![Page 1: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/1.jpg)
SIGNAL AND SYSTEMSIGNAL AND SYSTEMLECTURES SUMMARY
![Page 2: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/2.jpg)
General IntroductionGeneral Introduction
What are they?
Signal
System
![Page 3: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/3.jpg)
Fundamentals of Signals and SystemsFundamentals of Signals and Systems
Signal: a function of one or more variables that convey information on the nature of a physical phenomenon.
Examples: v(t),i(t),x(t),heartbeat, blood pressure, temperature, vibration.
• One-dimensional signals: function depends on a single variable, e.g., speech signal
• Multi-dimensional signals: function depends on two or more variables, e.g., image
![Page 4: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/4.jpg)
Fundamentals of Signals and SystemsFundamentals of Signals and Systems
System: an entity or operator that manipulates one or more signals to accomplish a function, thereby yielding new signals.
• Commonly encountered systems: communications systems
Automatic speaker recoginition system Aircraft landing system .
Input signal Output signalSystem
![Page 5: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/5.jpg)
1. CT and DT signals:
Classification of signalsClassification of signals
![Page 6: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/6.jpg)
Classification of signals (cont.)Classification of signals (cont.)
For many cases, x[n] is obtained by sampling x(t) as:
x[n] = x(nT) , n =0,+1,+2,…
Are there any requirements for the sampling?
![Page 7: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/7.jpg)
Classification of signals (cont.)Classification of signals (cont.)
2. Even and odd signals:Even: x(−t) = x(t) x[−n] = x[n]Odd: x(−t) = −x(t) x[−n] = −x[n]Any signal x(t) can be expressed as x(t) = xe(t) + xo(t) ) x(−t) = xe(t) − xo(t) where xe(t) = 1/2(x(t) + x(−t)) xo(t) = 1/2(x(t) − x(−t))
![Page 8: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/8.jpg)
Classification of signals (cont.)Classification of signals (cont.)
3. Periodic and non-periodic signals: CT signal: if x(t) = x(t + T), then x(t) is periodic. Smallest T=Fundamental period: To Fundamental frequency fo = 1/To (Hz or cycles/second) Angular frequency: o = 2 /To (rad/seconds)
DT signal: if x[n] = x[n + N], then x[n] is periodic. min(No): fundamental period Fo = 1/No (cycles/sample) =2 /N (rads/sample). If the unit of n is designated as
dimensionless, then is simply in radians.
Note: A sampled CT periodic signal may not be DT periodic. Any Condition addition of two periodic CT signals, resultant
must be periodic signal ?
![Page 9: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/9.jpg)
Classification of signals (cont.)Classification of signals (cont.)
4. Deterministic and random signals.• Deterministic signal: No uncertainty with respect
to its value at any time• Completely specified at any time
• Random signal: Uncertain before it occurs. E.g., thermal noise.
![Page 10: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/10.jpg)
Classification of signals (cont.)Classification of signals (cont.)
Energy and power signals:
• CT signal x(t):
Energy: E =
Power: P =
2 ( )x t dt
21( )
2limT
T T
x t dtT
![Page 11: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/11.jpg)
Classification of signals (cont.)Classification of signals (cont.)
• DT signal x[n]:
Energy: E =
Power:
Energy signal: if 0 < E <Power signal: if 0 < P <
2x n
21
2 1limN
N n N
x nN
![Page 12: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/12.jpg)
Classification of signals (cont.)Classification of signals (cont.)
Analog Signal and Digital Signal
![Page 13: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/13.jpg)
Basic operations on signalsBasic operations on signals
Basic Operations on SignalBasic Operations on Signal
![Page 14: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/14.jpg)
• Rule for time shifting and time scaling:
See figure below. Find y(t) = x(2t + 3).
Basic Operations on Signal(cont.)Basic Operations on Signal(cont.)
![Page 15: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/15.jpg)
Elementary signalsElementary signals
1. Exponential
2-Sinusoidal
![Page 16: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/16.jpg)
Elementary signals(cont.)Elementary signals(cont.)
3. Step function
![Page 17: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/17.jpg)
5.Unit ramp function
Elementary signals(cont.)Elementary signals(cont.)
4.Unit impulse function
![Page 18: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/18.jpg)
System PropertiesSystem Properties
![Page 19: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/19.jpg)
2.Memory /Memoryless• Memory system: present output value depend on
future/past input.• Memoryless system: present output value depend only on present input.• Example
System Properties(cont.)System Properties(cont.)
![Page 20: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/20.jpg)
System Properties(cont.)System Properties(cont.)
![Page 21: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/21.jpg)
System Properties(cont.)System Properties(cont.)
![Page 22: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/22.jpg)
Invertibility
x(t) x(t)y(t)H
1
H
System Properties(cont.)System Properties(cont.)
![Page 23: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/23.jpg)
Series(cascade) Interconnection
Parallel, Interconnection
Interconnection of systemsInterconnection of systems
System 1 System 2
System 1
System 2
+Input Output
Input Output
![Page 24: SIGNAL AND SYSTEM LECTURES SUMMARY. General Introduction What are they? Signal System](https://reader035.vdocuments.us/reader035/viewer/2022062300/56649f425503460f94c61dba/html5/thumbnails/24.jpg)
Interconnection of systemsInterconnection of systems
•Feedback Interconnection
System 1
System 2
Input Output