Fourier series and transforms

Suitable for a one or twosemester undergraduatelevel electrical engineering, computer engineering, and computer science course in Discrete Systems and Digital Signal Processing. Assumes some prior knowledge of advanced calculus, linear systems for continuoustime signals, and Fourier series and transforms. Giving students a sound balance of theory and practical application, this nononsense text presents the fundamental concepts and techniques of modern digital signal processing with related algorithms and applications.
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You will understand the physical meaning behind the mathematics of wireless signals and learn the intricacies and tradeoffs in signal selection and design.
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Digital Signal Processing (DSP) is formally defined as a digital operation performed on an input sequence of numbers (including feedback from the result of the digital operation). The sequence of numbers can represent anything from digitised human speech to stock price data, processed to detect hidden periodicities or pattern
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Lecture Signal processing: Fourier representation of signals include all of the following content: Sinusoidal signals and their properties, fourier representation of continuous – time signals, fourier representation of discrete – time signals, summary of fourier series and fourier transforms, properties of the discrete – time fourier transform.
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This book focuses on the Fourier transform applications in the analysis of some types of materials. The field of Fourier transform has seen explosive growth during the past decades, as phenomenal advances both in research and application have been made. During the preparation of this book, we found that almost all the textbooks on materials analysis have a section devoted to the Fourier transform theory. Most of those describe some formulas and algorithms, but one can easily be lost in seemingly incomprehensible mathematics....
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This book focuses on the Fourier transform applications in the analysis of some types of materials. The field of Fourier transform has seen explosive growth during the past decades, as phenomenal advances both in research and application have been made. During the preparation of this book, we found that almost all the textbooks on materials analysis have a section devoted to the Fourier transform theory. Most of those describe some formulas and algorithms, but one can easily be lost in seemingly incomprehensible mathematics.
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In this chapter, Fourier analysis will be discussed. Topics covered are Fourier series expansion, Fourier transform, discrete Fourier transform, and fast Fourier transform. Some applications of Fourier analysis, using MATLAB, will also be discussed.
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Fourier methods are commonly used for signal analysis and system design in modern telecommunications, radar, and image processing systems.
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Frequency analysis of any given signal involves the transformation of a timedomain signal into its frequency components. The need for describing a signal in the frequency domain exists because signal processing is generally accomplished using systems that are described in terms of frequency response. Converting the timedomain signals and systems into the frequency domain is extremely helpful in understanding the characteristics of both signals and systems. In Section 4.1, the Fourier series and Fourier transform will be introduced....
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In this chapter, Fourier analysis will be discussed. Topics covered are Fourier series expansion, Fourier transform, discrete Fourier transform, and fast Fourier transform. Some applications of Fourier analysis, using MATLAB, will also be discussed. 8.1 If a function FOURIER SERIES g (t ) is periodic with period Tp , i.e., (8.1) g (t ) = g (t ± Tp ) and in any finite interval g ( t ) has at most a finite number of discontinuities and a finite number of maxima and minima (Dirichlets conditions), and in addition, Tp ∫ g(t )dt ...
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Finite Impulse Response Filters • • • Introduction to the ztransform Design and implementation of ﬁnite impulse response (FIR) ﬁlters Programming examples using C and TMS320C6x code The ztransform is introduced in conjunction with discretetime signals. Mapping from the splane, associated with the Laplace transform, to the zplane, associated with the ztransform, is illustrated. FIR ﬁlters are designed with the Fourier series method and implemented by programming a discrete convolution equation.
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In this chapter, Fourier analysis will be discussed. Topics covered are Fourier series expansion, Fourier transform, discrete Fourier transform, and fast Fourier transform.
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POWER SPECTRUM AND CORRELATION Power Spectrum and Correlation Fourier Series: Representation of Periodic Signals Fourier Transform: Representation of Aperiodic Signals NonParametric Power Spectral Estimation ModelBased Power Spectral Estimation High Resolution Spectral Estimation Based on Subspace EigenAnalysis Summary T he power spectrum reveals the existence, or the absence, of repetitive patterns and correlation structures in a signal process.
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Frequency Analysis Frequency analysis of any given signal involves the transformation of a timedomain signal into its frequency components. The need for describing a signal in the frequency domain exists because signal processing is generally accomplished using systems that are described in terms of frequency response. Converting the timedomain signals and systems into the frequency domain is extremely helpful in understanding the characteristics of both signals and systems. In Section 4.1, the Fourier series and Fourier transform will be introduced.
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Discrete Wavelet Transform is a wavelet (DWT) transform that is widely used in numerical and functional analysis. Its key advantage over more traditional transforms, such as the Fourier transform, lies in its ability to offer temporal resolution, i.e. it captures both frequency and location (or time) information.
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CHAPTER EIGHT FOURIER ANALYSIS In this chapter, Fourier analysis will be discussed. Topics covered are Fourier series expansion, Fourier transform, discrete Fourier transform, and fast Fourier transform. Some applications of Fourier analysis, using MATLAB, will also be discussed. 8.1 If a function FOURIER SERIES g (t ) is periodic with period Tp , i.e., (8.1) g (t ) = g (t ± Tp ) and in any finite interval g ( t ) has at most a finite number of discontinuities and a finite number of maxima and minima (Dirichlets conditions), and in addition, Tp ∫ g(t )dt ...
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This edition of Optical Metrology contains a new chapter about computerized optical processes, including digital holography and digital speckle photography. Chapter 2, on Gaussian optics, and Chapter 5, on light sources and detectors, are greatly expanded to include descriptions of standard imaging systems, lightemitting diodes and solidstate detectors. Separate new sections on optical coherence tomography, speckle correlation, the Fast Fourier Transform, temporal phase unwrapping and fibre Bragg sensors are included. Finally, a new appendix about Fourier series is given.
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Introduction Fourier Series Representation of Continuous Time Periodic Signals Exponential Fourier Series • The Trigonometric Fourier Series • Convergence of the Fourier Series Properties of the Continuous Time Fourier Transform • Fourier Spectrum of the Continuous Time Sampling Model • Fourier Transform of Periodic Continuous Time Signals • The Generalized Complex Fourier Transform 1.3 The Classical Fourier Transform for Continuous Time Signals 1.4 1.
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Finite Impulse Response Filters Introduction to the ztransform Design and implementation of finite impulse response (FIR) filters Programming examples using C and TMS320C3x code The ztransform is introduced in conjunction with discretetime signals. Mapping from the splane, associated with the Laplace transform, to the zplane, associated with the ztransform, is illustrated. FIR filters are designed with the Fourier series method and implemented by programming a discrete convolution equation. Effects of window functions on the characteristics of FIR filters are covered. ...
43p doroxon 16082010 42 7 Download

In the chapter “Fourier Series, Fourier Transforms, and the DFT” by W. Kenneth Jenkins, many important Fourier transformconcepts in continuous and discrete time are presented. The discrete Fourier transform(DFT), which forms the backbone of modern digital signal processing as its most common signal analysis tool, is also described, together with an introduction to the fast Fourier transformalgorithms.
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