Lecture #9

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

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

3. Digitization of Audio Samples Step 2: Quantization • 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. Step 1: Sampling Step 2: Quantization The two step digitization process

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 Quantization is only an approximation. • 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.

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 Information Technology Inside and Outside • 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