Sampling theorem
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The document discusses periodic sampling of continuous-time signals to create discrete-time signals. It explains that when sampling a continuous-time signal x(t) at intervals of T seconds, the discrete-time signal x(n) equals x(nT). It also states that for the discrete-time signal x(n) to uniquely represent the original continuous-time signal x(t), the sampling frequency must be greater than twice the maximum frequency of x(t), which is known as the Nyquist rate.
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The presentation covers sampling theorem, ideal sampling, flat top sampling, natural sampling, reconstruction of signals from samples, aliasing effect, zero order hold, upsampling, downsampling, and discrete time processing of continuous time signals.
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Discrete time signals can be obtained by sampling an analog signal at regular intervals or by observing an inherently discrete process. Sampling is the process of breaking a continuous signal into discrete samples by recording the signal's value at time intervals called the sampling period. According to the sampling theorem, a signal can be uniquely reconstructed from its samples if it is sampled at a rate greater than twice its highest frequency component. Reconstruction involves isolating the baseband spectrum from the spectral images caused by sampling through the use of a low-pass filter, which corresponds to convolving the samples with a sinc function. Practical reconstruction uses an approximation to the ideal sinc filter.
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This document discusses the concepts of sampling theory including the sampling process, sampling theorem, reconstruction of signals, Nyquist interval, aliasing, quantization, and applications. The key points are:
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This document summarizes controlled sequential Monte Carlo, which aims to efficiently estimate intractable likelihoods p(y|θ) in state space models. It does this by defining a target path measure P(dx0:T) and proposal Markov chain Q(dx0:T) to approximate P(dx0:T). Standard sequential Monte Carlo (SMC) methods provide unbiased estimation but can have inadequate performance for practical particle sizes N due to discrepancy between P and Q. The document proposes using twisted path measures that depend on observations to better match P and Q, by defining proposal transitions P(dxt|xt-1,yt:T) that incorporate backward information filters ψ*t(xt)=P(yt
unit4 sampling.pptx
Sampling and reconstruction , Signals and systems
Representation Of CT Signal in terms of its Samples,
Reconstruction of Signal from its Samples
Sampling strategies for Sequential Monte Carlo (SMC) methods
Sequential Monte Carlo methods use importance sampling and resampling to estimate distributions in state space models recursively over time. This document discusses strategies for sampling in sequential Monte Carlo methods, including:
- Using the optimal proposal distribution of the one-step ahead predictive distribution to minimize weight variance.
- Approximating the predictive distribution using mixtures, expansions, auxiliary variables, or Markov chain Monte Carlo methods.
- Considering blocks of variables over time rather than individual time steps to better diffuse particles, such as using a lagged block, reweighting particles before resampling, or sampling an extended block with an augmented state space.
Controlled sequential Monte Carlo
This document summarizes a presentation on controlled sequential Monte Carlo. It discusses state space models, sequential Monte Carlo, and particle marginal Metropolis-Hastings for parameter inference. Controlled sequential Monte Carlo is proposed to lower the variance of the marginal likelihood estimator compared to standard sequential Monte Carlo, improving the performance of parameter inference methods. The method is illustrated on a neuroscience example where it reduces variance for different particle sizes.
2015 12-10 chabert
This document discusses periodic non-uniform sampling (PNS) for satellite communications. PNS can be used to overcome the challenges of high-rate analog-to-digital conversion in satellites, which require costly, complex and power-intensive electronics. PNS utilizes unsynchronized time-interleaved ADCs that introduce non-uniform sampling. It presents a PNS sampling scheme and reconstruction formulas that do not require synchronization. The document also describes improved PNS techniques for faster reconstruction, selective reconstruction with interference cancellation, and analytic signal reconstruction by estimating the sampling delays. PNS shifts complexity from analog to digital domains, allowing the use of lower-cost imperfect analog devices through subsequent digital processing.
EC202 SIGNALS & SYSTEMS Module1 QUESTION BANK
This document contains a question bank with 10 questions related to signals and systems for the module EC 202. The questions cover topics like determining if a signal is periodic, plotting signals, identifying if signals are energy or power signals, analyzing properties of systems like time invariance and causality, explaining classifications of signals, properties of systems, types of systems, and decomposing a signal into odd and even components.
ES_scintillation_detectors_06.ppt
Scintillation detectors consist of scintillator materials, light guides, and photomultiplier tubes. They measure the time of flight and energy deposition of particles to identify particle types. The time resolution is determined by the statistical fluctuations in the number of photoelectrons generated, combined with the intrinsic timing resolutions of the scintillator, light guides, and electronics. A time resolution of 0.1 ns or better is needed for particle identification using time-of-flight measurements.
Convolution
The document discusses convolution, which is a mathematical operation used in signal and image processing. Convolution provides a way to multiply two arrays of numbers to produce a third array. It defines convolution as an integral that calculates the output of a linear time-invariant system by integrating the product of the input and impulse response functions. The key properties of convolution are that it is commutative, distributive, and associative. Examples are provided to demonstrate calculating the convolution of different signals.
Signal fundamentals
This document provides an overview of signal fundamentals, including definitions, examples, and properties of signals. It discusses topics such as signal energy and power, signal transformations, periodic and exponential signals. Examples are provided to illustrate concepts such as determining if a signal has finite energy/power, applying signal transformations, decomposing signals into even and odd components, and plotting exponential signals. The document is from a university course on signal fundamentals and is intended to introduce basic signal processing concepts.
notes11.pdf
The document provides an overview of sampling and pulse modulation. It discusses key topics such as:
1) The sampling theorem which states that a signal with bandwidth B can be reconstructed from samples taken at a rate greater than 2B.
2) How sampling a signal mathematically is achieved by multiplying it by an impulse train.
3) In both the time and frequency domains, sampling a signal is equivalent to multiplying/convolving the signal by an impulse train.
Lecture13
1) Pulse amplitude modulation (PAM) encodes digital information by varying the amplitude of a periodic pulse train based on a sampled message signal. 2) A matched filter is used at the receiver to detect pulses in the presence of noise. The matched filter is a time-reversed and scaled version of the transmitted pulse shape. 3) Intersymbol interference can occur when pulses are transmitted too closely together. Adding a guard period between pulses or using a raised cosine pulse shape can eliminate intersymbol interference.
Signals and Systems.pptx
1) Signals can be classified as continuous-time or discrete-time based on how they are defined over time. Continuous-time signals are defined for every instant in time while discrete-time signals are defined at discrete time instances.
2) A system is defined as a set of elements or devices that produce an output response to an input signal. The relationship between input and output signals is represented by a system operator.
3) Signals and systems can be further classified based on their properties, such as being deterministic or random, periodic or aperiodic, causal or non-causal, and more. Basic operations on signals include time scaling, time reversal, and time shifting.
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一比一原版(USF毕业证)旧金山大学毕业证如何办理
原件一模一样【微信：95270640】【旧金山大学毕业证USF学位证成绩单】【微信：95270640】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
【业务选择办理准则】
一、工作未确定，回国需先给父母、亲戚朋友看下文凭的情况，办理一份就读学校的毕业证【微信：95270640】文凭即可
二、回国进私企、外企、自己做生意的情况，这些单位是不查询毕业证真伪的，而且国内没有渠道去查询国外文凭的真假，也不需要提供真实教育部认证。鉴于此，办理一份毕业证【微信：95270640】即可
三、进国企，银行，事业单位，考公务员等等，这些单位是必需要提供真实教育部认证的，办理教育部认证所需资料众多且烦琐，所有材料您都必须提供原件，我们凭借丰富的经验，快捷的绿色通道帮您快速整合材料，让您少走弯路。
留信网认证的作用:
1:该专业认证可证明留学生真实身份【微信：95270640】
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
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办理旧金山大学毕业证毕业证学位证USF学位证【微信：95270640 】外观非常精致，由特殊纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理旧金山大学毕业证USF学位证毕业证学位证【微信：95270640 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
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授予学位：本部分将注明获得的具体学位名称。
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综上所述，办理旧金山大学毕业证毕业证学位证USF学位证【微信：95270640 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。
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一比一原版(uofo毕业证书)美国俄勒冈大学毕业证如何办理
原版一模一样【微信：741003700 】【(uofo毕业证书)美国俄勒冈大学毕业证成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理(uofo毕业证书)美国俄勒冈大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(uofo毕业证书)美国俄勒冈大学毕业证【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(uofo毕业证书)美国俄勒冈大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理(uofo毕业证书)美国俄勒冈大学毕业证【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。
Prediction of Electrical Energy Efficiency Using Information on Consumer's Ac...
Energy efficiency has been important since the latter part of the last century. The main object of this survey is to determine the energy efficiency knowledge among consumers. Two separate districts in Bangladesh are selected to conduct the survey on households and showrooms about the energy and seller also. The survey uses the data to find some regression equations from which it is easy to predict energy efficiency knowledge. The data is analyzed and calculated based on five important criteria. The initial target was to find some factors that help predict a person's energy efficiency knowledge. From the survey, it is found that the energy efficiency awareness among the people of our country is very low. Relationships between household energy use behaviors are estimated using a unique dataset of about 40 households and 20 showrooms in Bangladesh's Chapainawabganj and Bagerhat districts. Knowledge of energy consumption and energy efficiency technology options is found to be associated with household use of energy conservation practices. Household characteristics also influence household energy use behavior. Younger household cohorts are more likely to adopt energy-efficient technologies and energy conservation practices and place primary importance on energy saving for environmental reasons. Education also influences attitudes toward energy conservation in Bangladesh. Low-education households indicate they primarily save electricity for the environment while high-education households indicate they are motivated by environmental concerns.
一比一原版(爱大毕业证书)爱荷华大学毕业证如何办理
原版一模一样【微信：741003700 】【(爱大毕业证书)爱荷华大学毕业证成绩单】【微信：741003700 】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
【主营项目】
一.毕业证【q微741003700】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【q/微741003700】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
办理(爱大毕业证书)爱荷华大学毕业证【微信：741003700 】外观非常简单，由纸质材料制成，上面印有校徽、校名、毕业生姓名、专业等信息。
办理(爱大毕业证书)爱荷华大学毕业证【微信：741003700 】格式相对统一，各专业都有相应的模板。通常包括以下部分：
校徽：象征着学校的荣誉和传承。
校名:学校英文全称
授予学位：本部分将注明获得的具体学位名称。
毕业生姓名：这是最重要的信息之一，标志着该证书是由特定人员获得的。
颁发日期：这是毕业正式生效的时间，也代表着毕业生学业的结束。
其他信息：根据不同的专业和学位，可能会有一些特定的信息或章节。
办理(爱大毕业证书)爱荷华大学毕业证【微信：741003700 】价值很高，需要妥善保管。一般来说，应放置在安全、干燥、防潮的地方，避免长时间暴露在阳光下。如需使用，最好使用复印件而不是原件，以免丢失。
综上所述，办理(爱大毕业证书)爱荷华大学毕业证【微信：741003700 】是证明身份和学历的高价值文件。外观简单庄重，格式统一，包括重要的个人信息和发布日期。对持有人来说，妥善保管是非常重要的。
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Sampling theorem
- 2. Continuous to Discrete-Time Signal C/DC/D T x(t) x(n)= x(nT) Sampling rate 01/06/19 2/10 SS/Dr.PP/Sampling
- 3. Continuous to Discrete-Time Signal Conversion from impulse train to discrete-time sequence Conversion from impulse train to discrete-time sequence x(t) x(nT) × s(t) xs(t) 01/06/19 3/10 SS/Dr.PP/Sampling
- 4. Sampling with Periodic Impulse train t x(t) 0 T 2T 3T 4T−T−2T−3T n x(n) 0 1 2 3 4−1−2−3 t x(t) 0 2T 4T 8T 10T−2T−4T−8T n x(n) 0 2 4 6 8−2−4−6 01/06/19 4/10 SS/Dr.PP/Sampling
- 5. Sampling with Periodic Impulse train t x(t) 0 T 2T 3T 4T−T−2T−3T n x(n) 0 1 2 3 4−1−2−3 t x(t) 0 2T 4T 8T 10T−2T−4T−8T n x(n) 0 2 4 6 8−2−4−6 What condition has to be placed on the sampling rate? What condition has to be placed on the sampling rate? We want to restore x(t) from x(n).We want to restore x(t) from x(n). 01/06/19 5/10 SS/Dr.PP/Sampling
- 6. Continuous to Discrete-Time Signal Conversion from impulse train to discrete-time sequence Conversion from impulse train to discrete-time sequence x (t) x(nT) × s(t) xs(t) ∑ ∞= −∞= −δ= n n nTtts )()( )()()( tstxtxs = ∑ ∞= −∞= −= n n nTttx )()( δ ∑ ∞= −∞= −= n n nTtnTx )()( δ 01/06/19 6/10 SS/Dr.PP/Sampling
- 7. Continuous to Discrete-Time Signal Conversion from impulse train to discrete-time sequence Conversion from impulse train to discrete-time sequence xc(t) x(n)= x(nT) × s(t) xs(t) ∑ ∞= −∞= −δ= n n nTtts )()( )()()( tstxtxs = ∑ ∞= −∞= −= n n nTttx )()( δ ∑ ∞= −∞= −= n n nTtnTx )()( δ )(*)( 2 1 )( ωω π ω jSjXjXs = T k T jS s k s π ωωωδ π ω 2 ,)( 2 )( =−= ∑ ∞ −∞= 01/06/19 7/10 SS/Dr.PP/Sampling
- 8. Continuous to Discrete-Time Signal )(*)( 2 1 )( ωω π ω jSjXjXs = T k T jS s k s π ωωωδ π ω 2 ,)( 2 )( =−= ∑ ∞ −∞= ωs: Sampling Frequency −= ∑ ∞ −∞=k ss k T jXjX )( 2 *)( 2 1 )( ωωδ π ω π ω 01/06/19 8/10 SS/Dr.PP/Sampling
- 9. Continuous to Discrete-Time Signal −= ∑ ∞ −∞=k ss k T jXjX )( 2 *)( 2 1 )( ωωδ π ω π ω ∑ ∞ −∞= −= k skjX T )(*)( 1 ωωδω ∑ ∞ −∞= −= k skjX T ))(( 1 ωω ∑ ∞ −∞= −= k ss kjX T jX ))(( 1 )( ωωω Therefore Xs(jω) is a periodic function of ω, consisting of a superposition of shifted replicas of X(jω), scaled by 1/T. 01/06/19 9/10 SS/Dr.PP/Sampling
- 10. Sampling Theroem Let x(t) be a band (frequency)-limited signal X(jω) = 0 for |ω|>ωM. Then x(t) is uniquely determined by its samples {x(nT)} when the sampling frequency satisfies: where ωs=2π/T. 2ωM is known as the Nyquist rate, as it represents the largest frequency that can be reproduced with the sample time 01/06/1910/10 SS/Dr.PP/Sampling