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Today's lecture
−Continuous and discrete-time signals
Distinction between discrete and digital
Examples
−The sequence
−Continuous and discrete-time systems
Notations
Examples
−Transformation of the independent axis
Time Shifting
Time Reversal
Time Scaling
Example
−Sinusoids
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Continuous-time signals
−A value of signal exists at every instant of time
Independent variable
Independent variable
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Discrete-time signals
−The value of signal exists only at equallyspaced discrete points in time
Independent variable
Independent variable
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Discrete-time signals
−Why to discretize
−How to discretize
How closely spaced are the samples
−Distinction between discrete & digital signals
−How to denote discrete signals
−Is the image a discrete or continuous signal
The image is generally considered to be acontinuous variable
Sampling can however be used to obtain adiscrete, two dimensional signal (sampledimage)
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Continuous and discrete signals
−A continuous-time signal is represented byenclosing the independent variable (time) inparentheses ()
−A discrete-time signal is represented byenclosing the independent variable (index) insquare brackets []
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Continuous and discrete signals
−Examples of continuous signals
Speech, video, image
The variation of atmospheric pressure, wind speedand temperature with altitude
−Examples of discrete signal
Demographic data, weekly stock position of acompany
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Continuous and discrete time system
−Like signals we have continuous and discrete-time systems as well
system
system
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Continuous and discrete time system
−Examples of continuous and discrete-time systems
Squaring System
Differentiator System
Accumulator System
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Transformations
−Transformations of the independent variable
Time Shift
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Transformations
Time reversal
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Transformations
Time scaling
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Transformations
Example
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Sinusoidal signals
−x(t) = A cos(ωt + Φ)
−A is the maximum amplitude of the sinusoidalsignal
−ω is the radian frequency
− is the phase shift