Assign1_BasicConcepts - x t and output y t related by Is...

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EE3210 Assignment 1: Basic Concepts Due Date: 5p.m., Sep 16, 2009. (Note: Since I will be on leave in Week 3, a box will be put outside my office on Sep 15 and Sep 16. Please put your assignment in the box. The grader of this course will collect it. Late submission will not be accepted.) 1. Determine whether or not each of the following signals is periodic. If the signal is periodic, determine its fundamental period. a) (continuous-time signal) t t x 2 sin ) ( = b) (discrete-time signal) 4 / ) 2 3 ( ] [ = n j e n x π 2. Determine the power of the following two signals. The first one is a real signal and the second one is a complex signal. a) ) cos( ) ( θ ω + = t A t x b) , where C is a complex number. t j Ce t y ) ( = 3. Show that the system described by the following equation is linear: ) ( ) ( 3 t x t y dt dy = + 4. Consider a continuous-time system with input
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Unformatted text preview: x ( t ) and output y ( t ) related by Is this system time invariant? Justify your answer. )). (sin( ) ( t x t y = 5. Determine whether the following system is invertible. If it is, find its inverse system and use a block diagram to represent the inverse system. ] [ ] [ ∑ −∞ = = n k k x n y 6. Show that a system having the superposition property must satisfy a) the additivity condition; and (Hint: Choose suitable values for a and b .) b) the scaling condition. (Hint: Use the same approach as in part (a).) 7. Is it always true that the power of the sum of two signals x 1 (t) + x 2 (t) equals the sum of the power of x 1 (t) and the power of x 2 (t)? If statement is correct, prove it. Otherwise, give a counter-example....
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This note was uploaded on 11/22/2009 for the course ELECTRONIC EE3210 taught by Professor Sungchiwan during the Spring '09 term at École Normale Supérieure.

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