Lecture 11 Fast Fourier Transform (FFT) Weinan E1‚2 and Tiejun Li2 1 Department of Mathematics‚ Princeton University‚ weinan@princeton.edu 2 School of Mathematical Sciences‚ Peking University‚ tieli@pku.edu.cn No.1 Science Building‚ 1575 Examples Fast Fourier Transform Outline Examples Fast Fourier Transform Applications Applications Examples Fast Fourier Transform Applications Signal processing Filtering: a polluted signal 1.5 1 0.5 0 −0.5 −1 −1.5 0 200 400 600 800
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Fourier Series Fourier series started life as a method to solve problems about the flow of heat through ordinary materials. It has grown so far that if you search our library’s data base for the keyword “Fourier” you will find 425 entries as of this date. It is a tool in abstract analysis and electromagnetism and statistics and radio communication and . . . . People have even tried to use it to analyze the stock market. (It didn’t help.) The representation of musical sounds as sums of waves of various
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year 1790 in his work on probability theorem. Application of Laplace Transform The Laplace transform technique is applicable in many fields of science and technology such as: Control Engineering Communication Signal Analysis and Design Image Processing System Analysis Solving Differential Equations (ordinary and partial) Advantages of Laplace transformation A Laplace transformation technique reduces the solutions of an ordinary differential equation to the solution of an algebraic
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The fundamental frequency‚ often referred to simply as the fundamental‚ is defined as the lowest frequency of a periodic waveform. In terms of a superposition of sinusoids (e.g. Fourier series)‚ the fundamental frequency is the lowest frequency sinusoidal in the sum. In some contexts‚ the fundamental is usually abbreviated as f0 (or FF)‚ indicating the lowest frequency counting from zero.[1][2][3] In other contexts‚ it is more common to abbreviate it as f1‚ the first harmonic.[4][5][6][7][8] (The
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TELECOMMUNICATION 1 2012-2013 Fall Project SINC FUNCTION‚ SSB-AM‚ FM Name: Onur Mustafa Erdoğan ID Number: 10014044 Submission Date: 24.12.2012 Abstract: In these project‚ I will analyze Fourier Transform of sinc function and it’s modulation.(SSB-AM‚FM) I will explain SSB-AM and FM theoretically and solve their math model in steps. After all‚ I’ll use simulations and graphics to prove my solutions and In the and‚ I will write my conclusions down. Introduction SSB-AM [1]In
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Lecture 13: Edge Detection c Bryan S. Morse‚ Brigham Young University‚ 1998–2000 Last modified on February 12‚ 2000 at 10:00 AM Contents 13.1 Introduction . . . . . . . . . . . . . . 13.2 First-Derivative Methods . . . . . . . 13.2.1 Roberts Kernels . . . . . . . . . 13.2.2 Kirsch Compass Kernels . . . . 13.2.3 Prewitt Kernels . . . . . . . . . 13.2.4 Sobel Kernels . . . . . . . . . . 13.2.5 Edge Extraction . . . . . . . . . 13.3 Second-Derivative Methods . . . . . . 13.3.1 Laplacian Operators
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1st 1998 OXFORD UNIVERSITY PRESS R-5 INTRODUCTION TO SIGNALS AND SYSTEMS DOUGLAS K. LINDNER 12th R-6 SIGNALS AND LINEAR SYSTEMS ROBERT A. GABEL‚ RICHARD A. ROBERTS 3rd JOHN WILEY & SONS R-7 SIGNALS AND SYSTEMS ANALYSIS USING TRANSFORM METHODS AND MATLAB M. J. ROBERTS 8th TMH R-8 SIGNALS AND SYSTEMS I. J. NAGRATH‚ S. N. 1st SHARAN‚ R. RANJAN‚ S. KUMAR TMH R-9 ANALOG AND DIGITAL SIGNAL PROCESSING ASHOK AMBARDAR BROOKE/COLE PUBLISHING
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SPECTRAL ANALYSIS OF NONPARAMETRIC METHODS & IMPROVED WELCH METHOD VIA CIRCULAR OVERLAP Svs Gopala Krishna‚ S.Mujassim‚ Prof.D.Ramachandra Reddy School of Electronics Engineering‚ VIT University‚ Vellore- 632014‚ Tamilnadu‚ India. gopal.svsemails@gmail.com; mujassim@rediffmail.com Abstract The objective of this paper is to overcome the drawback in the Welch method. The major problem with the Welch method is that the variance is not monotonically decreasing with respect to the amount of fraction
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Analog Communication Theory: A Text for EE501 Michael P. Fitz The Ohio State University fitz.7@osu.edu Fall 2001 2 Note to Students. This text is an evolving entity. Please help make an OSU education more valuable by providing me feedback on this work. Small things like catching typos or big things like highlighting sections that are not clear are both important. My goal in teaching communications (and in authoring this text) is to provide students with 1. the required theory‚ 2. an insight
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Circuits & Signals EEE/ INSTR C272 BITS Pilani Pilani Campus p ANU GUPTA EEE Time-domain analysis BITS Pilani Pilani Campus p Response of a LTIC system time-domain analysis linear‚ time-invariant‚ continuous-time (LTIC) systems--Total response = zero-input response + zero-state response zero-input response component that results only from the initial i t t th t lt l f th i iti l conditions at t = 0 with the input f(t) = 0 for t ≥ 0‚ zero-state zero state response component that
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