ERL & Coherent X-ray Applications Talk Outline Qun Shen Cornell High Energy Synchrotron Source (CHESS) Cornell University Introduction to x-ray coherence Coherent x-ray applications Desired ERL properties Options and improvements Conclusions x x’

ByEE 7730. 2D Fourier Transform. Summary of Lecture 2. We talked about the digital image properties, including spatial resolution and grayscale resolution. We reviewed linear systems and related concepts, including shift invariance, causality, convolution, etc. Fourier Transform.

ByFourier Transform J.B. Fourier 1768-1830. Image Enhancement in the Frequency Domain 1-D. A. A. sin(x). 3 sin(x). B. + 1 sin(3x). A+B. + 0.8 sin(5x). C. A+B+C. + 0.4 sin(7x). D. A+B+C+D. A sum of sines and cosines. =. Fourier spectrum of step function.

ByTheory of Reconstruction. What are inside the gantry?. Schematic Representation o f the Scanning Geometry of a CT System. X-ray. 2 % attenuation change detectable in film. CT. 0.2 % change in attenuation coefficient. y. x. f(x,y). CT, like X-ray measure line integrals.

ByChapter 2 Signals and Systems. Marcus Borengasser 8/24/10. Chapter 2 Introduction. The object being imaged is an input signal – Typically a 3D signal • The imaging system is a transformation of the input signal to an output signal • The image produced is an output signal

By38655 BMED-2300-02 Lecture 13: CT Reconstruction Ge Wang, PhD Biomedical Imaging Center CBIS/BME , RPI wangg6@rpi.edu March 6, 2018. Are Your Scores Good?. BB Schedule for S18. Office Hour: Ge Tue & Fri 3-4 @ CBIS 3209 | wangg6@rpi.edu

ByAn Overview of Fractional Order Signal Processing (FOSP) Techniques. YangQuan Chen*, Rongtao Sun+, Anhong Zhou#. *Center for Self-Organizing and Intelligent Systems (CSOIS), Department of Electrical & Computer Engineering, Utah State University +Phase Dynamics, Inc. Richardson,TX75081

ByFourier Transform. Analytic geometry gives a coordinate system for describing geometric objects. Fourier transform gives a coordinate system for functions. Decomposition of the image function. The image can be decomposed into a weighted sum of sinusoids and cosinuoids of different frequency.

ByInterstellar Levy Flights. Collaborators: Stas Boldyrev (U Chicago: Theory) Ramachandran (Berkeley: Pulsar Observing) Avinash Deshpande (Arecibo, Raman Inst: More Pulsars) Ben Stappers (Westerbork: Crucial pulsar person). Outline of Talk: Gambling with Pennies Statistics

ByImage Processing Basics. What are images?. An image is a 2-d rectilinear array of pixels. Pixels as samples. A pixel is a sample of a continuous function. Images are Ubiquitous. Input Optical photoreceptors Digital camera CCD array Rays in virtual camera (why?) Output TVs

ByFractional fourier transform. Presenter: Hong Wen-Chih. Outline. Introduction Definition of fractional fourier transform Linear canonical transform Implementation of FRFT/LCT The Direct Computation DFT-like Method Chirp Convolution Method Discrete fractional fourier transform

ByMRI Image Formation. Karla Miller FMRIB Physics Group. Image Formation. Gradients and spatial encoding Sampling k -space Trajectories and acquisition strategies Fast imaging Acquiring multiple slices Image reconstruction and artifacts. field strength. field offset.

ByVibrational Wavefunctions. Spectrometers - Prism. Diffraction. Gratings. Flash Photolysis. Signal-to-Noise. Fourier Transform. http://talklikeaphysicist.com/2008/must-see-fourier-transform-tattoo/. Microwave Spectrometers. Microwave Sources. Microwave Ovens. Spectrometers Compared.

ByLecture 11. Fourier Transforms. Fourier Series in exponential form. Consider the Fourier series of the 2T periodic function: Due to the Euler formula It can be rewritten as With the decomposition coefficients calculated as:. (1). (2). Fourier transform.

ByUnit 5. The Fourier Transform. Courtesy of Professor Alan M. Nathan, University of Illinois at Urbana-Champaign. Unit 5. Many, many different equations for Fourier Transforms . . . . . 1. Mathematician Approach 2. Engineering Approach Even within each approach there are many equations.

ByMatched Filters. By: Andy Wang. What is a matched filter? (1/1) . A matched filter is a filter used in communications to “match” a particular transit waveform.

ByENG4BF3 Medical Image Processing. Wavelet and Multiresolution Processing. Introduction. Unlike Fourier transform, whose basis functions are sinusoids, wavelet transforms are based on small waves, called wavelets, of limited duration.

ByOutline. Transmitters (Chapters 3 and 4, Source Coding and Modulation) (week 1 and 2) Receivers (Chapter 5) (week 3 and 4) Received Signal Synchronization (Chapter 6) (week 5) Channel Capacity (Chapter 7) (week 6) Error Correction Codes (Chapter 8) (week 7 and 8)

ByImage Compression - JPEG. Video Compression. MPEG Audio compression Lossy / perceptually lossless / lossless 3 layers Models based on speech generation (throat), or ear characterisitics Image compression JPEG based Images take much more memory than voice

BySymmetry and the DTFT. If we know a few things about the symmetry properties of the DTFT, it can make life simpler. First, for a real-valued sequence x(n), the amplitude spectrum (magnitude of the DTFT) is an EVEN function of w . To show this first show that,. Symmetry and the DTFT.

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