The Experts below are selected from a list of 651 Experts worldwide ranked by ideXlab platform
Luis F. Chaparro - One of the best experts on this subject based on the ideXlab platform.
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Frequency Analysis: The Fourier Transform
Signals and Systems Using MATLAB, 2015Co-Authors: Luis F. ChaparroAbstract:In this chapter, the frequency representation of periodic signals is extended to aperiodic signals. The Fourier transform is obtained from the Fourier series representation by a limiting process, and the concept of line spectrum for periodic signal is generalized to the Fourier spectrum for all possible signals. The frequency response of systems is obtained using the Eigenfunction Property of LTI systems. When determining the Fourier transform a special class of signals are those with Laplace transforms having region of convergence containing the jΩ j Ω -axis. Considering the inverse relation between time and frequency, duality between the direct and the inverse Fourier transform is applied when the Laplace connection cannot be used. The Fourier transform has properties similar to those for the Laplace transform and the Fourier series. Modulation and convolution are the two more important properties: modulation is basic in signal transmission, and convolution in linear filtering. Material in this chapter is fundamental in communications and analog filter design. MATLAB is used to illustrate the theory.
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Frequency Analysis: The Fourier Series
Signals and Systems Using MATLAB, 2015Co-Authors: Luis F. ChaparroAbstract:In this chapter we consider the frequency representation of periodic signals by means of the Fourier series, an infinite expansion in terms of orthonormal complex exponentials or sinusoids. Representing aperiodic signals in terms of periodic signals will permit us to extend the Fourier series representation to the Fourier Transform valid for periodic and aperiodic signals. The Fourier series coefficients are obtained using the orthonormality of complex exponentials or sinusoidal bases and efficiently computed using the Laplace transform of a period. The line spectrum, obtained from the Fourier series coefficients, indicates how the power of the signal is distributed to harmonic frequency components in the series. Properties of the Fourier series allow visualization of the power distribution over frequency, the symmetry of the spectrum, and the nature of the Fourier coefficients depending on the symmetry of the signal. Taking advantage of the Eigenfunction Property of linear time-invariant (LTI) systems, the steady-state response of these systems to periodic signals is easily obtained. MATLAB is used to represent and process periodic continuous-time signals.
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Introduction to the Design of Discrete Filters
Signals and Systems using MATLAB, 2011Co-Authors: Luis F. ChaparroAbstract:According to the Eigenfunction Property of LTI systems, filtering changes the frequency content of an input signal. In the discrete-time domain, two types of filters designs are possible: the infinite impulse response (IIR) filter resulting from rational approximation, and the finite impulse response (FIR) filter that results from polynomial approximation. These discrete filters are implemented using software or dedicated hardware and minimal direct, cascade, and parallel forms. The filter design consists in specifying a desired magnitude or impulse response followed by rational or polynomial approximation to obtain a stable and realizable filter. For IIR filters, the classical analog filter design methods together with the bilinear transformation, that maps the analog s -plane into the Z -plane, are used to design low-pass filters. Frequency transformations allow design of other filters. Given that the FIR filters are unique to the discrete domain, the approximation procedures for FIR filters are unique to that domain. A basic design uses windowing. The effect of different windows and the linearity of the phase are discussed. Design of IIR and FIR filters are illustrated using MATLAB.
Luis Chaparro - One of the best experts on this subject based on the ideXlab platform.
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Chapter 12 – Introduction to the Design of Discrete Filters
Signals and Systems Using MATLAB, 2015Co-Authors: Luis ChaparroAbstract:According to the Eigenfunction Property of LTI systems, filtering changes the frequency content of an input signal. In the discrete-time domain, two types of filters designs are possible: the infinite impulse response (IIR) filter resulting from rational approximation, and the finite impulse response (FIR) filter that results from polynomial approximation. These discrete filters are implemented using software or dedicated hardware and minimal direct, cascade, and parallel forms. The filter design consists in specifying a desired magnitude or impulse response followed by rational or polynomial approximation to obtain a stable and realizable filter. For IIR filters, the classical analog filter design methods together with the bilinear transformation, that maps the analog s-plane into the Z-plane, are used to design low-pass filters. Frequency transformations allow design of other filters. Given that the FIR filters are unique to the discrete domain, the approximation procedures for FIR filters are unique to that domain. A basic design uses windowing. The effect of different windows and the linearity of the phase are discussed. Design of IIR and FIR filters are illustrated using MATLAB.
Chandra Sekhar Seelamantula - One of the best experts on this subject based on the ideXlab platform.
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ICASSP - Quadrature approximation properties of the spiral-phase quadrature transform
2011 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2011Co-Authors: Haricharan Aragonda, Chandra Sekhar SeelamantulaAbstract:The notion of the 1-D analytic signal is well understood and has found many applications. At the heart of the analytic signal concept is the Hilbert transform. The problem in extending the concept of analytic signal to higher dimensions is that there is no unique multidimensional definition of the Hilbert transform. Also, the notion of analyticity is not so well understood in higher dimensions. Of the several 2-D extensions of the Hilbert transform, the spiral-phase quadrature transform or the Riesz transform seems to be the natural extension and has attracted a lot of attention mainly due to its isotropic properties. From the Riesz transform, Larkin et al. constructed a vortex operator, which approximates the quadratures based on asymptotic stationary-phase analysis. In this paper, we show an alternative proof for the quadrature approximation Property by invoking the quasi-Eigenfunction Property of linear, shift-invariant systems. We show that the vortex operator comes up as a natural consequence of applying this Property. We also characterize the quadrature approximation error in terms of its energy as well as the peak spatial-domain error. Such results are available for 1-D signals, but their counterpart for 2-D signals have not been provided. We also provide simulation results to supplement the analytical calculations.
Haricharan Aragonda - One of the best experts on this subject based on the ideXlab platform.
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ICASSP - Quadrature approximation properties of the spiral-phase quadrature transform
2011 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2011Co-Authors: Haricharan Aragonda, Chandra Sekhar SeelamantulaAbstract:The notion of the 1-D analytic signal is well understood and has found many applications. At the heart of the analytic signal concept is the Hilbert transform. The problem in extending the concept of analytic signal to higher dimensions is that there is no unique multidimensional definition of the Hilbert transform. Also, the notion of analyticity is not so well understood in higher dimensions. Of the several 2-D extensions of the Hilbert transform, the spiral-phase quadrature transform or the Riesz transform seems to be the natural extension and has attracted a lot of attention mainly due to its isotropic properties. From the Riesz transform, Larkin et al. constructed a vortex operator, which approximates the quadratures based on asymptotic stationary-phase analysis. In this paper, we show an alternative proof for the quadrature approximation Property by invoking the quasi-Eigenfunction Property of linear, shift-invariant systems. We show that the vortex operator comes up as a natural consequence of applying this Property. We also characterize the quadrature approximation error in terms of its energy as well as the peak spatial-domain error. Such results are available for 1-D signals, but their counterpart for 2-D signals have not been provided. We also provide simulation results to supplement the analytical calculations.
Paulo J. S. G. Ferreira - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear systems and exponential Eigenfunctions
IEEE Signal Processing Letters, 1999Co-Authors: Paulo J. S. G. FerreiraAbstract:It has been shown previously that homogeneous time-invariant systems produce exponential outputs in response to similar exponential inputs, but that the concepts of "impulse response" and "frequency response" are of little use for their analysis. It was also asked whether there exist more general classes of systems with exponential Eigenfunctions. In this paper, we recall that the concepts of impulse and frequency response can be useless even for certain linear, time-invariant systems. We discuss the role of time-invariance, commuting linear systems, and conditions under which they have common Eigenfunctions. Then we exhibit a class of nonlinear, nonhomogeneous, time-varying systems that still have exponential Eigenfunctions. This class contains homogeneous time-invariant systems, finite impulse response (FIR) filters and generalized feedforward filters as special cases, and it shows that the exponential Eigenfunction Property does not imply linearity, homogeneity, or time-invariance.