Chapter 2 (Lathi’s Book):
Introduction to Signals:
Classification of Signals
1. Continuous-Time and Discrete-time signals
Continuous-time signal: is a signal that is specified for every value of time t.
Examples are: telephone and video camera outputs.
Discrete-time signal: is a signal that is specified at discrete values of t. Examples are:
the quarterly gross national product (GNP), monthly sales of a corporation, and stock market daily averages.
The terms continuous-time and discrete-time describe the nature of signals along the time (horizontal) axis.
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To distinguish between continuous-time and discrete-time signals:
• The symbol t is used to denote the continuous-time independent variable and the symbol n is used to denote the discrete-time independent variable.
• The independent variable is enclosed in parentheses (.) for continuous-time signals, where the independent variable is enclosed in brackets [.] for discrete- time signals. For example, x(t) is a continuous-time signal and x[n] is a discrete- time signal.
A continuous-time signal can be converted into a discrete-time signal through a
‘sampling’ operation.
2. Analog and Digital Signals
The terms analog and digital describe the nature of signal amplitude along the vertical axis.
Analog signal: is a signal whose amplitude can have any value in a continuous range.
An analog signal can have an infinite number of values.
Digital signal: is a signal whose amplitude can have only a finite number of values.
For examples, signals associated with a digital computer are digital signals because they have only two values (binary signals). A digital signal whose amplitude can have M values is called an M-ary signal. The binary is a special case (M=2).
An analog signal can be converted into a digital signal [analog-to-digital (A/D) conversion] through ‘quantization’ (rounding off).
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3. Periodic and Aperiodic Signals
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4. Even and Odd Signals
A signal x(t) is referred to as even if it is identical to its time-reversed counterpart x(t), i.e.
x(– t) = x(t) A signal x(t) is referred to as odd if:
x(– t) = – x(t)
An odd signal must necessarily be 0 at t = 0, since by definition x(0) = – x(0).
Examples of even and odd signals are shown in the figure (a) and (b), respectively.
An important fact is that any signal can be broken into a sum of two signals, one of which is even and one of which is odd. The signal:
{ } [ ( ) ( ) ]
2 ) 1
( t x t x t
x
Ev = + −
is referred to as the even part of x(t). Similarly, the signal:
{ } [ ( ) ( ) ]
2 ) 1
( t x t x t
x
Od = − −
is referred to as the odd part of x(t). x(t) is the sum of the two parts.
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5. Energy and Power Signals
Problem
Solution
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6. Deterministic and Random Signals
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