数字信号处理邵曦lecture15

1、Chapter 7 Digital Filter Realization, Basic building blocks: adder, multiplier, delay Various realizations for a given I/O filtering equation They are “equivalent” and also “different” from each other.,7.1 Direct Form (Direct Form ),N（numerator 分子）D（denominator 分母）,Canonical realization form: The fi

2、rst filter is 1/D(z) and the second N(z), merging the two sets of delays.,An example ( second-order system) :,Canonical form of general H(z): Block diagram: Fig.7.2.4 ( The maximum order of N(z) and D(z) are the same here, M=L) Corresponding sample processing algorithm: (7.2.5 ) (where K=max(M,L) ),

3、Comparing the direct form and canonical form: (p.280) The direct form requires twice as many delays. The canonical form is usually preferred in practice.,7.3 Cascade Form Why Cascade Form ?,Hi(z): second-order section (SOS) 二阶（基本）节 real-valued coefficients; up to second order; usually realized in ca

4、nonical form,ith section Hi(z):,Sample processing algorithm for cascade form(Fig.7.3.1):,Advantage of the cascade form： Each SOS is related to a pair of zeros and a pair of poles. So its convenient to realize the desired zeros and poles and adjust the frequency response.,7.4 Cascade to Canonical Can

5、onical cascade realization : Finding root (根) factors（因式） of the numerator and denominator polynomials of H(z) and pairing them in complex conjugate pairs（复共轭对）; Each quadratic factor(二阶因式) from N(z) may be paired with a quadratic factor from D(z) to form a SOS.,cascade form: (omitted),7.6 Quantization Effects in Digital Filters Quantization effects(量化效应） in digital filters: quantization of the input and output signals; roundoff errors in the internal computations (运算舍入误差); coefficient quantization(系数量化)., rou