数字信号处理chapter4StructureofDigitalFilter

1、2020/12/3,1,Application of digital filter in engineering, Preprocess of test data,Simple ? Complex ? Experiments or Theories ? Application and Textbook ?,2020/12/3,2,Original waveform,2020/12/3,3,Original Spectrum,2020/12/3,4,Frequency response of the selected filter,2020/12/3,5,Waveform after filte

2、ring,2020/12/3,6,Spectrum after filtering,2020/12/3,7,Digital filter,1.Filter is a particularly important class of linear time-invariant system in DSP. 2.Purpose: Filter, detection and prediction of signal. 3.Content: characteristics structures design approach.,2020/12/3,8,CHAPTER 4 BASIC STRUCTURE

3、OF DIGITAL FILTER,h(k), k=0,1, (Impulse Response),x(n) (Input Sequence),y(n) (Output Sequence),2020/12/3,9,CONTENTS 4.1 Representation of Digital Filter 4.2 Structure of IIR Filter 4.3 Structure of FIR Filter 4.4 Review,2020/12/3,10,4.1 Representation of digital filter,1 Expression of digital filter

4、,（1）Difference equation Such as: one-order system,（2）Impulse response Such as: h(n),（3）System function Such as:,2020/12/3,11,2 Diagram,（1）Block-diagram Such as:,Diagram of one-order digital filter,Block diagram,z-1,z-1,a0,a1,b1,Delay,z-1,a,First-order Nth-order,Unit Delay,Constant multiplication,Add

5、ition,2020/12/3,12,（2）Flow-graph Such as:,Different structure will determine systems accuracy, error, stability, cost efficiency and speed, etc al.,2020/12/3,13,3 Implementation of the Digital Filter,（1）Hardware (Special-purpose) Digital signal processor （2）Software Digital Filter Algorithm,4 Classi

6、fication of the Digital Filter,(1) Finite Impulse Response (FIR) FIR filter (2) Infinite Impulse Response (IIR) IIR filter,2020/12/3,14,Finite Impulse Response Infinite Impulse Response h(n): Finite length h(n): infinite length Nonrecursively Recursively,2020/12/3,15,4.2 Structure of IIR filter,1. C

7、haracteristics of IIR filter,System function:,At least one coefficient bi is not zero, its difference equation is:,There are feedback loops in IIR structure, called recursively. There are poles inside unit circle on z-plane, otherwise unstable. IIR filters structure is not unique.,2020/12/3,16,Direc

8、t Form,Cascade Form,Parallel Form,The same H(z) may have different implementation structure cost efficiency computation error stability finite word-length sensitivity,2020/12/3,17,2. Structure of IIR filter （1）Direct Form,System function:,Difference equation:,2N delay units are required.,Direct Form

9、,2020/12/3,18,（2）Direct Form II,2020/12/3,19,（2）Direct Form II,N Delay Unit.,Direct Form II,2020/12/3,20,We can find that: Direct Form II requires N delay units. Common disadvantage of the two form: Coefficient ai , bi can not be adjusted conveniently. When N is large, too sensitive to finite word-l

10、ength Instability Errors.,2020/12/3,21,（3）Cascade Form,N-order transfer function can be expressed by its poles and zeros:,Because H(z)s parameter ai , bi is real value, zero ci and pole di are real roots or conjugate complex roots, that is:,are real roots, are complex roots，and N1+N2=N,2020/12/3,22,

11、Two-order Cascade Form,We can see: Cascade forms structure is flexible, pole and zero can be adjusted conveniently and do not influence each other. Two orders position can be selected arbitrarily, different scheme has different error and can be optimized.,2020/12/3,23,（4）Parallel Form,Transfer funct

12、ion can be expressed into partial fraction, and can be composed into parallel form:,expanding into real boots and conjugate complex roots form:,where: N=L+2M，L, one-order network, M, two order network.,2020/12/3,24,（4）Parallel Form,We can see: Pole can be adjusted independently, zero cannot; If ther

13、e are multi-order pole, partial fraction expansion is difficult. High speed computation, lower error than cascade form.,2020/12/3,25,4.3 Structure of FIR filter,1. Characteristic of FIR filter,h(n) is a finite-length sequence, its system function is:,FIR doesnt have feedback loop, it is not a recurs

14、ive form filter, so there is no problem of stability.,2. Structure of FIR filter,（1） Direct-form,Convolution sum,2020/12/3,26,Generally, h(n) is real value, H(z)s zero are real or conjugate complex value.Every pair of conjugate zero composed into a second-order coefficient, so:,Characteristics: Ever

15、y order zero can be controlled, so can be applied when transfer zero are required to be controlled. More coefficients. More computation time.,（2）Cascade form,Product of second-order factors,2020/12/3,27,4.4 Review,1.Structure of IIR filter Recursively form, problem of stability. Pole inside the unit circle. （1）Direct form: Adjust inconvenient, sensitive to word-length effect; （2）Cascade form: Pole and zero can be