Difference between revisions of "ECE301 Spring2013 Bonus point 1" - Rhea

Latest revision as of 10:58, 11 February 2013

1. Example of:

a.) Linear and non-linear system

Linear system: y[n] = x[n]+x[n-1]

Non-linear system: y(t) = ln(x(t))

b.) Casual and non-casual system

Causal system: y(t) = 1+ x(t)sin(πt)

Non-causal system: y(t) = x(-t)

c.) System with memory and without memory:

System with memory: y(t) = ∫ x(t)dt from 0 to t

System without memory: y[n] = √(x[n])

d.) Invertible and non-invertible system

Invertible system: y[n] = x[1-n]

Non-invertible system: y(t) = |x(t)|

e.) Stable and Unstable system

Stable system: y(t) = e^(-t)x(t)u(t)

Unstable system: y(t) = x(t) + y(t-1)

f.) Time variant and time invariant system

Time variant system y[n] = x[n]e^[jωn]

Time Invariant system y(t) = 2^(x(t))

2. Graphical Convolution problem:

x(t) = e^(-2t)u(t)

h(t) = u(t)-u(t-1)

Find y(t) = x(t) * h(t):

Solution:

3. What is the fundamental period of sin(6/5t)+e^(j3(1-t))?

sin(6/5t) has period of 5π/3

e^(j3(1-t)) = e^(j3)(cos(3t)-jsin(3t)) which has period of 2π/3

The fundamental period is the LCM which is 10π/3

Back to first bonus point opportunity, ECE301 Spring 2013