ECET 305 SA 2 Signals

ECET 305 SA 2 Signals - = 30 milliseconds in increments of...

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ECET-305 Supplementary Assignment 2 Signals 1. Sketch the following signals: a. The Dirac delta function δ(t-3) from t = 0 to t = 5. b. The impulse function δ[n-2] from n = 0 to n = 5. c. The Heaviside function u(t+2) from t= - 5 to t = +5. d. The step function u[n-3] from n = 0 to n = 5. 2. Using MATLAB, plot the following signals (copy, label , and attach the plots): a. ( ) cos(2 1) s t t = - from t = 0 to t = 10 in increments of 0.01 b. /2 ( ) cos(2 1) t s t e t = - from t = 0 to t = 10 in increments of 0.01 c. ( ) sin(2 100 ) 0.5sin(2 200 ) 0.5sin(2 300 ) s t t t t π = + + from t = 0 to t = 30 milliseconds in increments of 0.1 ms. d. A five-term Fourier series approximation to a 100 Hz square-wave from t = 0 to t = 30 milliseconds in increments of 0.01 ms. e. A five-term Fourier series approximation to a 100 Hz triangle-wave from t = 0 to t
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Unformatted text preview: = 30 milliseconds in increments of 0.01 ms. NOTE: The Fourier series for a square-wave can be found in many mathematics textbooks and engineering handbooks. The series is: [ ] sin 2 (2 1) 1 2 ( ) 2 (2 1) n f n t s t n = + = + + In this equation f is the fundamental frequency, t is time, and the summation index n determines the number of terms used. Thus a five-term Fourier series would have terms corresponding to n = 0,1,2,3,4. The formula for the triangle wave is: 2 2 cos[2 (2 1) ] 8 ( ) (2 1) n f n t s t n = + = + (Although these formulas are easily calculated in MATLAB, there are two custom M-files that automate the process called square_fourier and triangle . See Doc Sharing.)...
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