This document discusses various operations that can be performed on signals, including time shifting, time reversal, time scaling, signal addition, and signal multiplication. It provides examples and explanations of each operation. Time shifting involves shifting a signal along the time axis. Time reversal involves reversing a signal along the time axis. Time scaling involves compressing or expanding a signal along the time axis. Signal addition and multiplication involve combining two signals by adding or multiplying their corresponding sample values.

1. Operations of Signals
By
Md. Fazle Rabbi
16CSE057

2. 4.2
Introduction To Signal
 A Signal is the function of one or more independent
variables that carries some information to represent a
physical phenomenon
 A continuous-time signal, also called an analog signal, is
defined along a continuum of time

3. 4.3
Operations of Signals
1. Time shifting
2. Time reversal
3. Time scaling
4. Signal addition
5. Signal multiplication

4. 4.4
Time Shifting
x(t ± t0) is time shifted version of the signal x(t).
x (t + t0) → negative shift
x (t - t0) → positive shift

5. 4.5
Time Scaling
x(At) is time scaled version of the signal x(t).
where A is always positive.
|A| > 1 → Compression of the signal
|A| < 1 → Expansion of the signal

6. 4.6
Time Scaling Cont.
Example: Given x(t) and we are to find y(t) = x(2t)
The period of x(t) is 2 and the period of y(t) is 1,

7. 4.7
Time Reversal
Time reversal is also called time folding
In Time reversal signal is reversed with respect to
time i.e.
y(t) = x(-t) is obtained for the given function

8. 4.8
Signal Addition
 In discrete-time domain, the sum of two signals x1(n) and x2(n)
can be obtained by adding the corresponding sample values .
 the subtraction of x2(n) from x1(n) can be obtained by
subtracting each sample of x2(n) from the corresponding sample
of x1(n) as illustrated below.
If
x1(n) = {1, 2, 3, 1, 5} and x2(n) = {2, 3, 4, 1, –2}
Then
x1(n) + x2(n) = {1 + 2, 2 + 3, 3 + 4, 1 + 1, 5 – 2} = {3, 5, 7, 2, 3}
and
x1(n) – x2(n) = {1 – 2, 2 – 3, 3 – 4, 1 – 1, 5 + 2}
= {–1, –1, –1, 0, 7}

9. 4.9
Signal Multiplication
The multiplication of two discrete-time sequences can be
performed by multiplying their values at the sampling
instants as shown below.
If x1(n) = {1, –3, 2, 4, 1.5} and
x2(n) = {2, –1, 3, 1.5, 2}

10. 4.10
Thank You