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'''a.) Linear and non-linear system''' | '''a.) Linear and non-linear system''' | ||
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Linear system: y[n] = x[n]+x[n-1] | Linear system: y[n] = x[n]+x[n-1] | ||
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Non-linear system: y(t) = ln(x(t)) | Non-linear system: y(t) = ln(x(t)) | ||
'''b.) Casual and non-casual system''' | '''b.) Casual and non-casual system''' | ||
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Causal system: y(t) = 1+ x(t)sin(πt) | Causal system: y(t) = 1+ x(t)sin(πt) | ||
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Non-causal system: y(t) = x(-t) | Non-causal system: y(t) = x(-t) | ||
'''c.) System with memory and without memory:''' | '''c.) System with memory and without memory:''' | ||
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System with memory: y(t) = ∫ x(t)dt from 0 to t | System with memory: y(t) = ∫ x(t)dt from 0 to t | ||
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System without memory: y[n] = √(x[n]) | System without memory: y[n] = √(x[n]) | ||
'''d.) Invertible and non-invertible system''' | '''d.) Invertible and non-invertible system''' | ||
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Invertible system: y[n] = x[1-n] | Invertible system: y[n] = x[1-n] | ||
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Non-invertible system: y(t) = |x(t)| | Non-invertible system: y(t) = |x(t)| | ||
'''e.) Stable and Unstable system''' | '''e.) Stable and Unstable system''' | ||
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Stable system: y(t) = e^(-t)x(t)u(t) | Stable system: y(t) = e^(-t)x(t)u(t) | ||
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Unstable system: y(t) = x(t) + y(t-1) | Unstable system: y(t) = x(t) + y(t-1) | ||
'''f.) Time variant and time invariant system''' | '''f.) Time variant and time invariant system''' | ||
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Time variant system y[n] = x[n]e^[jωn] | Time variant system y[n] = x[n]e^[jωn] | ||
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Time Invariant system y(t) = 2^(x(t)) | Time Invariant system y(t) = 2^(x(t)) | ||
[[Category:convolution]] | [[Category:convolution]] | ||
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Graphical Convolution problem: | Graphical Convolution problem: | ||
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x(t) = e^(-2t)u(t) | x(t) = e^(-2t)u(t) | ||
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h(t) = u(t)-u(t-1) | h(t) = u(t)-u(t-1) | ||
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Find y(t) = x(t) * h(t): | Find y(t) = x(t) * h(t): | ||
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sin(6/5t) has period of 5pi/3 | sin(6/5t) has period of 5pi/3 | ||
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e^(j3(1-t)) = e^(j3)(cos(3t)-jsin(3t)) which has period of 2pi/3 | e^(j3(1-t)) = e^(j3)(cos(3t)-jsin(3t)) which has period of 2pi/3 | ||
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The fundamental period is the LCM which is 10pi/3 | The fundamental period is the LCM which is 10pi/3 | ||
[[Bonus_point_1_ECE301_Spring2013|Back to first bonus point opportunity, ECE301 Spring 2013]] | [[Bonus_point_1_ECE301_Spring2013|Back to first bonus point opportunity, ECE301 Spring 2013]] | ||
Revision as of 10:53, 11 February 2013
Examples 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))
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 5pi/3
e^(j3(1-t)) = e^(j3)(cos(3t)-jsin(3t)) which has period of 2pi/3
The fundamental period is the LCM which is 10pi/3
