Continuous-time Signal — The independent variable is continuous, and thus these signals are defined for a continuum of values of the independent variable.
Periodic Signal — Has the property that it is unchanged by a time shift of T. For example, A periodic continuous-time or discrete-time signal can be represented as: f (t) f (t nT ) f (n) f (n kT )
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Example
Noise Signal and Interfere Signal
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2. Periodic Signal and Aperiodic Signal
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A Speech Signal
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பைடு நூலகம்
A Picture
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Example
RLC circuit
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By interconnecting simpler subsystems. We can build more complex systems.
…… ……
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A Simple RC Circuit
The patterns of variation over time in the source voltage Vs and capacitor voltage Vc are examples of signals.
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1.1 Signals
Signals are functions of independent variables that carry information. The independent variables can be continuous or discrete. The independent variables can be 1-D, 2-D, ••• , n-D. For this course: Focus on a single (1-D) independent variable which we call “time”. Continuous-Time signals: x(t), t-continuous values. Discrete-Time signals: x(n), n-integer values only.
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1.3 Types of Signals
1. Certain Signal and Random Signal
Certain Signal — Can be represented mathematically as a function of certain time. Random Signal — Can’t be represented mathematically as a function of certain time. We only know the probability of certain value.
Aperiodic Signal — Has not the property that it is unchanged by a time shift of T.
Notice:
When T→∞,then Periodic Signal → Aperiodic Signal.
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Vertical Wind Profile
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1.2 Systems
For the most part, our view of systems will be from an input-output perspective. A system responds to applied input signals, and its response is described in terms of one or more output signals.
Example
f (t) A
－ T T
oT
T
2
2
－A
f (t)
…
…
t
－4 －2 0
246
k
Periodic Signal
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3. Continuous-time Signal and Discrete-time Signal
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Examples
Electrical signals — voltages and currents in a circuit. Acoustic signals — audio or speech signals. Video signals — intensity variations in an image. Biological signals — sequence of bases in a gene.