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.