Digital Signal Processing deals with the representation of signals by

sequences of numbers or symbols and the processing of these sequences. Note that

there are two unique features of Digital Signal Processing as opposed to plain

old ordinary digital processing:

- Signals come from the real world - this intimate connection with the real

world leads to many unique needs such as the need to react in real time and

a need to measure signals and convert them to digital numbers. - Signals are discrete - which means the information in between discrete

samples is lost.Â

The advantages of DSP are common to many digital systems. These are:

Versatility:

- Digital systems can be reprogrammed for other applications (at least where

programmable DSP chips are used). - Digital systems can be ported to different hardware configurations (for

example a different DSP chip or board level product).

Repeatability:

- Digital systems can be easily duplicated.
- Digital systems do not depend on strict component tolerances.
- Digital system responses do not change with temperature.

Simplicity:

- Some applications can be done more easily digitally than with analogue

systems.

DSP is preferred to ASP because of the following reasons:

1. Available technology at low cost (an analog circuit is expensive).

2. Speed and a more reliable circuit.

3. Flexibility in system design.

4. Storage capacity.

We start off with the basics of DSP which are necessary to understand the

subject.

Discrete time signals and systems

A signal can be defined as a function that conveys information about the

state or behavior of a physical system. In general, a signal can be represented

mathematically as a function of one or more independent variables.

Ex: A speech signal can be represented mathematically as a function of time.

Signals can be classified as:

1. Continuous time signal

2. Discrete time signal

3. Digital signal

4. Analog signal

Continuous Time Signals are defined at continuum of time and these are

represented by continuous variable functions.

Discrete time signals are defined at discrete time and thus the independent

variables take only discrete values.

Digital signals are those for which amplitude and time are discrete.

A digital time signal is defined only for discrete values of the independent

variable — time.

Generally time is quantized uniformly.

i.e. t=nT where n is an integer.

T is the interval between time samples.

A discrete time signal is represented mathematically as a sequence of numbers

whose amplitude may be taken on continuum of values. It is represented as x ={x(n)}

for -infinity

Various operations like time shifting, folding operation or reflexation

operation may be performed on the sequence to obtain the necessary output.

Classification of Discrete Time Signals

1. Static and Dynamic System.

2. Time variant and Time Invariant System.

3. Linear and Non-linear System.

4. Stable and Unstable System.

5. Causal and Non-Causal System.

Static and Dynamic System: A discrete time system is called static if its

output at any instant depends at most on the sample at the same instant but not

on past or future samples of the input.

Linear and Non-Linear System: A linear system is one that satisfies the

Superposition principle. The Superposition principle states that the response of

the system to sum of the dicrete time signals is equal to the corresponding sum

of the system to each of the individual input discrete time signal.

Causal and Non-Causal System: A system is said to be causal if the output

of the system at any instant depends only on the present and past input but does

not depend on the future input.

A system is said to be non-causal if the output does not only depend on the

present and past input but also on the future input.

Time Variant and Time Invariant System: A time variant system varies with

the passage of time and a time invariant system is not concerned with the

passage of time.

Stable and Unstable System: An arbitrarily relaxed system is said to be

bounded input, bounded output stable if and only if every bounded input produces

a bounded output.

These are just some of the commonly used terms in DSP and form the basis of

the more advanced concepts.