sec1solns - ECE 2200 Signals and Information Section 1...

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Unformatted text preview: ECE 2200 Signals and Information Section 1 (Week 2 Feb 1-4) Page 1 1. Find the cyclic frequency, radian frequency, period, phase shift and amplitude of the following signals: (i) x ( t ) = 6 . 5 cos(2 420 t- / 3) (ii) y ( t ) = 11 cos(0 . 2 ) cos(157( t + 0 . 02)) (iii) z ( t ) = (3 + 2 j )(3- 2 j ) cos(370 t + 0 . 7 ) Solution : (see Equation (2.1) for generic form, page 7 of the text) (i) x ( t ) = 6 . 5 cos(2 420 t- / 3) . A = 6 . 5 (amplitude) . = 2 420 rad/s (radian frequency) . f = 2 = 2 420 2 = 420 Hz (cyclic frequency) . T = 1 420 . 0024 sec (period) . =- 3 rad (phase shift) (ii) y ( t ) = 11 cos(0 . 2 ) cos(157( t + 0 . 02)) = 11 cos(0 . 2 ) cos(157 t + 3 . 14) . A = 11 cos(0 . 2 ) (amplitude) . = 157 rad/s (radian frequency) . f = 2 = 157 2 24 . 9873 Hz (cyclic frequency) . T = 2 157 . 04 sec (period) . = 3 . 14 rad (phase shift) (iii) z ( t ) = (3 + 2 j )(3- 2 j ) cos(370 t + 0 . 7 ) = 13 cos(370 t + 0 . 7 ) . A = 13 (amplitude) . = 370 rad/s (radian frequency) . f = 2 = 370 2 = 185 Hz (cyclic frequency) . T = 1 185 . 0054 sec (period) . = 0 . 7 rad (phase shift) ECE 2200 Signals and Information Section 1 (Week 2 Feb 1-4) Page 2 2. Simplify the following expressions by putting them in the form Ae j (i) 3 e j 2 + 4 e- j 3 (ii) ( 2- j 5) 10 (iii) ( 3- j 3)- 1 (iv) Re...
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This note was uploaded on 03/11/2010 for the course ECE 2200 taught by Professor Johnson during the Spring '05 term at Cornell University (Engineering School).

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sec1solns - ECE 2200 Signals and Information Section 1...

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