2. Analysis of Signals Figure 2.45.: Approximate FTs of two bandlimited signals ¾º½ º Ì ÀÐ ÖØ ÌÖ Ò× ÓÖÑ The Hilbert transform of a function is by definition‚ H {x(t)} = xh (t) = ∞ x(τ ) dτ t −τ −∞ 1 π (2.171) which is the convolution of x(t) with 1/π t‚ H {x(t)} = xh (t) = x(t) ∗ 1 πt (2.172) if we take the FT of this convolution‚ Xh (ω ) = X (ω ) × F 1 πt (2.173) From Example 2.24‚ F {sgn(t)} = 2 jω (2.174) and using duality from
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Solutions‚ Applications. Module 3 (13 hours) Fourier Analysis : Periodic functions - Fourier series‚ Functions of arbitrary period‚ Even and odd functions‚ Half Range Expansions‚ Harmonic analysis‚ Complex Fourier Series‚ Fourier Integrals‚ Fourier Cosine and Sine Transforms‚ Fourier Transforms. Module 4 (14 hours) Gamma functions and Beta functions‚ Definition and Properties. Laplace Transforms‚ Inverse Laplace Transforms‚ shifting Theorem‚ Transforms of derivatives and integrals‚ Solution of
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The Hilbert transform Mathias Johansson Master Thesis Mathematics/Applied Mathematics Supervisor: BÄrje Nilsson‚ VÄxjÄ University. o a o Examiner: BÄrje Nilsson‚ VÄxjÄ University. o a o Abstract The information about the Hilbert transform is often scattered in books about signal processing. Their authors frequently use mathematical formulas without explaining them thoroughly to the reader. The purpose of this report is to make a more stringent presentation of the Hilbert transform but still
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Introduction to Laplace Transforms for Engineers C.T.J. Dodson‚ School of Mathematics‚ Manchester University 1 What are Laplace Transforms‚ and Why? This is much easier to state than to motivate! We state the definition in two ways‚ first in words to explain it intuitively‚ then in symbols so that we can calculate transforms. Definition 1 Given f‚ a function of time‚ with value f (t) at time t‚ the Laplace transform of f is ˜ denoted f and it gives an average value of f taken over all
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voltage fluctuations in the wire that connects an mp3 player to a loudspeaker )‚ can be represented in Discrete Fourier Transform(DFT)‚ as a combination of pure frequencies. It’s universal in signal processing as well as can be used for applications such as the compression of images and audio files. The DFT is so prevalent due to the FFT algorithm which makes it possible to calculate Fourier transforms dynamically. Even then efforts to improve the calculation of DFT have a long and generally overlooked
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Feature Extraction and Image Processing Dedication We would like to dedicate this book to our parents: To Gloria and Joaquin Aguado‚ and to Brenda and the late Ian Nixon. Feature Extraction and Image Processing Second edition Mark S. Nixon Alberto S. Aguado Amsterdam • Boston • Heidelberg • London • New York • Oxford Paris • San Diego • San Francisco • Singapore • Sydney • Tokyo Academic Press is an imprint of Elsevier Academic Press is an imprint of Elsevier Linacre House‚ Jordan
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this course is to teach fundamentals of discrete time signals and discrete time systems followed by analysis of discrete time linear time invariant (LTI) systems. Further‚ it introduces Z-transform and its inverse and followed by their applications to the analysis of LTI systems. A framework for designing analog and digital filters (both FIR and IIR) is introduced starting with mapping of filter specifications from continuous Laplace transformation to Z-transform‚ structure realization based on Direct
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SMART ENERGY METER A smart meter is usually an electrical meter that records consumption of electric energy in intervals of an hour or less and communicates that information at least daily back to the utility for monitoring and billing purposes. Smart meters enable two-way communication between the meter and the central system. Unlike home energy monitors‚ smart meters can gather data for remote reporting. Smart Meters" usually involve real-time or near real-time sensors‚ power outage notification
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PIPELINED RADIX-2K FEED FORWARD FFT ARCHITECTURES ABSTRACT The Fast Fourier transform (FFT) is one of the most important algorithms in the field of digital signal processing. It is used to calculate the discrete Fourier transform (DFT) efficiently. In order to meet the high performance and real-time requirements of modern applications‚ hardware designers have always tried to implement efficient architectures for the computation of the FFT. In this context‚ pipelined hardware architectures are
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of the concepts presented‚ virtual test instrumentation is used. Laptop computers play an essential role during the class to provide actual "hands on" lab experience. The labs demonstrate the principles of sampling‚ Fourier series‚ sinusoidal waveforms‚ FFT/DFT/Inverse Fourier transforms‚ signal generation and other mixed signal testing concepts. Each student receives a personal copy of the DSP Lab software‚ which can be kept for later use and a 300+ page reference manual titled "Fundamentals of Mixed
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