•

0 likes•31 views

analog coomunication

Report

Share

Report

Share

Download to read offline

Importance sampling has been widely used to improve the efficiency of deterministic computer simulations where the simulation output is uniquely determined, given a fixed input. To represent complex system behavior more realistically, however, stochastic computer models are gaining popularity. Unlike deterministic computer simulations, stochastic simulations produce different outputs even at the same input. This extra degree of stochasticity presents a challenge for reliability assessment in engineering system designs. Our study tackles this challenge by providing a computationally efficient method to estimate a system's reliability. Specifically, we derive the optimal importance sampling density and allocation procedure that minimize the variance of a reliability estimator. The application of our method to a computationally intensive, aeroelastic wind turbine simulator demonstrates the benefits of the proposed approaches. GDRR Opening Workshop - Variance Reduction for Reliability Assessment with St...

GDRR Opening Workshop - Variance Reduction for Reliability Assessment with St...The Statistical and Applied Mathematical Sciences Institute

Importance sampling has been widely used to improve the efficiency of deterministic computer simulations where the simulation output is uniquely determined, given a fixed input. To represent complex system behavior more realistically, however, stochastic computer models are gaining popularity. Unlike deterministic computer simulations, stochastic simulations produce different outputs even at the same input. This extra degree of stochasticity presents a challenge for reliability assessment in engineering system designs. Our study tackles this challenge by providing a computationally efficient method to estimate a system's reliability. Specifically, we derive the optimal importance sampling density and allocation procedure that minimize the variance of a reliability estimator. The application of our method to a computationally intensive, aeroelastic wind turbine simulator demonstrates the benefits of the proposed approaches. GDRR Opening Workshop - Variance Reduction for Reliability Assessment with St...

GDRR Opening Workshop - Variance Reduction for Reliability Assessment with St...The Statistical and Applied Mathematical Sciences Institute

Overview of sampling

Overview of sampling

Sampling

Sampling

T01061142150

T01061142150

Performance Analysis of Fractional Sample Rate Converter Using Audio Applicat...

Performance Analysis of Fractional Sample Rate Converter Using Audio Applicat...

Digital signal processing part1

Digital signal processing part1

Multrate dsp

Multrate dsp

Tdm fdm

Tdm fdm

4.Sampling and Hilbert Transform

4.Sampling and Hilbert Transform

Chapter 6m

Chapter 6m

Lec2.pptx

Lec2.pptx

Dsp Lab Record

Dsp Lab Record

SignalDecompositionTheory.pptx

SignalDecompositionTheory.pptx

Pulse modulation

Pulse modulation

Spectral Analysis of Sample Rate Converter

Spectral Analysis of Sample Rate Converter

Fo3610221025

Fo3610221025

dsp dip.pptx

dsp dip.pptx

Basic concepts

Basic concepts

Slide Tín hiệu & Hệ thống - Lesson 1 Introduction to signals - Hoàng Gia Hưng...

Slide Tín hiệu & Hệ thống - Lesson 1 Introduction to signals - Hoàng Gia Hưng...

GDRR Opening Workshop - Variance Reduction for Reliability Assessment with St...

GDRR Opening Workshop - Variance Reduction for Reliability Assessment with St...

unit4 sampling.pptx

unit4 sampling.pptx

2 Aliasing (1).pdf

2 Aliasing (1).pdf

1.pdf

1.pdf

dsl-advances-0130938106-9780130938107.pdf

dsl-advances-0130938106-9780130938107.pdf

419907669-Linear-Algebra-by-Gilbert-Strang.pdf

419907669-Linear-Algebra-by-Gilbert-Strang.pdf

Cable Engineering for Local Area Networks (Barry J. Elliott) (Z-Library).pdf

Cable Engineering for Local Area Networks (Barry J. Elliott) (Z-Library).pdf

Module 1 (1).pdf

Module 1 (1).pdf

exfo_spec-sheet_maxtester-635_v16_en.pdf

exfo_spec-sheet_maxtester-635_v16_en.pdf

mod_2.pdf

mod_2.pdf

454022781-ODN-Planning-and-Design-Suggestions-TLF.pdf

454022781-ODN-Planning-and-Design-Suggestions-TLF.pdf

mod_3.pdf

mod_3.pdf

383934148-DWDM-101-Introduction-to-DWDM-2-pdf.pdf

383934148-DWDM-101-Introduction-to-DWDM-2-pdf.pdf

mod_4.pdf

mod_4.pdf

Applications of Operational Amplifiers 3rd generation techniques (Jerald G. G...

Applications of Operational Amplifiers 3rd generation techniques (Jerald G. G...

408375669-XDSL.pdf

408375669-XDSL.pdf

Exfo-CABLESHARK-P3-Specifications-11A67.pdf

Exfo-CABLESHARK-P3-Specifications-11A67.pdf

101483423-Fiber-Characterization-Training.pdf

101483423-Fiber-Characterization-Training.pdf

424185963-Introduction-to-VoLTE.pdf

424185963-Introduction-to-VoLTE.pdf

exfo_reference-guide_otn.pdf

exfo_reference-guide_otn.pdf

388865344-990dsl-Manu-copper-loop-tester.pdf

388865344-990dsl-Manu-copper-loop-tester.pdf

exfo_reference-guide_resistive-fault-location-methods_en.pdf

exfo_reference-guide_resistive-fault-location-methods_en.pdf

Differences between analog and digital communicationanalog-vs-digital-communication (concept of analog and digital).pptx

analog-vs-digital-communication (concept of analog and digital).pptxKarpagam Institute of Teechnology

Filters for Electromagnetic Compatibility Applications

Filters for Electromagnetic Compatibility Applications

Raashid final report on Embedded Systems

Raashid final report on Embedded Systems

Autodesk Construction Cloud (Autodesk Build).pptx

Autodesk Construction Cloud (Autodesk Build).pptx

Seismic Hazard Assessment Software in Python by Prof. Dr. Costas Sachpazis

Seismic Hazard Assessment Software in Python by Prof. Dr. Costas Sachpazis

Multivibrator and its types defination and usges.pptx

Multivibrator and its types defination and usges.pptx

Insurance management system project report.pdf

Insurance management system project report.pdf

8th International Conference on Soft Computing, Mathematics and Control (SMC ...

8th International Conference on Soft Computing, Mathematics and Control (SMC ...

analog-vs-digital-communication (concept of analog and digital).pptx

analog-vs-digital-communication (concept of analog and digital).pptx

Geometric constructions Engineering Drawing.pdf

Geometric constructions Engineering Drawing.pdf

Research Methodolgy & Intellectual Property Rights Series 2

Research Methodolgy & Intellectual Property Rights Series 2

"United Nations Park" Site Visit Report.

"United Nations Park" Site Visit Report.

Passive Air Cooling System and Solar Water Heater.ppt

Passive Air Cooling System and Solar Water Heater.ppt

Involute of a circle,Square, pentagon,HexagonInvolute_Engineering Drawing.pdf

Involute of a circle,Square, pentagon,HexagonInvolute_Engineering Drawing.pdf

Introduction to Artificial Intelligence and History of AI

Introduction to Artificial Intelligence and History of AI

UNIT-2 image enhancement.pdf Image Processing Unit 2 AKTU

UNIT-2 image enhancement.pdf Image Processing Unit 2 AKTU

Seizure stage detection of epileptic seizure using convolutional neural networks

Seizure stage detection of epileptic seizure using convolutional neural networks

Introduction to Arduino Programming: Features of Arduino

Introduction to Arduino Programming: Features of Arduino

5G and 6G refer to generations of mobile network technology, each representin...

5G and 6G refer to generations of mobile network technology, each representin...

Developing a smart system for infant incubators using the internet of things ...

Developing a smart system for infant incubators using the internet of things ...

Microkernel in Operating System | Operating System

Microkernel in Operating System | Operating System

- 1. Sampling & Signal Reconstruction with Applications Dr. Ali Hussein Muqaibel ver. 4.5 1 Analog to Digital Conversion (ADC) Part I Digital Transmission Part II Digital Communications
- 2. Class Objectives • Why Digital? • Analog to Digital Conversion (ADC) • Sampling • Sampling Theorem. • What is the spectrum of sampled signals? • Signal Reconstruction. • The interpolation function (sinc) • Zero hold and first order hold approximation • Practical Sampling Dr. Ali Hussein Muqaibel 2
- 3. Advantages of Digital Communication over Analog Communication ➢Immunity to Noise (possibility of regenerating the original digital signal if signal power to noise power ratio (SNR) is relatively high by using of devices called repeaters along the path of transmission). ➢Efficient use of communication bandwidth (through use of techniques like compression). ➢Digital communication provides higher security (data encryption). ➢Error Control Coding : the ability to detect errors and correct them if necessary. ➢Design and manufacturing of electronics for digital communication systems is much easier and much cheaper than the design and manufacturing of electronics for analog communication systems. Dr. Ali Hussein Muqaibel 3 What is the price for going digital ?
- 4. Analog to Digital Conversion PCM: Pulse Coded Modulation Source of continuous time message signal Low-pass filter Sampler Quantizer Encoder 01101110101 PCM signal applied to channel input Dr. Ali Hussein Muqaibel Continuous-time vs. Discrete time signal. Digital vs. Analog 4 Distorted PCM signal produced at channel output Regenerative repeater …… Regenerative repeater Regenerated PCM signal applied to the receiver Final channel output Regeneration circuit Decoder Reconstruction filter Destination
- 5. Sampling Theorem A signal whose spectrum is band limited to 𝐵 𝐻𝑧 [𝐺(𝑓) = 0 𝑓𝑜𝑟 |𝑓| > 𝐵] can be reconstructed exactly from its samples taken uniformly at a rate 𝑅 > 2𝐵 𝐻𝑧 (samples/ sec). i.e 𝑇𝑆 < 1 2𝐵 Minimum sampling frequency is 𝑓𝑠 = 2𝐵 𝐻𝑧 𝑁𝑦𝑞𝑢𝑖𝑠𝑡 𝑅𝑎𝑡𝑒 𝑇𝑠 = 1 2𝐵 Nyquist interval The 𝑛𝑡ℎ impulse located at 𝑡 = 𝑛𝑇𝑠 has a strength 𝑔 𝑛𝑇𝑠 the value of 𝑔(𝑡) at 𝑡 = 𝑛𝑇𝑠 t s s s s s s s s s s s s g(t) Dr. Ali Hussein Muqaibel 𝑇𝑠 = 1/𝑓𝑠 sampling interval 5
- 6. Math Representation of Sampling • 𝑔(𝑡) is a continuous–time signal with bandwidth 𝐵 𝐻𝑧 or (2𝐵 𝑟𝑎𝑑/𝑠). • Sampling is equivalent to multiplying 𝑔(𝑡) by a train consisting of unit impulses repeating periodically every 𝑇𝑠 second. A train of delta function 𝑇 𝑠 (𝑡) that occur every 𝑇𝑠 is given by 𝑇 𝑠 𝑡 = 𝑛=−∞ +∞ 𝛿(𝑡 − 𝑛𝑇𝑠) • The sampled signal ҧ 𝑔(𝑡) ҧ 𝑔 𝑡 = 𝑔(𝑡) 𝑛=−∞ +∞ 𝛿(𝑡 − 𝑛𝑇𝑠) = 𝑛=−∞ +∞ 𝑔(𝑡)𝛿(𝑡 − 𝑛𝑇𝑠) = 𝑛=−∞ +∞ 𝑔(𝒏𝑻𝒔)𝛿(𝑡 − 𝑛𝑇𝑠) Dr. Ali Hussein Muqaibel 6 𝛿𝑇(𝑡) t s s s s s s s s s s s s g(t)
- 7. Spectrum of Sampled Signal t s s s s s s s s s s s s g(t) t s s s s s s s s s s s s g(t) G() +2B 2B s s s s s s A G() +2B 2B s s s s s s A/Ts ... ... s+2B s–2B s+2B s–2B ҧ 𝑔 𝑡 = 𝑛=−∞ +∞ 𝑔 𝒏𝑻𝒔 𝛿 𝑡 − 𝑛𝑇𝑠 = 𝟏 𝑻𝒔 −∞ +∞ 𝑔 𝑡 𝑒𝑗𝑛2𝜋𝑓𝑠𝑡 ҧ 𝐺 𝑓 = 𝟏 𝑻𝒔 −∞ +∞ 𝐺(𝑓 − 𝑛𝑓𝑠) Dr. Ali Hussein Muqaibel 7 Using Fourier series representation: 𝜹𝑻𝒔 𝒕 = 𝑛=−∞ +∞ 𝛿(𝑡 − 𝑛𝑇𝑠) = 𝟏 𝑻𝒔 −∞ +∞ 𝑒𝑗𝑛2𝜋𝑓𝑠𝑡
- 8. Signal Reconstruction G() +2B 2B s s s s s s A/Ts ... ... s+2B s–2B s+2B s–2B LPF for reconstructing the origianl signal from the sampled signal Reconstructed Signal +2B 2B s s s s s s A/Ts Ts Magnitude of LPF should be Ts to cancel the scaling factor caused by sampling s > 2(2B) No interference between Images Dr. Ali Hussein Muqaibel 8
- 9. Signal Reconstruction (Interpolation) • Interpolation: the process of reconstructing continuous-time signal from its samples. • Use of lowpass filter of BW of 𝐵 𝐻𝑧 (ideal) 𝐻 𝑓 = 𝑇𝑆Π 𝑓 2𝐵 • In time domain (IFT) ℎ 𝑡 = 𝟐𝑩𝑻𝒔𝑠𝑖𝑛𝑐 2𝜋𝐵𝑡 • At Nyquist rate 𝟐𝑩𝑻𝒔 = 𝟏 ℎ 𝑡 = 𝑠𝑖𝑛𝑐 2𝜋𝐵𝑡 Observe ℎ 𝑡 = 0 at all Nyquist sampling interval 𝑡 = ± 𝑛 2𝐵 𝑒𝑥𝑐𝑒𝑝𝑡 𝑎𝑡 𝑡 = 0 Dr. Ali Hussein Muqaibel 9
- 10. • The output of the reconstruction system (discrete convolution) 𝑔 𝑡 = 𝑘 𝑔 𝑘𝑇𝑠 ℎ 𝑡 − 𝑘𝑇𝑠 𝑔(𝑡) = 𝑘 𝑔 𝑘𝑇𝑠 𝑠𝑖𝑛𝑐 2𝜋𝐵 𝑡 − 𝑘𝑇𝑠 • At Nyquist rate 𝑇𝑠 = 1 2𝐵 𝑔(𝑡) = 𝑘 𝑔 𝑘𝑇𝑠 𝑠𝑖𝑛𝑐 2𝜋𝐵𝑡 − 𝑘𝜋 • Interpolation formula yields the value of 𝑔(𝑡) between samples as a weighted sum of all sample values. Signal Reconstruction Reconstruction system ℎ 𝑡 = 𝑠𝑖𝑛𝑐 2𝜋𝐵𝑡 Dr. Ali Hussein Muqaibel 10
- 11. Example Find a signal 𝑔(𝑡) that is band-limited to 𝐵 𝐻𝑧 & whose samples are 𝒈 𝟎 = 𝟏 𝑎𝑛𝑑 𝑔 ±𝑇𝑠 = 𝑔 ±2𝑇𝑠 = 𝑔 ±3𝑇𝑠 = ⋯ = 0 where the sampling interval 𝑇𝑠 is the Nyquist interval for 𝑔 𝑡 , that is 𝑇𝑠 = 1/2𝐵. 𝑔(𝑡) = 𝑘 𝑔 𝑘𝑇𝑠 𝑠𝑖𝑛𝑐 2𝜋𝐵 𝑡 − 𝑘𝑇𝑠 𝑔(𝑡) = 𝑠𝑖𝑛𝑐 2𝜋𝐵𝑡 Dr. Ali Hussein Muqaibel 𝑔(𝑡) 11
- 12. Order of Signal Reconstruction (Reconstruction Filters) Zero–Order Hold Dr. Ali Hussein Muqaibel Ts g(t) Ts t h0(t) 1 Ts g(t) 1 Ts t h1(t) –Ts Ts g(t) First–Order Hold –2Ts 2Ts Ts –Ts 1 t hOO(t) Sinc Filter (Infinite–Order Hold) Ts g(t) 12 𝑦 𝑡 = ℎ 𝑡 ∗ ҧ 𝑔 𝑡 = ℎ 𝑡 ∗ [𝑔 𝑡 𝛿𝑇𝑠 𝑡 ]
- 13. Interpolation and hold Circuits in Frequency Dr. Ali Hussein Muqaibel 13 Zero–Order Hold Sinc Filter (Infinite–Order Hold) Interpolation function
- 14. Practical Sampling Pulses • Finite width practical pulses • Because it is periodic, using Fourier series representation 𝑃𝑇𝑠 = −∞ +∞ 𝐶𝑛𝑒𝑗2𝜋𝑛𝑓𝑠 • Not 𝜹𝑻𝒔 𝒕 = 𝟏 𝑻𝒔 −∞ +∞ 𝑒𝑗𝑛2𝜋𝑓𝑠𝑡 Dr. Ali Hussein Muqaibel 14
- 15. Practical Difficulty in Signal Reconstruction • To avoid the need for ideal filter 𝑓𝑠 > 2𝐵, we may use a filter with gradual cutoff characteristics. • Also we want the filter to be zero outside...(Impossible by Paley-Wiener criterion) but closely approximated. Dr. Ali Hussein Muqaibel 15 G() +2B 2B s s s s s s A/Ts ... ... s+2B s–2B s+2B s–2B LPF for reconstructing the origianl signal from the sampled signal Reconstructed Signal +2B 2B s s s s s s A/Ts Ts Magnitude of LPF should be Ts to cancel the scaling factor caused by sampling s > 2(2B) No interference between Images