Digital Filter Realization

1. F I L T E R S Digital Filter Realization From Computer and Electrical Dept. Doaa’ Jaber 220039350 Reham Habashi 220032945 Noura EL–Ramlawi 220031500 Submitted to: Dr. Hatem El-Aydi

2. Contents: • What is filtering? • Digital Filters • Digital Filter Characteristics • Digital Filter Classification • IIR filter. • Digital filter design. • What and why Realization? • Realization of IIR filters. • Direct form realization • Cascade realization • Parallel realization • State variable realization. • Direct Programming Realization • Nested Programming Realization • Transformed State Vector Realization • Conclusion. • References. F I L T E R S

3. What is filtering? • Filtering is a process of selecting, or suppressing, certain frequency components of a signal. • Filtering is often done to suppress noise. F I L T E R S

4. What is Digital Filters? • Digital filter is a discrete-time system that alters the spectral information contained in some discrete-time signal x producing a new discrete-time signal y • Sampled signals are represented digitally as sequences of numbers F I L T E R S

5. Digital Filter Characteristics • Algorithm running on a processing core. • Programmable. • Easily designed, tested, and implemented on PC. • Are not subject to drift or dependent on temperature. • Can accurately handle low-frequency signals. F I L T E R S

6. Digital Filter Classification • Digital filter are characterized by their impulse response. • A filter’s impulse response is its response to an impulse input. • Impulse response: • Completely (LTI) systems. • Uniquely determines frequency response. • Finite duration (FIR) or infinite duration (IIR). F I L T E R S

7. IIR Filters • IIR (infinite impulse response) filters allow zeros and poles; FIR allow zeros only. IIR can be more selective for a given filter order. • IIR also called recursive filters: output depends on past inputs and past outputs. • IIR designs are not guaranteed to be stable. F I L T E R S

8. Digital filter design Digital filter designis a process in which we construct a digital hardware or a program (software) that meets the given specification F I L T E R S • Define the specifications of filter • Selection of appropriate technique for filter’s coefficient evaluation • Selection of appropriate structure of filter • Analysis of finite word-length effect • Implementation

9. What and why Realization? • Realizationis the process of converting the transfer function into a block diagram or program (software); this block diagram or software is called the realization • Designers are interested in realizations which are economical, simple, and cheap, with short word-length and high dynamic range • Numerical values of the coefficients are calculated from the transfer function. F I L T E R S

10. Forms of realization of IIR filters: Direct. Cascade. Parallel. State Variable. Realization of IIR filters. F I L T E R S

11. Direct-form Realization. Direct-form I • filters are realized directly from the difference equation: F I L T E R S

12. By breaking H(z) into a product of two transfer functions: Direct-form II F I L T E R S

13. Example(1) Find the direct form I and direct form II of: Solu: First H(z) should be changed to rational poly in Then solution is: F I L T E R S

14. Realization blocks Direct form I Direct form II F I L T E R S

15. Cascade Realization of IIR Filter: F I L T E R S In the cascade realization, H(z) is broken into a product of transfer functions H1(z), H2(z), ... ,Hi(z), each a rational expression in z1- as follows: Also output equation is:

16. Cont: F I L T E R S • filters are realized as a cascade of first-order and second-order sections. Each section can be realized as direct-form I, direct-form II, or any other type.

17. Parallel realization • filters are realized as a parallel connection of first-order and second-order sections, that is, the outputs of the lower-order sections are connected to an adder. Each section can be realized as direct-form I, direct-form II, or any other type.

18. It is useful to represent a linear constant coefficient difference eq. by a system of first-order linear constant coefficient difference State variable representation F I L T E R S Definition:The state of the system is the minimal information required that along the input allows the determination of the output.

19. Cont. F I L T E R S let So y(n)=CTv(n)+dx(n)

20. Cont. F I L T E R S y(n)=Av(n)+Bx(n)

21. Direct Programming Realization F I L T E R S

22. Nested Programming Realization F I L T E R S

23. Transformed State Vector Realization. An infinite number of state variable representations can be obtained by performing special type of linear transformation on an existing state variable representation. • Let state model of the output eq is: F I L T E R S Define as product of v(n)by nonsingular matrix Q then:

24. Cont: Then inserting an identity matrix then we get: Recognize And insert an identity matrix between and v(n) we get: F I L T E R S

25. Cont: To join with main equations new variables defined as: Which providing an infinite number of possible state variable realization. F I L T E R S

26. Conclusion: • In this presentation we learn more about digital filter characteristics. • The definition of realization and its need for use are also mentioned. • Many form of realization are used in order to get the best structure of the filter. • Matlab program is use for implement the block diagram of the filter easily. F I L T E R S

27. References F I L T E R S

28. Thanks F I L T E R S