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Unformatted text preview: ENEE 241 02* READING ASSIGNMENT 21 Thu 04/30 Lecture Topics: introduction to linear timeinvariant filters; response to FIR filters to sinusoidal and exponential inputs; frequency response and system function Textbook References: sections 4.2.2, 4.3, 4.4.1, 4.4.3 Key Points: The inputoutput relationship y [ n ] = b x [ n ] + b 1 x [ n 1] + + b M x [ n M ] , n Z , describes a linear timeinvariant system known as a finite impulse response (FIR) filter. If the input x [ ] to a FIR filter is the complex exponential sequence x [ n ] = z n (where z C ), the output y [ ] is given by y [ n ] = H ( z ) z n , where H ( z ) = b + b 1 z 1 + + b M z M is the filters system function. In particular, when x [ n ] = e jn , the output is given y [ n ] = H ( e j ) e jn , where H ( e j ) = b + b 1 e j + + b M e jM is the filters frequency response. If all coefficients b k are realvalued, then the amplitude response  H ( e j )  is symmetric (even) about = 0 and , while the phase response H ( e j ) is antisymmetric (odd) about the same frequencies. The frequency response of an FIR filter with coefficient vector b = b 0: M can be obtained for N M + 1 uniformly spaced frequencies in [0 , 2 ) by zeropadding b to length N and computing a DFT. Theory and Examples: 1 . In developing the DFT, we considered discretetime signals which are either vectors (i.e., consisted of finitely many samples) or periodic extensions thereof. We now turn our attention to general discretetime signals, namely sequences such as x = x [ ] = { x [ n ] , n Z } If x is a linear combination of (not necessarily periodic) sinusoids, then it also has a spectrum . Its spectrum consists of the coefficients of these sinusoids given (or plotted) as a function of frequency....
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This note was uploaded on 10/18/2011 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.
 Spring '08
 staff
 Frequency

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