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# hw6 - 6 2-t(over Assignment#6 p.2 ECSE-2410...

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Assignment #6 - p.1 ECSE-2410 Signals & Systems - Fall 2005 Fri 09/20/05 1(10). Write the complex expression, ( 29 ( 29 3 1 1 ) 1 ( j j j j z + + - = , in polar form , i.e., ) arg( z j e z z = . Express the angle of z , i.e., arg( z ), as p π radians, where p is a fraction. Assume that the principal value of arg( z ) is π π < - ) arg( z 2(18). Given 3 1 j z + = , evaluate the following. Note that some of these expressions are simplest when expressed in polar form and others in rectangular form. Some are simply real numbers. (a) z (b) zz (c) 2 z (d) + z z (e) { } z e (f) z z 3(15). Use properties of convolution to find the overall impulse response of the following system in terms of h 1 , h 2 , and h 3 : 4(20). Sketch the following periodic signals and calculate their average values (dc values). (a) ) ( sin 2 ) ( t = t x π , which is the output of a half wave rectifier circuit . Sketch several periods of ) ( t x . (b) The signal ) ( t x of period 4, where one period is given by < < + - < < < < - - - 2 1 , 2 1 0 , 1 0 2 , 1 t t t t t . Sketch ) (

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Unformatted text preview: 6 2 -t . (over) Assignment #6 - p.2 ECSE-2410 Signals &amp;amp; Systems - Fall 2005 Fri 09/20/05 5(18). For the periodic signal, ) ( t x a , shown. (a)(2) Find the average value. (b)(1)Is ) ( t x a odd, even or neither? (c)(15)Find the exponential Fourier series coefficients, k a , for the first three nonzero terms, by direct integration of the defining equation, -= T t jk a T k dt e t x a ) ( 1 . 6(19) Consider the periodic signal ) ( t x b . (a)(2) Find the average value. (b)(1) Is ) ( t x b odd, even, or neither? (c)(15) Find the exponential Fourier series for ) ( t x b through the first three nonzero terms, by direct integration. (d)(1) Compare the terms found in (c) to those for ) ( t x a in problem 5(c). Which term(s) are different and why? ) ( t x a 2 2 3 1-1 t ) ( t x b 2 4 t 2...
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