Filter structures ELEC-E5410
|
|
- Randall Walsh
- 5 years ago
- Views:
Transcription
1 Filter structures ELEC-E5410
2 Contents FIR filter basics Ideal impulse responses Polyphase decomposition Fractional delay by polyphase structure Nyquist filters Half-band filters Gibbs phenomenon Discrete-time differentiator Hilbert transformer 2
3 Basic concepts Finite impulse response filters (FIR) Infinite impulse response filters (IIR) 3
4 Basic concepts Linear-phase FIR filters, types I-IV Odd/even length, symmetrical/anti-symmetrical Group delay Magnitude response H(e jω )
5 Basic concepts Impulse responses of FIR types I-IV Symmetric/antisymmetric odd/even length Ceil(N/2) independent parameters, N is the filter order Structure implies linear phase 5
6 Basic concepts Zero-phase/amplitude response Impossible to implement in practice, but easy to implement when causality is relaxed Unlike magnitude response, can be negative Zero-phase response of symmetric even-order N (Type I) FIR filter H(e j! )=e j!n/2 H(!) X H(!) =h[ N N/2 2 ]+2 X n=1 h[ N 2 n] cos(n!) Zero-phase response of Type I-IV FIR filters H(e j! )=e j!n/2 e j H(!) 6
7 Basic concepts Translation of filter s pass-band Modulation of filter coefficients Complementary filter G(z) = z -N/2 H(z) 7
8 Some ideal filter types Ideal lowpass filter Ideal highpass filter Ideal bandpass filter Ideal bandstop filter Ideal Hilbert transformer (90 deg phase shifter) Ideal integrator Ideal differentiator 8
9 Polyphase decomposition R.W. 9
10 Polyphase decomposition Consider the z-transform of sequence x[n] X(z) can be rewritten as Subsequences x k [n] are called polyphase components of x[n] Functions X k (z) are called polyphase components of X(z) R.W. 10
11 Type 1 polyphase decomposition Polyphase decomposition of FIR filter H(z) The structure is used to change filtering and downsampling to down-sampling and filtering The number of operations remains the same but the filter operates at lower frequency
12 Type 1 polyphase decomposition Transpose of the polyphase decomposition of FIR filter H(z) The structure is used to change up-sampling and filtering into filtering and upsampling
13 Type 2 polyphase decomposition Obtained by setting R i (z M ) = E M-i (z M ) In case of fractional sampling rate change L/M, polyphase decomposition can be used to filter at rate F s /M instead of LF s where F s refers to the original sampling rate
14 Computationally efficient decimator R.W. 14
15 Computationally efficient interpolator Type I Type II R.W. 15
16 Commutator representation of interpolation and decimation with polyphase structure interpolation decimation 16
17 Polyphase fractional sampling/ fractional delay filter Polyphase structure for P/Q fractional sampling Stage r provides a delay equal to r/p of the input sampling interval. Number of stages sets the resolution. h 0 (n) 1:Q h 1 (n) h P-2 (n) Commutator steps through branches with the increments of Q. h P-1 (n)
18 Polyphase fractional sampling/ fractional delay filter Suppose that we want to calculate the output in the place r+d (r +d needn t be rational any more) between the stages r and r+1. Linear interpolation of filter outputs between the nearest neighbors can be interpreted as interpolation of filter coefficients.
19 Nyquist filters
20 Nyquist filters/lth-band filters Under certain conditions, a low-pass filter can be designed to have a number of zero-valued coefficients When used as interpolation filters these filters preserve the nonzero samples of the up-sampler output at the interpolator output Due to the presence of zero-valued coefficients, these filters are computationally more efficient than other low-pass filters of the same order The structure is computationally attractive This is different from the sparse filter F(z L ) in IFIR, though Nyquist filters (root raised cosine) are typically used for pulse shaping in wireless transceivers
21 Nyquist filters Consider the factor-of-l interpolator x[n] X ΗL H(z) y[n] The input-output relation of the interpolator in the z-domain is Y (z) =H(z)X(z L ) H(z) in the L-branch polyphase form H(z) = LX 1 k=0 z k E k (z L ) 21
22 Nyquist filters Suppose that the ith polyphase component is a constant Then we can express Y(z) as H(z) =E 0 (z L )+ + z i+1 E i 1 (z L )+ z i + z i 1 E i+1 (z L )+ + z L+1 E L 1 (z L ) X Y (z) = z i X(z L )+ LX 1 k=0 k6=i X z k E k (z L )X(z L ) Therefore, ( y[ln + i] = x[n], 8n Thus, the input samples appear at the output without any distortion for all values of n, whereas, in-between output samples are determined by interpolation 22
23 Nyquist filters X Impulse response of an Lth band filter for i=0 satisfies h(ln) = (, n =0 0, otherwise X Example: Impulse response of a 2 nd -band (half-band) low-pass filter Every 2 nd coefficient is zero, except the center point 23
24 Half-band filters Impulse response of the half-band filter (L=2) satisfies The length is constrained to 4k + 3, k= 0,1,2, The transfer function is given by Therefore, 24
25 Half-band filters If the filter has real coefficients Thus, The frequency response is symmetrical w.r.t. half-band frequency π/2 25
26 Half-band filters Zero-phase response of a half-band filter Here in linear scale Can be negative Non-causal Symmetrical w.r.t. π/2 26
27 Design of Nyquist filters Several different ways to design A low-pass linear-phase Lth-band FIR filter can be readily designed via the windowed Fourier series approach The impulse response coefficients of the low-pass filter are given by h[n] = h lp [n] w[n], where h lp [n] is the impulse response of Xthe ideal low-pass filter with cut-off π/l and w[n] is a window function The impulse response of the ideal low-pass filter with cut-off π/l h lp [n] = sin( n/l), 1 apple n apple1 n Every Lth filter coefficient is zero 27
28 Design of Nyquist filters Impulse responses of ideal low-pass filter (sinc) with cut-off π/2, Hamming window used to weight the sinc pulse and the resulting half-band filter Hamming window w[n] = cos 2 n 2N +1 Other windows: Bartlett, Hann, Blackman, Kaiser, Chebyshev, N apple n apple N 28
29 Design of Nyquist filters Magnitude responses of the half-band filters using Hamming window or rectangular window The latter gives rise to Gibbs phenomenon 29
30 Gibbs phenomenon Oscillatory behavior in the magnitude responses of causal FIR filters obtained by truncating the impulse response coefficients of ideal filters Reasons for oscillations: - h lp [n] is infinitely long and not absolutely summable, and hence filter is unstable - Rectangular window has an abrupt transition to zero Gibbs phenomenon can be reduced either: - Using a window that tapers smoothly to zero at each end, or - Providing a smooth transition from passband to stopband in the magnitude specifications 30
31 Gibbs phenomenon As the length of the lowpass filter is increased, the number of ripples in both pass-band and stop-band increases, with a corresponding decrease in the ripple widths Height of the largest ripples remain the same independent of the length 31
32 Gibbs phenomenon One instance of convolution of the sinc and rectangle in frequency domain corresponding to rectangular windowing of the ideal low-pass filter in time domain 32
33 Gibbs phenomenon Two-sided magnitude response after rectangular windowing of the ideal lowpass filter 33
34 Differentiator
35 Differentiator Employed to perform the differentiation operation on the discrete-time version of a continuous-time signal A practical discrete-time differentiator is used to perform the differentiation operation in the low frequency range and is thus designed to have a linear magnitude response from dc to a frequency smaller than π No need to boost high-frequency noise
36 Digital differentiator in time From inverse Fourier transform Ideal frequency response of discrete-time differentiator Ideal impulse response
37 Digital differentiator First-difference differentiator/ zero-order FIR high-pass filter Main drawback of the firstdifference differentiator is that it also amplifies the high frequency noise Does not match to the impulse response in the previous page 37
38 Digital differentiator first-order differentiator Matches to the differentiator s impulse response Attenuates high frequencies Correponds to the formula of numerical derivation 38
39 Design Example: Applying rectangular window to the impulse response of the order 40 Gibbs phenomenon hits again One design option is to apply windowing, other than rectangular, to the ideal impulse response 39
40 Design by Taylor series Consider the impulse response of the form On the unit circle The approximation becomes 40
41 Design by Taylor series Taylor series expansion of sin() The first approximation: The second approximation: Choose coefficients to cancel higher order terms 41
42 Design by Taylor series Magnitude responses of different approximations 42
43 Hilbert transformer 43
44 Analytic signal A discrete-time analytic signal has a zero-valued spectrum for all negative frequencies Such a signal finds applications in, e.g., single-sideband digital communication systems and in envelope detection Analytic signal is a complex signal whose imaginary part is the Hilbert transform of a real signal
45 Hilbert transform Consider the analytic signal when x[n] and x [n] are real signals and x [n] is the Hilbert transform of x[n] When y[n] is an analytic signal This is satisfied when 45
46 Hilbert transform Imaginary part of the analytic signal is obtained by passing the real signal x[n] through the filter There is discontinuity in spectrum at π so the impulse response if of infinite length 46
47 Design Option 1: Apply windowing to the ideal impulse response Option 2: Take a half-band filter, subtract the center tap and do a frequency translation by modulating filter coefficients by exp(jnπ/2), and scale by 2. When H (z) is a half-band filter + several other ways 47
Stability 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 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 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 informationMultirate Digital Signal Processing
Multirate Digital Signal Processing Basic Sampling Rate Alteration Devices Up-sampler - Used to increase the sampling rate by an integer factor Down-sampler - Used to decrease the sampling rate by an integer
More informationFilter Design Problem
Filter Design Problem Design of frequency-selective filters usually starts with a specification of their frequency response function. Practical filters have passband and stopband ripples, while exhibiting
More informationLINEAR-PHASE FIR FILTERS DESIGN
LINEAR-PHASE FIR FILTERS DESIGN Prof. Siripong Potisuk inimum-phase Filters A digital filter is a minimum-phase filter if and only if all of its zeros lie inside or on the unit circle; otherwise, it is
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 informationBasic Design Approaches
(Classic) IIR filter design: Basic Design Approaches. Convert the digital filter specifications into an analog prototype lowpass filter specifications. Determine the analog lowpass filter transfer function
More informationDigital Signal Processing:
Digital Signal Processing: Mathematical and algorithmic manipulation of discretized and quantized or naturally digital signals in order to extract the most relevant and pertinent information that is carried
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 informationLAB 6: FIR Filter Design Summer 2011
University of Illinois at Urbana-Champaign Department of Electrical and Computer Engineering ECE 311: Digital Signal Processing Lab Chandra Radhakrishnan Peter Kairouz LAB 6: FIR Filter Design Summer 011
More informationECSE 512 Digital Signal Processing I Fall 2010 FINAL EXAMINATION
FINAL EXAMINATION 9:00 am 12:00 pm, December 20, 2010 Duration: 180 minutes Examiner: Prof. M. Vu Assoc. Examiner: Prof. B. Champagne There are 6 questions for a total of 120 points. This is a closed book
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 informationQuadrature-Mirror Filter Bank
Quadrature-Mirror Filter Bank In many applications, a discrete-time signal x[n] is split into a number of subband signals { v k [ n]} by means of an analysis filter bank The subband signals are then processed
More informationLABORATORY 3 FINITE IMPULSE RESPONSE FILTERS
LABORATORY 3 FINITE IMPULSE RESPONSE FILTERS 3.. Introduction A digital filter is a discrete system, used with the purpose of changing the amplitude and/or phase spectrum of a signal. The systems (filters)
More informationIT DIGITAL SIGNAL PROCESSING (2013 regulation) UNIT-1 SIGNALS AND SYSTEMS PART-A
DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING IT6502 - DIGITAL SIGNAL PROCESSING (2013 regulation) UNIT-1 SIGNALS AND SYSTEMS PART-A 1. What is a continuous and discrete time signal? Continuous
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 informationResponses of Digital Filters Chapter Intended Learning Outcomes:
Responses of Digital Filters Chapter Intended Learning Outcomes: (i) Understanding the relationships between impulse response, frequency response, difference equation and transfer function in characterizing
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 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 informationDISCRETE-TIME SIGNAL PROCESSING
THIRD EDITION DISCRETE-TIME SIGNAL PROCESSING ALAN V. OPPENHEIM MASSACHUSETTS INSTITUTE OF TECHNOLOGY RONALD W. SCHÄFER HEWLETT-PACKARD LABORATORIES Upper Saddle River Boston Columbus San Francisco New
More informationComputer-Aided Design of Digital Filters. Digital Filters. Digital Filters. Digital Filters. Design of Equiripple Linear-Phase FIR Filters
Computer-Aided Design of Digital Filters The FIR filter design techniques discussed so far can be easily implemented on a computer In addition, there are a number of FIR filter design algorithms that rely
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 informationReview of Fundamentals of Digital Signal Processing
Solution Manual for Theory and Applications of Digital Speech Processing by Lawrence Rabiner and Ronald Schafer Click here to Purchase full Solution Manual at http://solutionmanuals.info Link download
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 informationReview of Fundamentals of Digital Signal Processing
Chapter 2 Review of Fundamentals of Digital Signal Processing 2.1 (a) This system is not linear (the constant term makes it non linear) but is shift-invariant (b) This system is linear but not shift-invariant
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 informationTransform analysis of LTI systems Oppenheim and Schafer, Second edition pp For LTI systems we can write
Transform analysis of LTI systems Oppenheim and Schafer, Second edition pp. 4 9. For LTI systems we can write yœn D xœn hœn D X kd xœkhœn Alternatively, this relationship can be expressed in the z-transform
More information# FIR. [ ] = b k. # [ ]x[ n " k] [ ] = h k. x[ n] = Ae j" e j# ˆ n Complex exponential input. [ ]Ae j" e j ˆ. ˆ )Ae j# e j ˆ. y n. y n.
[ ] = h k M [ ] = b k x[ n " k] FIR k= M [ ]x[ n " k] convolution k= x[ n] = Ae j" e j ˆ n Complex exponential input [ ] = h k M % k= [ ]Ae j" e j ˆ % M = ' h[ k]e " j ˆ & k= k = H (" ˆ )Ae j e j ˆ ( )
More information1 1.27z z 2. 1 z H 2
E481 Digital Signal Processing Exam Date: Thursday -1-1 16:15 18:45 Final Exam - Solutions Dan Ellis 1. (a) In this direct-form II second-order-section filter, the first stage has
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 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 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 informationIntroduction to Digital Signal Processing
Introduction to Digital Signal Processing 1.1 What is DSP? DSP is a technique of performing the mathematical operations on the signals in digital domain. As real time signals are analog in nature we need
More informationDFT & Fast Fourier Transform PART-A. 7. Calculate the number of multiplications needed in the calculation of DFT and FFT with 64 point sequence.
SHRI ANGALAMMAN COLLEGE OF ENGINEERING & TECHNOLOGY (An ISO 9001:2008 Certified Institution) SIRUGANOOR,TRICHY-621105. DEPARTMENT OF ELECTRONICS AND COMMUNICATION ENGINEERING UNIT I DFT & Fast Fourier
More informationExercises in Digital Signal Processing
Exercises in Digital Signal Processing Ivan W. Selesnick September, 5 Contents The Discrete Fourier Transform The Fast Fourier Transform 8 3 Filters and Review 4 Linear-Phase FIR Digital Filters 5 5 Windows
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 information2.161 Signal Processing: Continuous and Discrete Fall 2008
IT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete all 2008 or information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. assachusetts
More informationAnalog LTI system Digital LTI system
Sampling Decimation Seismometer Amplifier AAA filter DAA filter Analog LTI system Digital LTI system Filtering (Digital Systems) input output filter xn [ ] X ~ [ k] Convolution of Sequences hn [ ] yn [
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 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 informationR13 SET - 1
R13 SET - 1 III B. Tech II Semester Regular Examinations, April - 2016 DIGITAL SIGNAL PROCESSING (Electronics and Communication Engineering) Time: 3 hours Maximum Marks: 70 Note: 1. Question Paper consists
More informationCast of Characters. Some Symbols, Functions, and Variables Used in the Book
Page 1 of 6 Cast of Characters Some s, Functions, and Variables Used in the Book Digital Signal Processing and the Microcontroller by Dale Grover and John R. Deller ISBN 0-13-081348-6 Prentice Hall, 1998
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 informationLecture 19 IIR Filters
Lecture 19 IIR Filters Fundamentals of Digital Signal Processing Spring, 2012 Wei-Ta Chu 2012/5/10 1 General IIR Difference Equation IIR system: infinite-impulse response system The most general class
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 informationWavelets and Multiresolution Processing
Wavelets and Multiresolution Processing Wavelets Fourier transform has it basis functions in sinusoids Wavelets based on small waves of varying frequency and limited duration In addition to frequency,
More informationThe Discrete-Time Fourier
Chapter 3 The Discrete-Time Fourier Transform 清大電機系林嘉文 cwlin@ee.nthu.edu.tw 03-5731152 Original PowerPoint slides prepared by S. K. Mitra 3-1-1 Continuous-Time Fourier Transform Definition The CTFT of
More information1. FIR Filter Design
ELEN E4810: Digital Signal Processing Topic 9: Filter Design: FIR 1. Windowed Impulse Response 2. Window Shapes 3. Design by Iterative Optimization 1 1. FIR Filter Design! FIR filters! no poles (just zeros)!
More informationFourier Series Representation of
Fourier Series Representation of Periodic Signals Rui Wang, Assistant professor Dept. of Information and Communication Tongji University it Email: ruiwang@tongji.edu.cn Outline The response of LIT system
More informationDigital Speech Processing Lecture 10. Short-Time Fourier Analysis Methods - Filter Bank Design
Digital Speech Processing Lecture Short-Time Fourier Analysis Methods - Filter Bank Design Review of STFT j j ˆ m ˆ. X e x[ mw ] [ nˆ m] e nˆ function of nˆ looks like a time sequence function of ˆ looks
More informationUNIVERSITY OF OSLO. Please make sure that your copy of the problem set is complete before you attempt to answer anything.
UNIVERSITY OF OSLO Faculty of mathematics and natural sciences Examination in INF3470/4470 Digital signal processing Day of examination: December 9th, 011 Examination hours: 14.30 18.30 This problem set
More informationVel Tech High Tech Dr.Ranagarajan Dr.Sakunthala Engineering College Department of ECE
Subject Code: EC6502 Course Code:C302 Course Name: PRINCIPLES OF DIGITAL SIGNAL PROCESSING L-3 : T-1 : P-0 : Credits 4 COURSE OBJECTIVES: 1. To learn discrete Fourier transform and its properties 2. To
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 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 informationSignal Processing. Lecture 10: FIR Filter Design. Ahmet Taha Koru, Ph. D. Yildiz Technical University Fall
Signal Processing Lecture 10: FIR Filter Design Ahmet Taha Koru, Ph. D. Yildiz Technical University 2017-2018 Fall ATK (YTU) Signal Processing 2017-2018 Fall 1 / 47 Introduction Introduction ATK (YTU)
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 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 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 informationFilter Banks II. Prof. Dr.-Ing. G. Schuller. Fraunhofer IDMT & Ilmenau University of Technology Ilmenau, Germany
Filter Banks II Prof. Dr.-Ing. G. Schuller Fraunhofer IDMT & Ilmenau University of Technology Ilmenau, Germany Page Modulated Filter Banks Extending the DCT The DCT IV transform can be seen as modulated
More informationGATE EE Topic wise Questions SIGNALS & SYSTEMS
www.gatehelp.com GATE EE Topic wise Questions YEAR 010 ONE MARK Question. 1 For the system /( s + 1), the approximate time taken for a step response to reach 98% of the final value is (A) 1 s (B) s (C)
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 informationOptimum Ordering and Pole-Zero Pairing of the Cascade Form IIR. Digital Filter
Optimum Ordering and Pole-Zero Pairing of the Cascade Form IIR Digital Filter There are many possible cascade realiations of a higher order IIR transfer function obtained by different pole-ero pairings
More informationInterchange of Filtering and Downsampling/Upsampling
Interchange of Filtering and Downsampling/Upsampling Downsampling and upsampling are linear systems, but not LTI systems. They cannot be implemented by difference equations, and so we cannot apply z-transform
More informationDigital Filters Ying Sun
Digital Filters Ying Sun Digital filters Finite impulse response (FIR filter: h[n] has a finite numbers of terms. Infinite impulse response (IIR filter: h[n] has infinite numbers of terms. Causal filter:
More informationUNIT - 7: FIR Filter Design
UNIT - 7: FIR Filter Design Dr. Manjunatha. P manjup.jnnce@gmail.com Professor Dept. of ECE J.N.N. College of Engineering, Shimoga October 5, 06 Unit 7 Syllabus Introduction FIR Filter Design:[,, 3, 4]
More informationContents. Digital Signal Processing, Part II: Power Spectrum Estimation
Contents Digital Signal Processing, Part II: Power Spectrum Estimation 5. Application of the FFT for 7. Parametric Spectrum Est. Filtering and Spectrum Estimation 7.1 ARMA-Models 5.1 Fast Convolution 7.2
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 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 informationREAL TIME DIGITAL SIGNAL PROCESSING
REAL TIME DIGITAL SIGNAL PROCESSING www.electron.frba.utn.edu.ar/dplab Digital Filters FIR and IIR. Design parameters. Implementation types. Constraints. Filters: General classification Filters: General
More informationDigital Filter Structures
Chapter 8 Digital Filter Structures 清大電機系林嘉文 cwlin@ee.nthu.edu.tw 03-5731152 8-1 Block Diagram Representation The convolution sum description of an LTI discrete-time system can, in principle, be used to
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 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 informationDEPARTMENT OF EI DIGITAL SIGNAL PROCESSING ASSIGNMENT 1
This PDF is Created by Simpo PDF Creator unregistered version - http://wwwsimpopdfcom Study hard, for the well is deep, and our brains are shallow DEPARTMENT OF EI DIGITAL SIGNAL PROCESSING ASSIGNMENT
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 informationINSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad
INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad - 500 043 Title Code Regulation ELECTRONICS AND COMMUNICATION ENGINEERING TUTORIAL QUESTION BANK DIGITAL SIGNAL PROCESSING A60421 R13 Structure
More informationLet H(z) = P(z)/Q(z) be the system function of a rational form. Let us represent both P(z) and Q(z) as polynomials of z (not z -1 )
Review: Poles and Zeros of Fractional Form Let H() = P()/Q() be the system function of a rational form. Let us represent both P() and Q() as polynomials of (not - ) Then Poles: the roots of Q()=0 Zeros:
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 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 informationDSP. Chapter-3 : Filter Design. Marc Moonen. Dept. E.E./ESAT-STADIUS, KU Leuven
DSP Chapter-3 : Filter Design Marc Moonen Dept. E.E./ESAT-STADIUS, KU Leuven marc.moonen@esat.kuleuven.be www.esat.kuleuven.be/stadius/ Filter Design Process Step-1 : Define filter specs Pass-band, stop-band,
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 informationECE503: Digital Signal Processing Lecture 5
ECE53: Digital Signal Processing Lecture 5 D. Richard Brown III WPI 3-February-22 WPI D. Richard Brown III 3-February-22 / 32 Lecture 5 Topics. Magnitude and phase characterization of transfer functions
More informationThe basic structure of the L-channel QMF bank is shown below
-Channel QMF Bans The basic structure of the -channel QMF ban is shown below The expressions for the -transforms of various intermediate signals in the above structure are given by Copyright, S. K. Mitra
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 informationDigital Signal Processing, Homework 1, Spring 2013, Prof. C.D. Chung
Digital Signal Processing, Homework, Spring 203, Prof. C.D. Chung. (0.5%) Page 99, Problem 2.2 (a) The impulse response h [n] of an LTI system is known to be zero, except in the interval N 0 n N. The input
More informationZ Transform (Part - II)
Z Transform (Part - II). The Z Transform of the following real exponential sequence x(nt) = a n, nt 0 = 0, nt < 0, a > 0 (a) ; z > (c) for all z z (b) ; z (d) ; z < a > a az az Soln. The given sequence
More informationDigital Filter Structures. Basic IIR Digital Filter Structures. of an LTI digital filter is given by the convolution sum or, by the linear constant
Digital Filter Chapter 8 Digital Filter Block Diagram Representation Equivalent Basic FIR Digital Filter Basic IIR Digital Filter. Block Diagram Representation In the time domain, the input-output relations
More informationLinear Convolution Using FFT
Linear Convolution Using FFT Another useful property is that we can perform circular convolution and see how many points remain the same as those of linear convolution. When P < L and an L-point circular
More informationCh. 7: Z-transform Reading
c J. Fessler, June 9, 3, 6:3 (student version) 7. Ch. 7: Z-transform Definition Properties linearity / superposition time shift convolution: y[n] =h[n] x[n] Y (z) =H(z) X(z) Inverse z-transform by coefficient
More informationHilbert Transforms in Signal Processing
Hilbert Transforms in Signal Processing Stefan L. Hahn Artech House Boston London Contents Preface xiii Introduction 1 Chapter 1 Theory of the One-Dimensional Hilbert Transformation 3 1.1 The Concepts
More informationEE 313 Linear Signals & Systems (Fall 2018) Solution Set for Homework #7 on Infinite Impulse Response (IIR) Filters CORRECTED
EE 33 Linear Signals & Systems (Fall 208) Solution Set for Homework #7 on Infinite Impulse Response (IIR) Filters CORRECTED By: Mr. Houshang Salimian and Prof. Brian L. Evans Prolog for the Solution Set.
More informationEE123 Digital Signal Processing. M. Lustig, EECS UC Berkeley
EE123 Digital Signal Processing Today Last time: DTFT - Ch 2 Today: Continue DTFT Z-Transform Ch. 3 Properties of the DTFT cont. Time-Freq Shifting/modulation: M. Lustig, EE123 UCB M. Lustig, EE123 UCB
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 & Systems
Chapter 2 Discrete-Time Signals & Systems 清大電機系林嘉文 cwlin@ee.nthu.edu.tw 03-5731152 Original PowerPoint slides prepared by S. K. Mitra 2-1-1 Discrete-Time Signals: Time-Domain Representation (1/10) Signals
More informationDiscrete-time Symmetric/Antisymmetric FIR Filter Design
Discrete-time Symmetric/Antisymmetric FIR Filter Design Presenter: Dr. Bingo Wing-Kuen Ling Center for Digital Signal Processing Research, Department of Electronic Engineering, King s College London. Collaborators
More informationComputer Engineering 4TL4: Digital Signal Processing
Computer Engineering 4TL4: Digital Signal Processing Day Class Instructor: Dr. I. C. BRUCE Duration of Examination: 3 Hours McMaster University Final Examination December, 2003 This examination paper includes
More informationA New Twist to Fourier Transforms
Hamish D. Meikle A New Twist to Fourier Transforms WILEY VCH WILEY-VCH Verlag GmbH &, Co. KGaA Table ofcontents 1 The Fourier Transform and the Helix 1 1.1 Fourier Transform Conventions 1 1.1.1 Fourier
More informationHow to manipulate Frequencies in Discrete-time Domain? Two Main Approaches
How to manipulate Frequencies in Discrete-time Domain? Two Main Approaches Difference Equations (an LTI system) x[n]: input, y[n]: output That is, building a system that maes use of the current and previous
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 information