# hw1 - x e ( n ) and x o ( n ) for any sequence x(n). 5. Is...

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EE210 Signals and Systems January 15, 2009 Problem Set 1 1. Establish the orthogonality relationship given in class, namely, (a) 1 T Z T 0 e jmw 0 t e - jnw 0 t dt = 1 , for m = n = 0 , otherwise w 0 = 2 π T (b) 1 2 π Z π - π e j Ω m e - j Ω n d Ω = 1 , for m = n = 0 , otherwise (c) 1 N N - 1 X k =0 e j 2 πmk N e - j 2 πnk N = 1 , for n - m = lN = 0 , otherwise 2. Mention with justiﬁcation, at least two other sets of functions which are orthogonal. 3. Show that δ (2 t ) = 1 2 δ ( t ). Note that this is in contrast to ”normal” functions where x (2 t ) 6 = 1 2 x ( t ). Figure 1: For problem no. 4 4. x(n) can be expressed as x ( n ) = x e ( n ) + x o ( n ) Where x e ( n ) is an even sequence and x o ( n ) is an odd sequence. Find x e ( n ) and x o ( n ) for the sequence in Figure 1. Now give a general expression for

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Unformatted text preview: x e ( n ) and x o ( n ) for any sequence x(n). 5. Is . y ( t ) =-αy ( t ) + x ( t ) a linear system? Give reasons. 6. Consider the input x ( n ) for a discrete time system shown in Figure 2. Sketch: Figure 2: For problem no. 6 (a) x (2 n + 1) (b) y ( n ) = x ( n 2 ) n even = n odd (c) x (3 n ) δ ( n-1) 7. Is the following statement true or false? Give reasons. ”The series interconnection of two non-linear systems is non-linear.”...
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## This note was uploaded on 02/01/2012 for the course EE 210 taught by Professor Prof.h.narayanan during the Spring '07 term at IIT Bombay.

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hw1 - x e ( n ) and x o ( n ) for any sequence x(n). 5. Is...

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