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# A#07 - for part(a k a 5(30 4(40 Use properties(Text Table...

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Assignment #07 ECSE-2410 Signals & Systems - Spring 2009 Due Fri 02/06/09 1(10).Express 4 2 ) 3 1 ( π j e j j z + = in polar form , i.e., ) arg( z j e z z = , π π < ) arg( z . Write arg ( z ) as p π radians, where p is a fraction. AND sketch z in complex plane. 2(10). Express ( ) + + = 2 4 1 1 π π j j e e j j z , in rectangular form, i.e., { } { } z m j z e z + = AND sketch. 3(32). Given ( ) ( ) 2 1 1 2 j j j z + = , calculate the following and show that (a)=(b), and (c)=(d). (a) (b) (c) + z z { } z e 2 z z (d) 2 z 4(18). (a)(9) Express the periodic signal ( ) ) 2 ( cos 4 ) cos( 2 1 2 t t t x + + = as an exponential Fourier series. (b)(9) Sketch the exponential Fourier series spectrum,
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Unformatted text preview: , for part (a). k a 5(30). 4(40). Use properties (Text Table 3.1) to find the exponential Fourier series coefficients, , k a (including ) of the following periodic waveforms. Note that we derived a very general formula for square pulse trains. Feel free to use this formula and results from one part of the problems below in any other part. a (a)(15) (b)(15) ) ( t x • • • • • • • • • • • • 1 2 3 4 5 6 7 8 -1-2 1 -8 -7 -6 -5 -4 -3 t t ) ( t x 2 1...
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