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# HW3 - ELEN3801 Fall 2009 Homework 3 Due Thursday October...

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ELEN3801 - Fall 2009 Homework 3 Due Thursday October 1st at the beginning of class (Mudd 227 9:10am) 1 Carefully justify ALL your answers 3.1 - Let f ( t ) be a signal with energy E f . Show that the energy of the signals - f ( t ), f ( - t ) and f ( t - T ) where T R is also E f . What is the energy of the signal g ( t ) = cf ( at - b ), where a,b,c R and a 6 = 0? (Hint: write the energy integral for the various signals, and use a change of variables to express it in terms of E f ) 3.2 - Find and sketch R t -∞ f ( x ) dx for the signals in panels (a) and (b) depicted below. (Hint: recall what is the area of a continuous-time impulse func- tion) 3.3 - Consider the continuous-time systems below, described in terms of an in- put/output relationship, where the input is f ( t ) and the output is y ( t ). Determine if the systems are linear or non-linear. (Justify your answer fully, simply stating the answer will give you no credit) (a) dy dt ( t ) + 3 ty ( t ) = t 2 f ( t ) (b) 3 y ( t

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HW3 - ELEN3801 Fall 2009 Homework 3 Due Thursday October...

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