Signals Systems and Networks: Assignment-1 1 Problem Find the following summatio

Signals Systems and Networks: Assignment-1 1 Problem Find the following summations: 1. n=1 n=??1e2n(n ?? 2) 2. n=1 n=??1n2(n + 2) 2 Problem Let X(t) be an arbitrary signals with even and odd parts denoted by Xe(t) and Xo(t) respectively. Show that: R1??1 X2(t)dt = R1??1 X2e (t)dt + R1??1 X2o (t)dt 3 Problem Determine whether the following signals are periodic and determine the fundamental period if they are? 1. x(t) = cos( 32t) 2. x(t) = jej5t 3. x(n) = cos(2n) 4. x(t) = Sin(50t) 5. x(t) = 2cos(10t + 1) + sin(4t ?? 1) 6. x(t) = cos(60t) + sin(50t) 1
7. x(t) = exp(j 76t) + exp(j 56t) 8.
Signals Systems and Networks: Assignment-1 1 Problem Find the following summations: 1. n=1 n=??1e2n(n ?? 2) 2. n=1 n=??1n2(n + 2) 2 Problem Let X(t) be an arbitrary signals with even and odd parts denoted by Xe(t) and Xo(t) respectively. Show that: R1??1 X2(t)dt = R1??1 X2e (t)dt + R1??1 X2o (t)dt 3 Problem Determine whether the following signals are periodic and determine the fundamental period if they are? 1. x(t) = cos( 32t) 2. x(t) = jej5t 3. x(n) = cos(2n) 4. x(t) = Sin(50t) 5. x(t) = 2cos(10t + 1) + sin(4t ?? 1) 6. x(t) = cos(60t) + sin(50t) 1
7. x(t) = exp(j 76t) + exp(j 56t) 8. x(t) = exp(j 56t) + exp( 16t) 9. x(t) = sin( 25t)cos( 43t) 10. x(t) = 2u(t) + 2sin(2t) 11. x(t) = 3cos(4t) + 2sin(t) 12. x[n] = sin( 67 n + 1) 4 Problem Determine whether the following signals are power or energy signals or nei- ther. Justify your answer. 1. x(t) = Asin(t) 2. x(t) = Aexp(bt) b > 0 3. x(t) = tsin( 53 t) 4. x(t) = exp(??2jtj)sin(t) 5. x(t) = exp(j 56t) 6. x(n) = cos(4 n) 5 Problem Sketch the following signals: 1. x(t) = u(t) ?? u(t ?? 5) 2. x(t) = t[u(t) ?? u(t ?? 5)] 3. x(t) = r(t) ?? r(t ?? 2) ?? 2u(t ?? 3) 4. x(t) = u(??t + 1) 5. x(t) = ??2u(t ?? 1) 6. x[n] = u[n + 2] ?? u[n ?? 3] 7. x[n] = u[n]u[??n + 2] 2
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