Lecture 16: Filter Design: Impulse Invariance and Bilinear Transform
|
|
- Gladys Hampton
- 6 years ago
- Views:
Transcription
1 EE58 Digital Signal Processing University of Washington Autumn 2 Dept. of Electrical Engineering Lecture 6: Filter Design: Impulse Invariance and Bilinear Transform Nov 26, 2 Prof: J. Bilmes <bilmes@ee.washington.edu> TA: Mingzhou Song <msong@u.washington.edu> 6. Introduction to Filter Design Filter design is the most important practical application of this course. Filter, any modification of the signal according to design specifications. Frequency selectivity Causal filters (real time without delay) Note ideal filters are not realizable. We can t have perfect magnitude response. For example, the ideal low pass filter is not realizable because it requires infinite length sinc function. We would like causal filters: IIR ok FIR sometimes even better Ex: typical way to specify low pass filter Design specifications for a low pass filter is shown in Fig 6.. H(e jω ) + δ Transition δ PSfrag replacements Passband Stopband δ 2 ω p ω s π ω Figure 6.: Low pass filter design specifications. 6-
2 6-2 In the low pass filter, δ is the tolerance at the pass band, δ 2 is the tolerance at the stop band. In transition band, we do not care too much about what happens. The quantitative relationship for the maganitude response within the pass band and stop band are given as follows: δ H(e jω + δ, ω ω p H(e jω δ 2, ω s ω p π where δ and δ 2 are usually small positive numbers, e.g., δ can be 6 or 9. Usually discrete time filter designis done in terms of normalized discrete time. Normalization in time by T is equivalent to normalization in frequency by /T. So in frequency domain, π/t is normalized to π. Or even sometimes for plotting, frquency is further normalized by π and a normalized corresponds to π in radians. Note: If we use linear phase systems, we can just specify magnitude response, which will produce a system with only a delay and is easy to deal with. If we use IIR system, we might have to deal with phase. There are two different design procedures: ) start with continuous time filter and then map it to a discrete time filter. So we can use analog techniques to do filter design. 2) use new techniques to design filter directly in discrete time. 6.2 Design of Discrete Time Filter from Continuous Time Filter We can apply transform technique to obtain H(z) and h[n] for discrete time fiters from H c (s) and h c (t) as shown below: H c (s) h c (t) Transform Techniques H(z) h[n] Recall Laplace transfrom, a generalization of Fourier transform, is defined as X(s) = x(t)e st dt (6.) Plugging jω into X(s) we get Fourier transform X( jω). Here is a summary of three continuous time low pass filters. Butterworth Filters The magnitude response of Butterworth filters are in the following form as shown in Fig 6.2 Properties: H c ( jω) = + (Ω/Ω c ) 2N (6.2) ) N-th order filter has first (2N ) derivatives of H c ( jω). The derivatives are zero at Ω =.
3 f (Hz) Figure 6.2: Magnitude response of Butterworth filters. 2) monotonic in stop and pass band. 3) It is hard to control where approximately the tolerance will be. 4) Error reduces as N increases, but the filter is harder to implement. Chebychev Filters The magnitude response of Chebychev filters is where H c ( jω) = + ε 2 V 2 N (ω/ω c) V N (x) = cos(n cos x) (6.3) Note V N (x) can be described by the following initial values and recurrence equation: N =, V (x) = N =, V (x) = cos(cos x) = x N = 2, V 2 (x) = cos(n cos x) = 2x 2 V N+ (x) = 2xV N (x) V N (x) The magnitude response of Chebychev filter is shown in Fig 6.3. Properties: ) equiripple in passband (resp. stop band) and monotonic in the stop band (resp. pass band) for type I (resp type II) filters. 2) better for design to have error distributed over pass band or stop band by equiripple and can often lower N which leads to simpler implementation. Elliptic Filters The magnitude response of Elliptic filters is H c ( jω) = + ε 2 V 2 N (Ω) (6.4)
4 f (Hz) Figure 6.3: Magnitude response of Chebychev filters. where V N (Ω) is a Jacobian elliptic function. The magnitude response of elliptic filter is shown in Fig f (Hz) Figure 6.4: Magnitude response of elliptic filters. Error distribute over both pass band and stop band. This is as best as can be done for given Ω p, δ, δ 2, and transitive region (Ω p to Ω s ) Impulse Invariance Sampling the continuous time impulse response with sampling period T d, we obtain h[n] = T d h c (nt d ) Then If H c ( jω) = for Ω π/t d, H(e jω ) = k= H(e jω ) = H c ( jω/t d) H c ( j ω T d + j 2π T d k) ω π
5 6-5 Will aliasing occur for the previous H c ( jω)? Yes. Consider Butterworth filter. But if order of filter N is high enough, aliasing will be small enough to be acceptable, i.e., within our tolerance δ 2. Question: Can we control aliasing by changing T d, the sampling period? Choose cut-off frequency ω c in discrete time. Transform to Ω c = ω c /T d. Larger T d needs a continuous filter with larger Ω c and wider frequency spread, so T d doesn t control aliasing. Aliasing can is controlled by order N and types of filters. Question: How to choose T d? Choose T d so that relevant details of h c (t) is captured. Continuous to Discrete-Time in terms of Laplace to z-transform If a causal LTI system has then the impulse response is H c (s) = N k= A k s s k { t < h c (t) = N k= A ke s kt t By impulse response, and h[n] = T d h c (nt d ) = u[n] N k= H(z) = T d A k e s knt d = u[n] N k= T d A k e s kt d z N k= T d A k ( e s k T d ) n The pole at s = s k in s-plane become pole at z = e s kt d in z-plane. That a stable and causal H c (s) has Re(s k ) < for all its poles implies H(z) is also stable and causal because all the poles must have e s kt d <, i.e. with the unit circle in z-plane. However, zeros have a more complex mapping. Note: impulse invariance works only for bandlimited filters, i.e., not continuous time high pass filters since that would cause big aliasing Bilinear Transform We can find z-transform directly from Laplace transform by mappling the jω axis in s-plane to the unit circle on z-plane, i.e., < Ω < maps to π < ω < π, which is a non-linear mapping. The bilinear transform is defined by which is accomplished by replacing s using Note T d has no effect again. Points: ( 2 z ) H(z) = H c T d + z (6.5) s = 2 T d z + z (6.6) ) Left half of s-plane mapping to inside of the unit circle in z-plane, i.e., s = σ + jω, σ < z <
6 6-6 2) Right half of s-plane mapping to outside of the unit circle in z-plane, i.e., s = σ + jω, σ > z > Hence, a causal and stable continuous time system will be mapped to a causal and stable discrete-time system. 3) jω is mapped to unit circle. Why? z = + (T d/2)s (T d /2)s = + σ(t d/2) + jω(t d /2) σ(t d /2) jω(t d /2) When σ =, which says Why is unit circle spanned? So we have z = + jω(t d/2) jω(t d /2) z = σ + jω = s = 2 T d e jω + e jω = j 2 T d tan(ω/2) Ω = 2 T d tan(ω/2) σ = Therefore which is shown in Fig 6.5 ω = 2tan (ΩT d /2) PSfrag replacements π ω Ω π Figure 6.5: ω Ω plot for bilinear transform. An example is shown in Fig 7.8 (O&S, pg 452). Some of the bilinear transform mapping relationships are shown in Fig 6.6. Points: ) 2) 3) σ < z < σ > z > jω e jω
7 6-7 jω s-plane 2/T d 4/T d 2/T d /T d 2/T d 4/T d σ 2/T d z-plane replacements z = /T d Figure 6.6: Bilinear mapping between s-plane and z-plane.
8 6-8 4) real axis mappling the black x at z = comes from s = ± and s = ± j. the red x at z = comes from s =. as s goes from to, z goes from to. z = at s = 2/T d (light green x ). as s goes from to 2/T d, z goes from to. as s goes from 2/T d to, z goes from to. 5) the yellow line moves up, smaller yellow circles. 6) the pink line moves down, smaller pink circles. 7) light blue circle bigger than red circle ( z = ) is vertical line between σ = and σ = 2/T d. 8) dark blue circle (on the left) is vertical s-plane line. Other notes: this produces both frequency warping and phase warping, i.e., linear phase in continuous time maps to non-linear phase in discrete time. the technique is particularly good idealized functions that are piecewise constant such as high-pass filters (HPF), low-pass filters (LPF), band-pass filters (BPF), etc., since they are easy to analyze in terms of the endpoints where the responses change.
Digital Signal Processing IIR Filter Design via Bilinear Transform
Digital Signal Processing IIR Filter Design via Bilinear Transform D. Richard Brown III D. Richard Brown III 1 / 12 Basic Procedure We assume here that we ve already decided to use an IIR filter. The basic
More informationDigital Signal Processing
COMP ENG 4TL4: Digital Signal Processing Notes for Lecture #24 Tuesday, November 4, 2003 6.8 IIR Filter Design Properties of IIR Filters: IIR filters may be unstable Causal IIR filters with rational system
More informationEE482: Digital Signal Processing Applications
Professor Brendan Morris, SEB 3216, brendan.morris@unlv.edu EE482: Digital Signal Processing Applications Spring 2014 TTh 14:30-15:45 CBC C222 Lecture 05 IIR Design 14/03/04 http://www.ee.unlv.edu/~b1morris/ee482/
More informationDesign of IIR filters
Design of IIR filters Standard methods of design of digital infinite impulse response (IIR) filters usually consist of three steps, namely: 1 design of a continuous-time (CT) prototype low-pass filter;
More informationLecture 8: Signal Reconstruction, DT vs CT Processing. 8.1 Reconstruction of a Band-limited Signal from its Samples
EE518 Digital Signal Processing University of Washington Autumn 2001 Dept. of Electrical Engineering Lecture 8: Signal Reconstruction, D vs C Processing Oct 24, 2001 Prof: J. Bilmes
More informationLecture 7 Discrete Systems
Lecture 7 Discrete Systems EE 52: Instrumentation and Measurements Lecture Notes Update on November, 29 Aly El-Osery, Electrical Engineering Dept., New Mexico Tech 7. Contents The z-transform 2 Linear
More informationDigital Signal Processing Lecture 8 - Filter Design - IIR
Digital Signal Processing - Filter Design - IIR Electrical Engineering and Computer Science University of Tennessee, Knoxville October 20, 2015 Overview 1 2 3 4 5 6 Roadmap Discrete-time signals and systems
More informationLecture 13: Pole/Zero Diagrams and All Pass Systems
EE518 Digital Signal Processing University of Washington Autumn 2001 Dept. of Electrical Engineering Lecture 13: Pole/Zero Diagrams and All Pass Systems No4, 2001 Prof: J. Bilmes
More informationEE 521: Instrumentation and Measurements
Aly El-Osery Electrical Engineering Department, New Mexico Tech Socorro, New Mexico, USA November 1, 2009 1 / 27 1 The z-transform 2 Linear Time-Invariant System 3 Filter Design IIR Filters FIR Filters
More informationLecture 8 - IIR Filters (II)
Lecture 8 - IIR Filters (II) James Barnes (James.Barnes@colostate.edu) Spring 2009 Colorado State University Dept of Electrical and Computer Engineering ECE423 1 / 27 Lecture 8 Outline Introduction Digital
More informationFilter Analysis and Design
Filter Analysis and Design Butterworth Filters Butterworth filters have a transfer function whose squared magnitude has the form H a ( jω ) 2 = 1 ( ) 2n. 1+ ω / ω c * M. J. Roberts - All Rights Reserved
More informationLecture 14: Minimum Phase Systems and Linear Phase
EE518 Digital Signal Processing University of Washington Autumn 2001 Dept. of Electrical Engineering Lecture 14: Minimum Phase Systems and Linear Phase Nov 19, 2001 Prof: J. Bilmes
More informationDIGITAL SIGNAL PROCESSING. Chapter 6 IIR Filter Design
DIGITAL SIGNAL PROCESSING Chapter 6 IIR Filter Design OER Digital Signal Processing by Dr. Norizam Sulaiman work is under licensed Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
More informationLike bilateral Laplace transforms, ROC must be used to determine a unique inverse z-transform.
Inversion of the z-transform Focus on rational z-transform of z 1. Apply partial fraction expansion. Like bilateral Laplace transforms, ROC must be used to determine a unique inverse z-transform. Let X(z)
More informationECE 410 DIGITAL SIGNAL PROCESSING D. Munson University of Illinois Chapter 12
. ECE 40 DIGITAL SIGNAL PROCESSING D. Munson University of Illinois Chapter IIR Filter Design ) Based on Analog Prototype a) Impulse invariant design b) Bilinear transformation ( ) ~ widely used ) Computer-Aided
More informationDiscrete-Time David Johns and Ken Martin University of Toronto
Discrete-Time David Johns and Ken Martin University of Toronto (johns@eecg.toronto.edu) (martin@eecg.toronto.edu) University of Toronto 1 of 40 Overview of Some Signal Spectra x c () t st () x s () t xn
More informationUNIT - III PART A. 2. Mention any two techniques for digitizing the transfer function of an analog filter?
UNIT - III PART A. Mention the important features of the IIR filters? i) The physically realizable IIR filters does not have linear phase. ii) The IIR filter specification includes the desired characteristics
More informationLecture 9 Infinite Impulse Response Filters
Lecture 9 Infinite Impulse Response Filters Outline 9 Infinite Impulse Response Filters 9 First-Order Low-Pass Filter 93 IIR Filter Design 5 93 CT Butterworth filter design 5 93 Bilinear transform 7 9
More informationINFINITE-IMPULSE RESPONSE DIGITAL FILTERS Classical analog filters and their conversion to digital filters 4. THE BUTTERWORTH ANALOG FILTER
INFINITE-IMPULSE RESPONSE DIGITAL FILTERS Classical analog filters and their conversion to digital filters. INTRODUCTION 2. IIR FILTER DESIGN 3. ANALOG FILTERS 4. THE BUTTERWORTH ANALOG FILTER 5. THE CHEBYSHEV-I
More informationLecture 19: Discrete Fourier Series
EE518 Digital Signal Processing University of Washington Autumn 2001 Dept. of Electrical Engineering Lecture 19: Discrete Fourier Series Dec 5, 2001 Prof: J. Bilmes TA: Mingzhou
More informationLecture 8 - IIR Filters (II)
Lecture 8 - IIR Filters (II) James Barnes (James.Barnes@colostate.edu) Spring 24 Colorado State University Dept of Electrical and Computer Engineering ECE423 1 / 29 Lecture 8 Outline Introduction Digital
More informationChapter 7: IIR Filter Design Techniques
IUST-EE Chapter 7: IIR Filter Design Techniques Contents Performance Specifications Pole-Zero Placement Method Impulse Invariant Method Bilinear Transformation Classical Analog Filters DSP-Shokouhi Advantages
More informationDIGITAL SIGNAL PROCESSING UNIT III INFINITE IMPULSE RESPONSE DIGITAL FILTERS. 3.6 Design of Digital Filter using Digital to Digital
DIGITAL SIGNAL PROCESSING UNIT III INFINITE IMPULSE RESPONSE DIGITAL FILTERS Contents: 3.1 Introduction IIR Filters 3.2 Transformation Function Derivation 3.3 Review of Analog IIR Filters 3.3.1 Butterworth
More informationReview of Discrete-Time System
Review of Discrete-Time System Electrical & Computer Engineering University of Maryland, College Park Acknowledgment: ENEE630 slides were based on class notes developed by Profs. K.J. Ray Liu and Min Wu.
More informationLecture 3 - Design of Digital Filters
Lecture 3 - Design of Digital Filters 3.1 Simple filters In the previous lecture we considered the polynomial fit as a case example of designing a smoothing filter. The approximation to an ideal LPF can
More information2.161 Signal Processing: Continuous and Discrete Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. I Reading:
More informationESE 531: Digital Signal Processing
ESE 531: Digital Signal Processing Lec 8: February 12th, 2019 Sampling and Reconstruction Lecture Outline! Review " Ideal sampling " Frequency response of sampled signal " Reconstruction " Anti-aliasing
More informationESE 531: Digital Signal Processing
ESE 531: Digital Signal Processing Lec 8: February 7th, 2017 Sampling and Reconstruction Lecture Outline! Review " Ideal sampling " Frequency response of sampled signal " Reconstruction " Anti-aliasing
More informationDigital Signal Processing
COMP ENG 4TL4: Digital Signal Processing Notes for Lecture #20 Wednesday, October 22, 2003 6.4 The Phase Response and Distortionless Transmission In most filter applications, the magnitude response H(e
More informationSignals and Systems. Problem Set: The z-transform and DT Fourier Transform
Signals and Systems Problem Set: The z-transform and DT Fourier Transform Updated: October 9, 7 Problem Set Problem - Transfer functions in MATLAB A discrete-time, causal LTI system is described by the
More informationPS403 - Digital Signal processing
PS403 - Digital Signal processing 6. DSP - Recursive (IIR) Digital Filters Key Text: Digital Signal Processing with Computer Applications (2 nd Ed.) Paul A Lynn and Wolfgang Fuerst, (Publisher: John Wiley
More informationEE 225D LECTURE ON DIGITAL FILTERS. University of California Berkeley
University of California Berkeley College of Engineering Department of Electrical Engineering and Computer Sciences Professors : N.Morgan / B.Gold EE225D Digital Filters Spring,1999 Lecture 7 N.MORGAN
More informationAPPLIED SIGNAL PROCESSING
APPLIED SIGNAL PROCESSING DIGITAL FILTERS Digital filters are discrete-time linear systems { x[n] } G { y[n] } Impulse response: y[n] = h[0]x[n] + h[1]x[n 1] + 2 DIGITAL FILTER TYPES FIR (Finite Impulse
More informationStability Condition in Terms of the Pole Locations
Stability Condition in Terms of the Pole Locations A causal LTI digital filter is BIBO stable if and only if its impulse response h[n] is absolutely summable, i.e., 1 = S h [ n] < n= We now develop a stability
More informationELEG 305: Digital Signal Processing
ELEG 305: Digital Signal Processing Lecture : Design of Digital IIR Filters (Part I) Kenneth E. Barner Department of Electrical and Computer Engineering University of Delaware Fall 008 K. E. Barner (Univ.
More informationLecture 7: z-transform Properties, Sampling and Nyquist Sampling Theorem
EE518 Digital Signal Proessing University of Washington Autumn 21 Dept. of Eletrial Engineering ure 7: z-ransform Properties, Sampling and Nyquist Sampling heorem Ot 22, 21 Prof: J. Bilmes
More informationV. IIR Digital Filters
Digital Signal Processing 5 March 5, V. IIR Digital Filters (Deleted in 7 Syllabus). (dded in 7 Syllabus). 7 Syllabus: nalog filter approximations Butterworth and Chebyshev, Design of IIR digital filters
More informationINF3440/INF4440. Design of digital filters
Last week lecture Today s lecture: Chapter 8.1-8.3, 8.4.2, 8.5.3 INF3440/INF4440. Design of digital filters October 2004 Last week lecture Today s lecture: Chapter 8.1-8.3, 8.4.2, 8.5.3 Last lectures:
More informationLecture 4: FT Pairs, Random Signals and z-transform
EE518 Digital Signal Processing University of Washington Autumn 2001 Dept. of Electrical Engineering Lecture 4: T Pairs, Rom Signals z-transform Wed., Oct. 10, 2001 Prof: J. Bilmes
More informationMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science. Fall Solutions for Problem Set 2
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science Issued: Tuesday, September 5. 6.: Discrete-Time Signal Processing Fall 5 Solutions for Problem Set Problem.
More informationELEG 5173L Digital Signal Processing Ch. 5 Digital Filters
Department of Electrical Engineering University of Aransas ELEG 573L Digital Signal Processing Ch. 5 Digital Filters Dr. Jingxian Wu wuj@uar.edu OUTLINE 2 FIR and IIR Filters Filter Structures Analog Filters
More informationDigital Signal Processing Lecture 9 - Design of Digital Filters - FIR
Digital Signal Processing - Design of Digital Filters - FIR Electrical Engineering and Computer Science University of Tennessee, Knoxville November 3, 2015 Overview 1 2 3 4 Roadmap Introduction Discrete-time
More informationToday. ESE 531: Digital Signal Processing. IIR Filter Design. Impulse Invariance. Impulse Invariance. Impulse Invariance. ω < π.
Today ESE 53: Digital Signal Processing! IIR Filter Design " Lec 8: March 30, 207 IIR Filters and Adaptive Filters " Bilinear Transformation! Transformation of DT Filters! Adaptive Filters! LMS Algorithm
More information(Refer Slide Time: 01:28 03:51 min)
Digital Signal Processing Prof. S. C. Dutta Roy Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture 40 FIR Design by Windowing This is the 40 th lecture and our topic for
More informationAn Iir-Filter Example: A Butterworth Filter
An Iir-Filter Example: A Butterworth Filter Josef Goette Bern University of Applied Sciences, Biel Institute of Human Centered Engineering - microlab JosefGoette@bfhch February 7, 2017 Contents 1 Introduction
More informationDigital Control & Digital Filters. Lectures 21 & 22
Digital Controls & Digital Filters Lectures 2 & 22, Professor Department of Electrical and Computer Engineering Colorado State University Spring 205 Review of Analog Filters-Cont. Types of Analog Filters:
More information-Digital Signal Processing- FIR Filter Design. Lecture May-16
-Digital Signal Processing- FIR Filter Design Lecture-17 24-May-16 FIR Filter Design! FIR filters can also be designed from a frequency response specification.! The equivalent sampled impulse response
More informationDigital Signal Processing
COMP ENG 4TL4: Digital Signal Processing Notes for Lecture #21 Friday, October 24, 2003 Types of causal FIR (generalized) linear-phase filters: Type I: Symmetric impulse response: with order M an even
More informationLecture 20: Discrete Fourier Transform and FFT
EE518 Digital Signal Processing University of Washington Autumn 2001 Dept of Electrical Engineering Lecture 20: Discrete Fourier Transform and FFT Dec 10, 2001 Prof: J Bilmes TA:
More informationAnalog and Digital Filter Design
Analog and Digital Filter Design by Jens Hee http://jenshee.dk October 208 Change log 28. september 208. Document started.. october 208. Figures added. 6. october 208. Bilinear transform chapter extended.
More informationSignals & Systems. Lecture 5 Continuous-Time Fourier Transform. Alp Ertürk
Signals & Systems Lecture 5 Continuous-Time Fourier Transform Alp Ertürk alp.erturk@kocaeli.edu.tr Fourier Series Representation of Continuous-Time Periodic Signals Synthesis equation: x t = a k e jkω
More informationEE123 Digital Signal Processing
Optimality H d (e j! ) EE13 Digital Signal Processing Lecture 3 Least Squares: Z! p! s Z Don t Care!care Variation: weighted least-squares H(e j! ) H d (e j! ) d! W (!) H(e j! ) H d (e j! ) d! Design Through
More informationNAME: ht () 1 2π. Hj0 ( ) dω Find the value of BW for the system having the following impulse response.
University of California at Berkeley Department of Electrical Engineering and Computer Sciences Professor J. M. Kahn, EECS 120, Fall 1998 Final Examination, Wednesday, December 16, 1998, 5-8 pm NAME: 1.
More informationLecture 14: Windowing
Lecture 14: Windowing ECE 401: Signal and Image Analysis University of Illinois 3/29/2017 1 DTFT Review 2 Windowing 3 Practical Windows Outline 1 DTFT Review 2 Windowing 3 Practical Windows DTFT Review
More informationFROM ANALOGUE TO DIGITAL
SIGNALS AND SYSTEMS: PAPER 3C1 HANDOUT 7. Dr David Corrigan 1. Electronic and Electrical Engineering Dept. corrigad@tcd.ie www.mee.tcd.ie/ corrigad FROM ANALOGUE TO DIGITAL To digitize signals it is necessary
More informationLecture 5 - Assembly Programming(II), Intro to Digital Filters
GoBack Lecture 5 - Assembly Programming(II), Intro to Digital Filters James Barnes (James.Barnes@colostate.edu) Spring 2009 Colorado State University Dept of Electrical and Computer Engineering ECE423
More informationMultimedia Signals and Systems - Audio and Video. Signal, Image, Video Processing Review-Introduction, MP3 and MPEG2
Multimedia Signals and Systems - Audio and Video Signal, Image, Video Processing Review-Introduction, MP3 and MPEG2 Kunio Takaya Electrical and Computer Engineering University of Saskatchewan December
More informationDHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EC2314- DIGITAL SIGNAL PROCESSING UNIT I INTRODUCTION PART A
DHANALAKSHMI COLLEGE OF ENGINEERING DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EC2314- DIGITAL SIGNAL PROCESSING UNIT I INTRODUCTION PART A Classification of systems : Continuous and Discrete
More informationMultirate signal processing
Multirate signal processing Discrete-time systems with different sampling rates at various parts of the system are called multirate systems. The need for such systems arises in many applications, including
More informationVALLIAMMAI ENGINEERING COLLEGE. SRM Nagar, Kattankulathur DEPARTMENT OF INFORMATION TECHNOLOGY. Academic Year
VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur- 603 203 DEPARTMENT OF INFORMATION TECHNOLOGY Academic Year 2016-2017 QUESTION BANK-ODD SEMESTER NAME OF THE SUBJECT SUBJECT CODE SEMESTER YEAR
More informationQuestion Bank. UNIT 1 Part-A
FATIMA MICHAEL COLLEGE OF ENGINEERING & TECHNOLOGY Senkottai Village, Madurai Sivagangai Main Road, Madurai -625 020 An ISO 9001:2008 Certified Institution Question Bank DEPARTMENT OF ELECTRONICS AND COMMUNICATION
More informationDigital Signal Processing Lecture 10 - Discrete Fourier Transform
Digital Signal Processing - Discrete Fourier Transform Electrical Engineering and Computer Science University of Tennessee, Knoxville November 12, 2015 Overview 1 2 3 4 Review - 1 Introduction Discrete-time
More informationNAME: 11 December 2013 Digital Signal Processing I Final Exam Fall Cover Sheet
NAME: December Digital Signal Processing I Final Exam Fall Cover Sheet Test Duration: minutes. Open Book but Closed Notes. Three 8.5 x crib sheets allowed Calculators NOT allowed. This test contains four
More informationELEN 4810 Midterm Exam
ELEN 4810 Midterm Exam Wednesday, October 26, 2016, 10:10-11:25 AM. One sheet of handwritten notes is allowed. No electronics of any kind are allowed. Please record your answers in the exam booklet. Raise
More information/ (2π) X(e jω ) dω. 4. An 8 point sequence is given by x(n) = {2,2,2,2,1,1,1,1}. Compute 8 point DFT of x(n) by
Code No: RR320402 Set No. 1 III B.Tech II Semester Regular Examinations, Apr/May 2006 DIGITAL SIGNAL PROCESSING ( Common to Electronics & Communication Engineering, Electronics & Instrumentation Engineering,
More informationGrades will be determined by the correctness of your answers (explanations are not required).
6.00 (Fall 2011) Final Examination December 19, 2011 Name: Kerberos Username: Please circle your section number: Section Time 2 11 am 1 pm 4 2 pm Grades will be determined by the correctness of your answers
More information( ) John A. Quinn Lecture. ESE 531: Digital Signal Processing. Lecture Outline. Frequency Response of LTI System. Example: Zero on Real Axis
John A. Quinn Lecture ESE 531: Digital Signal Processing Lec 15: March 21, 2017 Review, Generalized Linear Phase Systems Penn ESE 531 Spring 2017 Khanna Lecture Outline!!! 2 Frequency Response of LTI System
More informationUNIVERSITI SAINS MALAYSIA. EEE 512/4 Advanced Digital Signal and Image Processing
-1- [EEE 512/4] UNIVERSITI SAINS MALAYSIA First Semester Examination 2013/2014 Academic Session December 2013 / January 2014 EEE 512/4 Advanced Digital Signal and Image Processing Duration : 3 hours Please
More informationEach problem is worth 25 points, and you may solve the problems in any order.
EE 120: Signals & Systems Department of Electrical Engineering and Computer Sciences University of California, Berkeley Midterm Exam #2 April 11, 2016, 2:10-4:00pm Instructions: There are four questions
More informationDSP-CIS. Chapter-4: FIR & IIR Filter Design. Marc Moonen
DSP-CIS Chapter-4: FIR & IIR Filter Design Marc Moonen Dept. E.E./ESAT-STADIUS, KU Leuven marc.moonen@esat.kuleuven.be www.esat.kuleuven.be/stadius/ PART-II : Filter Design/Realization Step-1 : Define
More informationLecture 2 OKAN UNIVERSITY FACULTY OF ENGINEERING AND ARCHITECTURE
OKAN UNIVERSITY FACULTY OF ENGINEERING AND ARCHITECTURE EEE 43 DIGITAL SIGNAL PROCESSING (DSP) 2 DIFFERENCE EQUATIONS AND THE Z- TRANSFORM FALL 22 Yrd. Doç. Dr. Didem Kivanc Tureli didemk@ieee.org didem.kivanc@okan.edu.tr
More informationEECE 301 Signals & Systems Prof. Mark Fowler
EECE 3 Signals & Systems Prof. ark Fowler Note Set #28 D-T Systems: DT Filters Ideal & Practical /4 Ideal D-T Filters Just as in the CT case we can specify filters. We looked at the ideal filter for the
More informationChapter 7: Filter Design 7.1 Practical Filter Terminology
hapter 7: Filter Design 7. Practical Filter Terminology Analog and digital filters and their designs constitute one of the major emphasis areas in signal processing and communication systems. This is due
More informationOptimal Design of Real and Complex Minimum Phase Digital FIR Filters
Optimal Design of Real and Complex Minimum Phase Digital FIR Filters Niranjan Damera-Venkata and Brian L. Evans Embedded Signal Processing Laboratory Dept. of Electrical and Computer Engineering The University
More informationRoll No. :... Invigilator s Signature :.. CS/B.Tech (EE-N)/SEM-6/EC-611/ DIGITAL SIGNAL PROCESSING. Time Allotted : 3 Hours Full Marks : 70
Name : Roll No. :.... Invigilator s Signature :.. CS/B.Tech (EE-N)/SEM-6/EC-611/2011 2011 DIGITAL SIGNAL PROCESSING Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks.
More informationLecture 7 - IIR Filters
Lecture 7 - IIR Filters James Barnes (James.Barnes@colostate.edu) Spring 204 Colorado State University Dept of Electrical and Computer Engineering ECE423 / 2 Outline. IIR Filter Representations Difference
More information! Introduction. ! Discrete Time Signals & Systems. ! Z-Transform. ! Inverse Z-Transform. ! Sampling of Continuous Time Signals
ESE 531: Digital Signal Processing Lec 25: April 24, 2018 Review Course Content! Introduction! Discrete Time Signals & Systems! Discrete Time Fourier Transform! Z-Transform! Inverse Z-Transform! Sampling
More informationEE 4372 Tomography. Carlos E. Davila, Dept. of Electrical Engineering Southern Methodist University
EE 4372 Tomography Carlos E. Davila, Dept. of Electrical Engineering Southern Methodist University EE 4372, SMU Department of Electrical Engineering 86 Tomography: Background 1-D Fourier Transform: F(
More informationDigital Signal Processing
Digital Signal Proceing IIR Filter Deign Manar Mohaien Office: F8 Email: manar.ubhi@kut.ac.kr School of IT Engineering Review of the Precedent Lecture Propertie of FIR Filter Application of FIR Filter
More informationFinal Exam January 31, Solutions
Final Exam January 31, 014 Signals & Systems (151-0575-01) Prof. R. D Andrea & P. Reist Solutions Exam Duration: Number of Problems: Total Points: Permitted aids: Important: 150 minutes 7 problems 50 points
More informationEE Homework 13 - Solutions
EE3054 - Homework 3 - Solutions. (a) The Laplace transform of e t u(t) is s+. The pole of the Laplace transform is at which lies in the left half plane. Hence, the Fourier transform is simply the Laplace
More informationElectronic Circuits EE359A
Electronic Circuits EE359A Bruce McNair B26 bmcnair@stevens.edu 21-216-5549 Lecture 22 578 Second order LCR resonator-poles V o I 1 1 = = Y 1 1 + sc + sl R s = C 2 s 1 s + + CR LC s = C 2 sω 2 s + + ω
More informationIIR digital filter design for low pass filter based on impulse invariance and bilinear transformation methods using butterworth analog filter
IIR digital filter design for low pass filter based on impulse invariance and bilinear transformation methods using butterworth analog filter Nasser M. Abbasi May 5, 0 compiled on hursday January, 07 at
More information2.161 Signal Processing: Continuous and Discrete Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. Massachusetts
More informationEEL3135: Homework #4
EEL335: Homework #4 Problem : For each of the systems below, determine whether or not the system is () linear, () time-invariant, and (3) causal: (a) (b) (c) xn [ ] cos( 04πn) (d) xn [ ] xn [ ] xn [ 5]
More informationConvolution. Define a mathematical operation on discrete-time signals called convolution, represented by *. Given two discrete-time signals x 1, x 2,
Filters Filters So far: Sound signals, connection to Fourier Series, Introduction to Fourier Series and Transforms, Introduction to the FFT Today Filters Filters: Keep part of the signal we are interested
More informationEE 224 Signals and Systems I Review 1/10
EE 224 Signals and Systems I Review 1/10 Class Contents Signals and Systems Continuous-Time and Discrete-Time Time-Domain and Frequency Domain (all these dimensions are tightly coupled) SIGNALS SYSTEMS
More informationA system that is both linear and time-invariant is called linear time-invariant (LTI).
The Cooper Union Department of Electrical Engineering ECE111 Signal Processing & Systems Analysis Lecture Notes: Time, Frequency & Transform Domains February 28, 2012 Signals & Systems Signals are mapped
More informationChapter 5 Frequency Domain Analysis of Systems
Chapter 5 Frequency Domain Analysis of Systems CT, LTI Systems Consider the following CT LTI system: xt () ht () yt () Assumption: the impulse response h(t) is absolutely integrable, i.e., ht ( ) dt< (this
More informationMAHALAKSHMI ENGINEERING COLLEGE-TRICHY
DIGITAL SIGNAL PROCESSING DEPT./SEM.: CSE /VII DIGITAL FILTER DESIGN-IIR & FIR FILTER DESIGN PART-A. Lit the different type of tructure for realiation of IIR ytem? AUC APR 09 The different type of tructure
More informationEE482: Digital Signal Processing Applications
Professor Brendan Morris, SEB 3216, brendan.morris@unlv.edu EE482: Digital Signal Processing Applications Spring 2014 TTh 14:30-15:45 CBC C222 Lecture 02 DSP Fundamentals 14/01/21 http://www.ee.unlv.edu/~b1morris/ee482/
More informationDigital Signal Processing Lecture 4
Remote Sensing Laboratory Dept. of Information Engineering and Computer Science University of Trento Via Sommarive, 14, I-38123 Povo, Trento, Italy Digital Signal Processing Lecture 4 Begüm Demir E-mail:
More informationDiscrete-time Signals and Systems in
Discrete-time Signals and Systems in the Frequency Domain Chapter 3, Sections 3.1-39 3.9 Chapter 4, Sections 4.8-4.9 Dr. Iyad Jafar Outline Introduction The Continuous-Time FourierTransform (CTFT) The
More informationDiscrete-Time Signals and Systems
ECE 46 Lec Viewgraph of 35 Discrete-Time Signals and Systems Sequences: x { x[ n] }, < n
More informationLecture 8 Finite Impulse Response Filters
Lecture 8 Finite Impulse Response Filters Outline 8. Finite Impulse Response Filters.......................... 8. oving Average Filter............................... 8.. Phase response...............................
More informationGrades will be determined by the correctness of your answers (explanations are not required).
6.00 (Fall 20) Final Examination December 9, 20 Name: Kerberos Username: Please circle your section number: Section Time 2 am pm 4 2 pm Grades will be determined by the correctness of your answers (explanations
More informationECE 3084 QUIZ 2 SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING GEORGIA INSTITUTE OF TECHNOLOGY APRIL 2, Name:
ECE 3084 QUIZ 2 SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING GEORGIA INSTITUTE OF TECHNOLOGY APRIL 2, 205 Name:. The quiz is closed book, except for one 2-sided sheet of handwritten notes. 2. Turn off
More informationUNIVERSITY OF OSLO. Faculty of mathematics and natural sciences. Forslag til fasit, versjon-01: Problem 1 Signals and systems.
UNIVERSITY OF OSLO Faculty of mathematics and natural sciences Examination in INF3470/4470 Digital signal processing Day of examination: December 1th, 016 Examination hours: 14:30 18.30 This problem set
More informationChapter 5 Frequency Domain Analysis of Systems
Chapter 5 Frequency Domain Analysis of Systems CT, LTI Systems Consider the following CT LTI system: xt () ht () yt () Assumption: the impulse response h(t) is absolutely integrable, i.e., ht ( ) dt< (this
More informationFinal Exam Solutions : Wednesday, Dec 13, Prof: J. Bilmes TA: Mingzhou Song
1 of 9 EE518 Digital Signal Processing University of Washington Autumn 2000 Dept of Electrical Engineering Final Exam Solutions : Wednesday, Dec 13, 2000 Prof: J Bilmes TA: Mingzhou
More information