tailieunhanh - Signals And Systems With Matlab Applications P2

You must, for your benefit, make an honest effort to solve the problems without first looking at the solutions that follow. It is recommended that first you go through and solve those you feel that you know. For the exercises that you are uncertain, review this chapter and try again. If your results do not agree with those provided, look over your procedures for inconsistencies and computational errors. Refer to the solutions as a last resort and rework those problems at a later date. | Summary int d Integrate the delta function ans Heaviside t-a k Summary The unit step function u0 t that is defined as I 0 u0 t 1 1 t 0 t 0 The unit step function offers a convenient method of describing the sudden application of a voltage or current source. The unit ramp function denoted as u1 t is defined as u1 t J u0 t dT -TO The unit impulse or delta function denoted as 8 t is the derivative of the unit step u0 t . It is also defined as J 8 t dr u0 t -TO and 8 t 0 for all t 0 The sampling property of the delta function states that f t 8 t - a f a 8 t or when a 0 f t d t f 0 5 t The sifting property of the delta function states that TO J f t 3 t- a dt f a -TO The sampling property of the doublet function 8 t states that f t V t - a f a 8 t - a -f a 8 t - a 1-19 Signals and Systems with MATLAB Applications Second Edition Orchard Publications Chapter 1 Elementary Signals Exercises 1. Evaluate the following functions a. sintSI t- - V 6 b. cos2ts t - n V 44 c. cos2tSft - n V 24 d. tan2tS t- n V 84 e. J t2 e S t - 2 dt -TO f. sin2tS1 f t - n V 24 2. a. Express the voltage waveform v t shown in Figure as a sum of unit step functions for the time interval 0 t 7 s . b. Using the result of part a compute the derivative of v t and sketch its waveform. Figure . Waveform for Exercise 2 1-20 Signals and Systems with MATLAB Applications Second Edition Orchard Publications Solutions to Exercises Solutions to Exercises Dear Reader The remaining pages on this chapter contain the solutions to the exercises. You must for your benefit make an honest effort to solve the problems without first looking at the solutions that follow. It is recommended that first you go through and solve those you feel that you know. For the exercises that you are uncertain review this chapter and try again. If your results do not agree with those provided look over your procedures for inconsistencies and computational errors. Refer to the solutions as a last resort and rework those