UNIT I – INTRODUCTION
Introduction to Digital Signal Processing: Discrete time signals & sequences, linear shift invariant systems,
stability, and causality. Linear constant coefficient difference equations. Frequency domain representation of
discrete time signals and systems.
A signal is any physical quantity that carries information, and that varies with time, space, or any other
independent variable or variables. Mathematically, a signal is defined as a function of one or more independent
1 – Dimensional signals mostly have time as the independent variable. For example,
Eg., S1 (t) = 20 t2
2 – Dimensional signals have two independent variables. For example, image is a 2 – D signal whose
independent variables are the two spatial coordinates (x,y)
Eg., S2 (t) = 3x + 2xy + 10y2
Video is a 3 – dimensional signal whose independent variables are the two spatial coordinates, (x,y) and time
Similarly, a 3 – D picture is also a 3 – D signal whose independent variables are the three spatial coordinates
Signals S1 (t) and S2 (t) belong to a class that are precisely defined by specifying the functional dependence on
the independent variables.
Natural signals like speech signal, ECG, EEG, images, videos, etc. belong to the class which cannot be
described functionally by mathematical expressions.
A system is a physical device that performs an operation on a signal. For example, natural signals are generated
by a system that responds to a stimulus or force.
For eg., speech signals are generated by forcing air through the vocal cords. Here, the vocal cord and the vocal
tract constitute the system (also called the vocal cavity). The air is the stimulus.
The stimulus along with the system is called a signal source.
An electronic filter is also a system. Here, the system performs an operation on the signal, which has the effect
of reducing the noise and interference from the desired information – bearing signal.
When the signal is passed through a system, the signal is said to have been processed.
The operation performed on the signal by the system is called Signal Processing. The system is characterized
by the type of operation that it performs on the signal. For example, if the operation is linear, the system is
called linear system, and so on.
DIGITAL SIGNAL PROCESSING