EE200_Weber_9-28

EE200_Weber_9-28 - of weighted and time shifted impulse...

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1 EE 200 FIR Filters A “running-aveage filter” averages a finite number of input samples to produce an output sample y [ n ] = 1 3 ( x [ n ] + x [ n + 1] + x [ n + 2]) n x[n] 2 4 2 4 6 n y[n] 2 4 2 4 14/3 2/3 2/3
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2 EE 200 FIR Filters A causal version of the same filter only uses present and past input values to calculate the output value. y [ n ] = 1 3 ( x [ n ] + x [ n " 1] + x [ n " 2]) n x[n] 2 4 2 4 6 n y[n] 2 4 2 4 14/3 2/3 2/3
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3 EE 200 Unit Impulse Sequence The impulse signal is non-zero at time zero, and zero everywhere else. For discrete-time signals, the Kronecker delta function " ( n ) = 1 if n = 0 0 otherwise # $ % δ (n) n 1
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4 EE 200 Unit Impulse Sequence The impulse can be shifted ahead and back in the sequence. δ (n-2) n 1 δ (n+3) n 1
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5 EE 200 Unit Impulse Sequence Impulses can be scaled and added together. x[n] n 1 x [ n ] = 2 " [ n # 1] + 3 [ n + 2]
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6 EE 200 Unit Impulse Sequence Any discrete-time signal can be represented as a sum
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Unformatted text preview: of weighted and time shifted impulse functions. Example: x [ n ] = x [ k ] " [ n # k ] k = #$ $ % x [ n ] = 2 [ n ] + 4 [ n # 1] # 3 [ n # 2] + [ n # 3] x(n) n 4 3 2 1-1-2-3 7 EE 200 Unit Impulse Sequence The Kronecker delta function has a sifting property when used in a summation. For each value of n, summation consists of an infinite number of x[k] [n-k] terms. Only one term, when k=n , is non-zero and is a delta function weighted by the value of x[k] . The delta function picks out the value of the function at one value of n. x [ n ] = x [ k ] " [ n # k ] k = #$ $ %...
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EE200_Weber_9-28 - of weighted and time shifted impulse...

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