Chapt 01 Signal and Systems Digital Signal Processing
Prepared Pre by IRDC India
10/7/2009
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For education purpose. Commercialization of this material is strictly not allowed without permission from author.
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Signal • Definition: It is the function that describes the variation of a physical variable with respect to independent variable( time, space etc.) in a physical process. Mathematically, S=f(x) Where s is signal /function and x independent variable Examples: 1) Change in temperature sensed by the sensor placed in boiler. t(msec)
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Temp(0C)
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T=f(t) Here, time t is independent variable.
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Contd.. 2) The digital data to be sent over a transmission channel t(msec)
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Digital data
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3) Pixel intensities in an image
Image, I=f(x,y) In this example intensity in image is the function / or signal which is dependent on independent variable spatial coordinate x and y.
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Contd.. 4) The voltage across capacitor
V = e − t / RC 5) share value fluctuation in stock market during year ( month wise) Month
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Share value( Rs)
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Common Discrete time signals It is general practice to represent complex signals by using common or standards signals.In descrete time signals independent variable ,t, can be equivalently seen as nT where T is samling period and n is sample number. Thuis , n becomes independent variable in descrete time signal. Some of the common signals are given here. a)Unit impulse function
δ (n) = 1 0
n = 0;
b) Unit step function u(n): It is defined as u(n) =
1
n ≠ 0;
0
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c)Unit ramp function ( r(n)):
n≥0
r(n) = n 0
n≥0
n
