Speech Processing by Computer

LECTURE 2

DIGITAL SYSTEMS

Objectives

By the end of the session you should:

• appreciate the difference between digital signals and digital systems

• know what is meant by a linear time-invariant digital system

• know that the possible mathematical operations of a LTI system are limited to weighted combinations of past input and output samples and delays

• appreciate that the specification of the characteristics of an LTI system can be expressed equivalently in the frequency and in the time domains

• have a qualitative understanding of convolution

• be able to explain how LTI systems can be implentations of amplifiers, attenuators, integrators, and differentiators

• appreciate that recursive implementations of LTI systems can be more efficient than non-recursive implementations

• know that a resonator is one of the simplest recursive LTI systems

Outline

2. Digital Systems

2.1. Processing environment

2.1.1. ADC - Process – DAC

2.1.2. Mathematical manipulation

2.1.3. Stream processing

2.2. Time and Frequency processing

2.2.1. Specification in frequency domain

2.2.2. Impulse response

2.2.3. Convolution

2.3. Non-recursive processing

2.3.1. General formula

2.3.2. Amplifiers/attenuators

2.3.3. Integrator = kind of low-pass filter

2.3.4. Differentiator = kind of high pass filter

2.4. Recursive processing

2.4.1. Efficiency concerns of non-recursive processing

2.4.2. Challenges of recursive processing

2.4.3. Simple resonator

Reading

P.Lynn & W.Fuerst, Introductory Digital Signal Processing, Wiley, 1989, Sections 2.1, 2.2, 2.3, 2.4.1.