This document provides an overview of digital audio concepts including digitization of audio samples through sampling and quantization, reconstruction of audio signals from digital samples, and quantization error. It discusses how audio signals are made discrete in both time and amplitude for digital representation through sampling at regular time intervals according to the Nyquist rate and quantizing signal amplitudes to discrete integer values using bit encoding. The process of reconstruction from digital samples to analog signals is also summarized.

1. IT-101
Section 001
Lecture #9
Introduction to Information
Technology

2. Overview
Chapter 12
 Digital Audio
 Digitization of Audio Samples
 Quantization
 Reconstruction
 Quantization error

3. Digitization of Audio Samples
 Audio signals are continuous in time and amplitude
 Audio signal must be digitized in both time and amplitude to
be represented in binary form.
 Discrete in time by sampling – Nyquist
 Discrete in amplitude by quantization
 Once samples have been captured, they must be made
discrete in amplitude.
The two step digitization process
Step 1: Sampling Step 2: Quantization
Step 2: Quantization

4. Quantization
 Quantization
 Converts actual sample values (usually voltage
measurements) into an integer approximation
 Process of rounding off a continuous value so that it can
be represented by a fixed number of binary digits
 Tradeoff between number of bits required and error
 Human perception limitations affect allowable error
 Specific application affects allowable error
 Two approaches to quantization
 Rounding the sample to the closest integer.
 (e.g. round 3.14 to 3)
 Create a Quantizer table that generates a staircase pattern
of values based on a step size.

5.  Consider an audio signal with a voltage range between -10 and
+10
 Assume the audio waveform has already been time sampled, as
shown
 How can the amplitude also be converted into discrete values?

6.  For this example, let’s choose to represent each sample by 4 bits
 There are an infinite number of voltages
between -10 and 10.
 We will have to assign a range of voltages
to each 4-bit codeword.
 There will be 16 steps. Why?
 How large will each step be?

7. Reconstruction
 Analog-to-Digital Converter (ADC) provides the sampled and
quantized binary code.
 Digital-to-Analog Converter (DAC) converts the quantized
binary code back into an approximation of the analog
signal by clocking the code to the same sample rate as the
ADC conversion.
 Quantization and Reconstruction example on next two
slides:

8. QUANTIZATION

9. RECONSTRUCTION

10. Quantization Error
 After quantization, some information is lost
 Errors (noise) introduced
 The difference between the original sample value and the
rounded value is called the quantization error
 A signal to noise ratio (SNR) is the ratio of the relative sizes of
the signal values and the errors.
 The higher the SNR, the smaller the average error is with
respect to the signal value, and the better the fidelity.
Quantization is only an approximation.

11. Comments for next class
Chapter 13
 The Telephone System: wired and wireless
 Analog Telephone system
 Digital telephone system
 Cellular telephone system

12. Chapters Read So Far
 Everyone should have read the following chapters thus
far:
 Chapter 1: What is the Information in the Information
Revolution?
 Chapter 3: Representing Information in Bits
 Chapter 4: The Need and Basis for Data Protocols
 Chapter 5: From the Real World to Images and Video
 Chapter 7: Compressing Information
 Chapter 8: Image Compression
 Chapter 9: Digital Video
 Chapter 10: Audio as Information
 Chapter 11: Sampling of Audio Signals
 Chapter 12: Digital Audio
Information Technology Inside and Outside