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DSP_ch2 - DSP EEE 407/591 by Andreas Spanias Ph.D Chapter 2...

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Copyright ©Andreas Spanias 1 DSP EEE 407/591 by Andreas Spanias, Ph.D. Chapter 2 [email protected] http://www.eas.asu.edu/~spanias Copyright ©Andreas Spanias 2 Discrete-time Linear Systems – Digital Filters x(n) h(n) y(n) The output is produced by convolving the input with the impulse response ) ( * ) ( ) ( ) ( ) ( m x m h m n x m h n y m = = −∞ = This operation can also involve a finite-length impulse response(FIR) sequence = = L m m n x m h n y 0 ) ( ) ( ) ( An FIR filter is programmed using a multiply-accumulate instruction
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Copyright ©Andreas Spanias 3 Some Definitions •A digital filter is linear if it has the property of generalized superposition. •A digital filter is causal if it non anticipatory, i.e., the present output does not depend on future inputs. •All real-time systems are causal. • Non-causalities arise in image processing where the signal indexes are spatial instead of temporal. • Unless otherwise stated all systems in this course will be assumed causal Copyright ©Andreas Spanias 4 Some More Definitions L b . 1 z T or ;unit delay x(n) x(n-1) x(n) b L x(n) x(n) x(n-1) x(n)+x(n-1) ;signal scaling by a filter coefficient ;signal addition x(n) x(n-1)
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