**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.