Lecture 3_Signals and Systems
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This document discusses different types of signals including: - Deterministic vs random signals - Energy vs power signals - Even vs odd signals - Periodic vs aperiodic signals - Causal vs non-causal signals - Continuous time vs discrete time signals It provides examples and definitions for each signal type to explain their key characteristics and differences.
![Even signal Odd signal
Even signals are symmetric around vertical axis Odd signals are symmetric about
origin
x(t)=x(-t)
x(t)=-x(-t) or
x(-t)=-x(t)
Any signal is a sum of unique odd and even signals.
)()()( txtxtx oe
)]()([
2
1
)( txtxtxe )]()([
2
1
)( txtxtxo ](https://image.slidesharecdn.com/lecture321-200522171935/85/Lecture-3_Signals-and-Systems-8-320.jpg)
![15
1. Continuous Time signal
A signal which is defined for every
instant of time is called as continuous time
signal. It means that there are no breaks in
the signal. The continuous time signal is
denoted by x(t). Where t is the independent
variable.
2. Discrete Time Signal
A signal which is defined only
at particular interval of time is called
as Discrete time signal.
The DT signal is denoted by x[n]
where n is the independent variable.](https://image.slidesharecdn.com/lecture321-200522171935/85/Lecture-3_Signals-and-Systems-15-320.jpg)
Lecture 3_Signals and Systems
- 1. Department of E&TC , SVERI's COE, Pandharpur By Prof.N.S.Patil
- 2. Classification of signals Deterministic and random signal Energy and power signal Even and Odd signal Periodic and Aperiodic signal Causal and non causal signal Continuous time and discrete time signal 22 PCDE
- 3. Deterministic signal Random signal Behavior of these signals is predictable w.r.t time Behavior is unpredictable w.r.to Time There is no uncertainty with respect to its value at any time. There is an uncertainty w.r.t its value at any time These signals can be expressed mathematically. These signals can’t be expressed mathematically. For example, x(t) = sin(3t) is deterministic signal Noise signal, Thermal noise
- 4. Energy signal Power signal E=0<E<∞, finite energy P= 0<P<∞, finite power Power is zero Energy is infinite For finite duration Signal, For finite duration signal, For infinite duration signal, For infinite duration signal, Aperiodic signal are energy signal Periodic signals are power signal A signal cannot be both energy signal and power signal dttxE T T .)(2 dttxTE T T Lim .)(2 dttx T P T T .)( 2 1 2 dttx T TP T T Lim .)( 2 1 2
- 5. Example on energy and power signal Q. If a signal f(t) has the energy E, the energy of signal f(2t) is, a) E b) E/2 c) 2E d) 4E
- 8. Even signal Odd signal Even signals are symmetric around vertical axis Odd signals are symmetric about origin x(t)=x(-t) x(t)=-x(-t) or x(-t)=-x(t) Any signal is a sum of unique odd and even signals. )()()( txtxtx oe )]()([ 2 1 )( txtxtxe )]()([ 2 1 )( txtxtxo
- 11. Periodic signal Aperiodic signal Signal which repeats itself at a particular interval of time is called as periodic signal x(t)=x(t+T) Signal which doesn’t repeats itself after a particular interval of time is called as Aperiodic signal. x(t)≠x(t+T) Can be represented by a mathematical expression Cannot be represented by any mathematical expression. These are deterministic signals These are random signals
- 12. Q.1 The fundamental period of the signal X (t) = 10 cos2(10 πt) is ---------- a) 0.2 b) 0.1 c) 0.5 d) No fundamental period exists )1cos2(2cos 2 tt Hint:
- 14. Causal signal Non causal signal Causal Signals are signals that are zero for all negative time A non causal signal has values for negative time is called as anticausal signal or non causal signal. A continuous time signal x(t), is said to be casual if : x(t)=0 for every t<0, the signal x(t) does not start before t=0. A continuous time signal x(t), is said to be casual if : x(t)=0 for every t<0, the signal x(t) does not start before t=0.
- 15. 15 1. Continuous Time signal A signal which is defined for every instant of time is called as continuous time signal. It means that there are no breaks in the signal. The continuous time signal is denoted by x(t). Where t is the independent variable. 2. Discrete Time Signal A signal which is defined only at particular interval of time is called as Discrete time signal. The DT signal is denoted by x[n] where n is the independent variable.
Editor's Notes
- #13: Ans. b) 0.1: Use the formula,