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Introduction to Digital Filters
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23 Terms
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1
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A discrete time signal is the ___ of scaled and _ --- impulses
sum of scaled and delayed impulses
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Discrete time systems
A systems that maps input sequence to an output sequence
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superposition
weighted sum of inputs = weighted sum of outputs
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A linear systems obeys the principle of
superposition i.e weighted sum of inputs = weighted sum of outputs
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The principle of superposition consists of
Additivity and Homogeneity (scaling)
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Time invariant systems
a time shift in the input results a in a corresponding time shift in the output
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Discrete time signal representation is given as
x\[k\]δ\[n-k\]
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LTI Systems response is aka the
Convolution sum
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impusle response
systems output given to an impulse input
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in the time domain, LTI systems are characterised by their
Impulse Response
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Convolution properties
Commutative
Associative
Distributive
\
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Constant Coefficient Difference Equations
y\[n\] = ∑bx\[n-k\] - ∑ay\[n-k\]
weighted sum of current input and previous input and output
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The order of the filter and the length of the filter is given as
N and N+1
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IIR
Infinite Impulse Response
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FIR
Finite Impulse Response
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IIR filter is one which has dependence on previous output
Yes it has, The FIR doesn’t depend on previous outputs
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IIR filter has a finite response to a single impulse
No it has unlimited response but FIR has finite response
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Casual system depends
only on the current and present inputs but not future inputs
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Response of the LTI system to an sinusoidal input is
the scaled magnitude and phase version of the sinusoid
y\[n\] = H(Ω)exp(jΩn)
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exp(jΩn) is the ___ AND H(Ω) is the _--
Eigenfunction and Eigen value
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to ensure stablity in the z domain
the poles must be within the unit circle
\
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if p1 > 1 in a first order c transform what occurs
exponential growth in Output.
y\[n\] = p^n for n >= 0
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