Digital Filter Realization 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

Contents: F I L T E R S 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

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

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

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

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

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

Digital filter design F I L T E R S Digital filter design is 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

What and why Realization? Realization is 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

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

Direct-form Realization. S Direct-form I filters are realized directly from the difference equation:

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

Example(1) F I L T E R S 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

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

Cascade Realization of IIR Filter: 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: F I L T E R S

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.

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.

State variable representation It is useful to represent a linear constant coefficient difference eq. by a system of first-order linear constant coefficient difference 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.

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

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

Direct Programming Realization F I L T E R S

Nested Programming Realization F I L T E R S

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:

Cont: F I L T E R S 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

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

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

References F I L T E R S

Thanks F I L T E R S