ECE
Homework #1

# Homework #1 - Christopher Belcastro I.D 904424264 ECE 2704...

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Christopher Belcastro I.D. – 904424264 ECE 2704 – Homework #1 8 September 2006 1. a) Use Matlab to plot the function : x ( t ) = Sa (2 t). Explain your choice of interval for the t axis. a. I chose to use -6π < t < 6π in the Sa(2 t ) function because it provides plenty of space to exemplify the task of the equation. More notably the function crosses the x-axis t at π, 2π, 3π, etc. This justifies using some multiple of π for the interval. -20 -15 -10 -5 0 5 10 15 20 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Time Sa(2t) Function Plot b) Use Matlab to plot the function: x ( t ) = sinc(2 t ). b. I chose to use the same interval for t in the sinc function.

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-20 -15 -10 -5 0 5 10 15 20 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Time Sinc(2t) Function Plot c) What is the relationship between the functions in part (a) and part (b) in terms for the concepts
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Unformatted text preview: introduced in Section 5.2 c. Sa(2 t ) is, in general, a scaling of the sinc function. 5.2.1 Sketch the following signals: x ( t ) = sgn( t ) 2 5.2.3 Sketch the following signals: x( t ) = Π ( t /10) 4 . Evaluate the following integrals, if possible. If not possible, say why. a. ∫ ∞ ∞--e t ) 2 ( δ-3t dt = e-3t 2 = e-6 = 0.0024787 = 0.0025 b. ∫-∞-+ 1 ) 1 ( t sinc(3t)dt = Undefined Reason : t 2 = (-1) & t = (-1); therefore the integral is undefined. If one of the limits of the integral falls where the argument of the function is zero, then the limit of the integral must be redefined. 3...
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• Spring '08
• DJStilwell
• Calculus, Limit, Gamma function, Christopher Belcastro

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