sec1solns

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

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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 π 420 t- π/ 3) (ii) y ( t ) = 11 cos(0 . 2 π ) cos(157( t + 0 . 02)) (iii) z ( t ) = (3 + 2 j )(3- 2 j ) cos(370 πt + 0 . 7 π ) Solution : (see Equation (2.1) for generic form, page 7 of the text) (i) x ( t ) = 6 . 5 cos(2 π 420 t- π/ 3) . A = 6 . 5 (amplitude) . ω = 2 π 420 rad/s (radian frequency) . f = ω 2 π = 2 π 420 2 π = 420 Hz (cyclic frequency) . T = 1 420 ≈ . 0024 sec (period) . φ =- π 3 rad (phase shift) (ii) y ( t ) = 11 cos(0 . 2 π ) cos(157( t + 0 . 02)) = 11 cos(0 . 2 π ) cos(157 t + 3 . 14) . A = 11 cos(0 . 2 π ) (amplitude) . ω = 157 rad/s (radian frequency) . f = ω 2 π = 157 2 π ≈ 24 . 9873 Hz (cyclic frequency) . T = 2 π 157 ≈ . 04 sec (period) . φ = 3 . 14 rad (phase shift) (iii) z ( t ) = (3 + 2 j )(3- 2 j ) cos(370 πt + 0 . 7 π ) = 13 cos(370 πt + 0 . 7 π ) . A = 13 (amplitude) . ω = 370 π rad/s (radian frequency) . f = ω 2 π = 370 π 2 π = 185 Hz (cyclic frequency) . T = 1 185 ≈ . 0054 sec (period) . φ = 0 . 7 π 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 jθ (i) 3 e j π 2 + 4 e- j π 3 (ii) ( √ 2- j 5) 10 (iii) ( √ 3- j 3)- 1 (iv) Re...
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sec1solns - ECE 2200 Signals and Information – Section...

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