second, the accurate the representation of the original signal.

Bit rate/Quantization – number of bits per sample Refers to the overall resolution and dynamic range of a signal.

Higher bit depth yields wider dynamic range, lower bit depth results in limited dyanmic range (1 bit audio results in an on or off signal)

Nyquist Theorem

To digitally represent a signal containing frequency components up to X Hz, the sampling rate must be at least 2X Hz

Maximum frequency perspective refers to sampling frequency in reference to the highest frequency in the signal, for example:

The maximum frequency sampled at SR is SR/2 Hertz.

The 2x frequency is also called the Nyquist frequency

Types of Sampling

Undersampling

Undersampling contains frequency content that is beyond the sampling rate

In undersampling there are actually frequencies in the original signal that are not captured and represented in the sampled digitized version of the signal

In other words, undersampling is bad and results in digital distortion and aliasing

Undersampling

INSERT IMAGE OF UNDERSAMPLING AND DIGITAL PHOTOGRAPHY ALIASING

Critical Sampling

Critical sampling is when the sample rate and the highest frequency in the original signal are the same value

This may capture the original signal with no problem, but could result in distortion, aliasing and foldover Because the original signal hits 0 points (when the sample

rate and signal are at the same frequency)

Foldover – when the signal moves more quickly or as quickly as the sampling rate

Critical Sampling

INSERT IMAGE OF CRITICAL SAMPLING HERE

Oversampling

When the sampling rate is higher than the highest frequency in the original signal

Oversampling captures all audible frequencies in the original signal and some that are outside the audible frequency band.

Oversampling is the most desirable method of sampling

Sample rates: 44.1 kHz, 48 kHz, 96 kHz CD audio sampling rate is 44.1 kHz

History of Sampling Rate

Early digital master recordings were stored on magnetic video tape

Bits were stored as black and white pixels on the tape

The sampling rate was determined with the following figures: 525 lines per frame with 35 blank lines = 490 lines per frame 3 samples are stored on each line Tape is taken at 60 fields per second, at 245 lines per frame

(490/2) So, 3 x 245 x 60 = 44100 (in other words, 44.1 kHz)

Quantization

Resolution with each sample is recorded Dependent of how many bits are available to represent

the signal data

Determines the amount of original signal to amount of unwanted noise The unwanted noise is referred to as quantization error,

and is unavoidable in the digital conversion process

Quantization error is also referred to as the signal-to-noise ratio

Signal-to-Noise Ratio

Ratio of original signal to amount of quantization error

Dependent on the nature of the audio content Quantization error is less noticeable in high-level signals It is more obvious in low-level signals. Why? Because low-level

signals don’t use all available bits in the conversion process? Less bits means the signal-to-error level is greater and

quantization error becomes audible

Problems with quantization error result in digital distortion and low-level noise (we’ll talk about how to remove this from recordings later)

Dither

Dither – low-level noise added to signal before it is sampled

What? Adding noise to the signal?

Adds random error to the signal. Transforms quantization error into added noise, and makes noise becomes a constant factor.

This noise can be removed to the point that it is not audible, but still removes quantization error from low-level recordings, helping them to sound cleaner with less system noise