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 Page 2


3. Time scaling: if x(t) is a signal (continuous/discrete) then x(at) is the time scaled
version of x(t) where a is a constant.
4. Periodic signal: A periodic signal has a property that there is a positive value of T
such that x(t) = x(t+nT) for n = 0, 1, 2 … and T is a constant known as period.
5. Even or odd signal: From time reversal if the mirror image of the signal is same
as that of the image. That is if x(-t) = x(t) then the signal is even else if the signal
x(-t) = -x(t) then the signal is odd. Note that any signal can be broken to sum of
signal one which is even and other is odd as given below: -
Even {x(t)}=1/2[x(t)+x(-t)]
Odd {x(t)}=1/2[x(t)-x(-t)]
Exponential and sinusoidal signals:-
Continuous time complex exponential signal is of the form
x(t) = Ce
at
where C and a are generally complex number.
1. Real and exponential signal that is if ‘C’ and ‘a’ are real then the signal is as
follows:
Page 3


3. Time scaling: if x(t) is a signal (continuous/discrete) then x(at) is the time scaled
version of x(t) where a is a constant.
4. Periodic signal: A periodic signal has a property that there is a positive value of T
such that x(t) = x(t+nT) for n = 0, 1, 2 … and T is a constant known as period.
5. Even or odd signal: From time reversal if the mirror image of the signal is same
as that of the image. That is if x(-t) = x(t) then the signal is even else if the signal
x(-t) = -x(t) then the signal is odd. Note that any signal can be broken to sum of
signal one which is even and other is odd as given below: -
Even {x(t)}=1/2[x(t)+x(-t)]
Odd {x(t)}=1/2[x(t)-x(-t)]
Exponential and sinusoidal signals:-
Continuous time complex exponential signal is of the form
x(t) = Ce
at
where C and a are generally complex number.
1. Real and exponential signal that is if ‘C’ and ‘a’ are real then the signal is as
follows:
2. Periodic complex exponential and sinusoidal signal: That is ‘a’ is imaginary
x(t) = Ce
jwot
x(t) = Ce
jwo(t+T)
=C. e
jwot
.e
jwoT
but e
jwoT
=1
i.e. if w
0
=0 then x(t)=1 and if w
0
?0 then T=2p/|w
0
|
Signal closely related is x(t)= a cos(w
0
t+f)
Euler’s relation: e
jwot
=cosw
0
t+jsinw
0
t
Acos(w
0
t+f)=A.Re{e
j(wot+f)
} and Asin(w
0
t+f)=A.Im{e
j(wot+f)
}
3. Growing and decaying sinusoidal signal:
x(t)=Ce
rt
cos(w
0
t+f) if r>0 then growing signal and if r<0 then decaying signal
Sinusoidal signal multiplied by decaying exponential is referred as damped
exponential. Similarly for the discrete time characteristic where t becomes n.
Unit impulse and unit step function:
Page 4


3. Time scaling: if x(t) is a signal (continuous/discrete) then x(at) is the time scaled
version of x(t) where a is a constant.
4. Periodic signal: A periodic signal has a property that there is a positive value of T
such that x(t) = x(t+nT) for n = 0, 1, 2 … and T is a constant known as period.
5. Even or odd signal: From time reversal if the mirror image of the signal is same
as that of the image. That is if x(-t) = x(t) then the signal is even else if the signal
x(-t) = -x(t) then the signal is odd. Note that any signal can be broken to sum of
signal one which is even and other is odd as given below: -
Even {x(t)}=1/2[x(t)+x(-t)]
Odd {x(t)}=1/2[x(t)-x(-t)]
Exponential and sinusoidal signals:-
Continuous time complex exponential signal is of the form
x(t) = Ce
at
where C and a are generally complex number.
1. Real and exponential signal that is if ‘C’ and ‘a’ are real then the signal is as
follows:
2. Periodic complex exponential and sinusoidal signal: That is ‘a’ is imaginary
x(t) = Ce
jwot
x(t) = Ce
jwo(t+T)
=C. e
jwot
.e
jwoT
but e
jwoT
=1
i.e. if w
0
=0 then x(t)=1 and if w
0
?0 then T=2p/|w
0
|
Signal closely related is x(t)= a cos(w
0
t+f)
Euler’s relation: e
jwot
=cosw
0
t+jsinw
0
t
Acos(w
0
t+f)=A.Re{e
j(wot+f)
} and Asin(w
0
t+f)=A.Im{e
j(wot+f)
}
3. Growing and decaying sinusoidal signal:
x(t)=Ce
rt
cos(w
0
t+f) if r>0 then growing signal and if r<0 then decaying signal
Sinusoidal signal multiplied by decaying exponential is referred as damped
exponential. Similarly for the discrete time characteristic where t becomes n.
Unit impulse and unit step function:
Important Properties of Signals:
Page 5


3. Time scaling: if x(t) is a signal (continuous/discrete) then x(at) is the time scaled
version of x(t) where a is a constant.
4. Periodic signal: A periodic signal has a property that there is a positive value of T
such that x(t) = x(t+nT) for n = 0, 1, 2 … and T is a constant known as period.
5. Even or odd signal: From time reversal if the mirror image of the signal is same
as that of the image. That is if x(-t) = x(t) then the signal is even else if the signal
x(-t) = -x(t) then the signal is odd. Note that any signal can be broken to sum of
signal one which is even and other is odd as given below: -
Even {x(t)}=1/2[x(t)+x(-t)]
Odd {x(t)}=1/2[x(t)-x(-t)]
Exponential and sinusoidal signals:-
Continuous time complex exponential signal is of the form
x(t) = Ce
at
where C and a are generally complex number.
1. Real and exponential signal that is if ‘C’ and ‘a’ are real then the signal is as
follows:
2. Periodic complex exponential and sinusoidal signal: That is ‘a’ is imaginary
x(t) = Ce
jwot
x(t) = Ce
jwo(t+T)
=C. e
jwot
.e
jwoT
but e
jwoT
=1
i.e. if w
0
=0 then x(t)=1 and if w
0
?0 then T=2p/|w
0
|
Signal closely related is x(t)= a cos(w
0
t+f)
Euler’s relation: e
jwot
=cosw
0
t+jsinw
0
t
Acos(w
0
t+f)=A.Re{e
j(wot+f)
} and Asin(w
0
t+f)=A.Im{e
j(wot+f)
}
3. Growing and decaying sinusoidal signal:
x(t)=Ce
rt
cos(w
0
t+f) if r>0 then growing signal and if r<0 then decaying signal
Sinusoidal signal multiplied by decaying exponential is referred as damped
exponential. Similarly for the discrete time characteristic where t becomes n.
Unit impulse and unit step function:
Important Properties of Signals:
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FAQs on Introduction to Signal and Systems - Short Notes for Electrical Engineering - Electrical Engineering (EE)

1. What is the Laplace transform in signal and systems?
Ans. The Laplace transform is a mathematical technique used in signal and systems to analyze and transform time-domain functions into the frequency domain. It is particularly useful in solving differential equations and simplifying complex systems.
2. How are signals classified in signal and systems?
Ans. Signals in signal and systems are classified as continuous-time signals or discrete-time signals. Continuous-time signals are defined for all values of time, while discrete-time signals are only defined at discrete time instances.
3. What is the impulse response of a system in signal and systems?
Ans. The impulse response of a system in signal and systems is the output of the system when an impulse function is applied as the input. It characterizes the behavior of the system and is used to analyze its properties and performance.
4. How is convolution used in signal and systems analysis?
Ans. Convolution is a mathematical operation used in signal and systems to calculate the output of a system when an input signal is passed through it. It is a fundamental operation in analyzing linear time-invariant systems.
5. What are the applications of signal and systems in electrical engineering?
Ans. Signal and systems theory is essential in various applications in electrical engineering, such as communication systems, control systems, image processing, and audio signal processing. It plays a crucial role in analyzing and designing systems to process signals efficiently.
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