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1、Chapter 6Digital Filter Structures1Copyright 2001, S. K. Mitra必考！必考！2Copyright 2001, S. K. MitraBasic Building BlocksAn LTI digital filter can be conveniently represented in block diagram form using the basic building blocks shown belowxnynwnAxnynynxnxnxnxnAdderUnit delayMultiplierPick-off nodeBasic
2、 Building Blocks3Copyright 2001, S. K. Mitra4Copyright 2001, S. K. MitraCanonic and Noncanonic StructuresA digital filter structure is said to be canonic if the number of delays in the block diagram representation is equal to the order of the transfer functionOtherwise, it is a noncanonic structure5
3、Copyright 2001, S. K. MitraCanonic and Noncanonic StructuresThe structure shown below is noncanonic as it employs two delays to realize a first-order difference equationSignal Flow-Graph6Copyright 2001, S. K. Mitra7Copyright 2001, S. K. MitraEquivalent StructuresTwo digital filter structures are def
4、ined to be equivalent if they have the same transfer functionA fairly simple way to generate an equivalent structure from a given realization is via the transpose operation不要求！8Copyright 2001, S. K. MitraEquivalent StructuresTranspose Operation(1) Reverse all paths(2) Replace pick-off nodes by adder
5、s, and vice versa(3) Interchange the input and output nodesAll other methods for developing equivalent structures are based on a specific algorithm for each structure不要求！9Copyright 2001, S. K. Mitra不要求！10Copyright 2001, S. K. MitraBasic FIR Digital Filter StructuresA causal FIR filter of order N is
6、characterized by a transfer function H(z) given bywhich is a polynomial inIn the time-domain the input-output relation of the above FIR filter is given byN+1 multipliers and N two-input addersFIR Digital Filter StructuresDirect form structureCascade form structureLinear-phase FIR structure11Copyrigh
7、t 2001, S. K. Mitra12Copyright 2001, S. K. MitraDirect Form FIR Digital Filter StructuresAn FIR filter of order N is characterized by N+1 coefficients and, in general, require N+1 multipliers and N two-input addersStructures in which the multiplier coefficients are precisely the coefficients of the
8、transfer function are called direct form structures 13Copyright 2001, S. K. MitraDirect Form FIR Digital Filter StructuresA direct form realization of an FIR filter can be indicated below for N = 414Copyright 2001, S. K. MitraDirect Form FIR Digital Filter StructuresAn analysis of this structure yie
9、ldswhich is precisely of the form of the convolution sum description15Copyright 2001, S. K. MitraDirect Form FIR Digital Filter StructuresThe transpose of the direct form structure shown earlier is indicated belowBoth direct form structures are canonic with respect to delays不要求！16Copyright 2001, S.
10、K. MitraCascade Form FIR Digital Filter StructuresA higher-order FIR transfer function can also be realized as a cascade of second-order FIR sections and possibly a first-order sectionTo this end we express H(z) aswhere if N is even, and if N is odd, with 17Copyright 2001, S. K. MitraCascade Form FI
11、R Digital Filter StructuresA cascade realization for N = 6 is shown below(1-0.9z-1)(1-0.9z-1)=1-1.8z-1+0.81z-2 its block diagram/signal flow-graph in direct form and cascade form: (1-0.9z-1)5=()()()=()()()()()0.95=0.59049Linear-Phase FIR StructuresLinear-phase FIR filter of length N+1 is characteriz
12、ed by the symmetric impulse responseor an antisymmetric impulse responseSymmetry of the impulse response coefficients can be used to reduce the number of multiplications18Copyright 2001, S. K. MitraLinear-Phase FIR StructuresType1 FIR filter, Length N+1=7 is odd19Copyright 2001, S. K. MitraLinear-Ph
13、ase FIR Structures20Copyright 2001, S. K. Mitra21Copyright 2001, S. K. MitraLinear-Phase FIR StructuresA similar decomposition can be applied to a Type 2 FIR transfer functionFor example, a length-8 Type 2 FIR transfer function can be expressed asLinear-Phase FIR StructuresThe corresponding realization is shown below22Copyright 2001, S. K. MitraLinear-Phase FIR Structures23Copyright 2001, S. K. MitraN:the order of filter以ppt为准1.线性相位 2.实现更经济简单
