View source for ECE301 Spring2013 Bonus point 1 - Rhea

[[Category:ECE301Spring2013JVK]] [[Category:ECE]] [[Category:ECE301]] [[Category:probability]] [[Category:problem solving]]

[[Category:LTI systems]]

== 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))

[[Category:convolution]]


== 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:[[Image:Convolusion.jpg]]

[[Category:period]]


== 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

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