Cross-/auto-correlation of time-varying signals using block pulse functions and determination of power spectral densities
01 Jan 1994-International Journal of Systems Science (Taylor & Francis Group)-Vol. 25, Iss: 1, pp 113-128
TL;DR: In this article, a method based on block pulse function (BPF) analysis for the determination of cross-/ auto-correlation of time-varying signals is proposed, which is used subsequently to evaluate power spectral densities (PSD) of a few codes for communication.
Abstract: The present work proposes a method based on block pulse function ( BPF) analysis for the determination of cross-/ auto-correlation of time-varying signals. These results are used subsequently to evaluate power spectral densities ( PSD) of a few codes for communication. Two Lebesgue integrable time-varying functions are represented by means of their respective equivalent BPF spectra. The BPF spectral coefficients are used to develop positive and negative correlation matrices of an operational nature. These matrices, when combined, result in a correlation matrix that is used to determine cross-/ auto-correlation of the input functions over the entire time scale. The results thus obtained in the BPF domain are utilized to determine the PSDs of a few communication codes employing the well-known fast Fourier transform algorithm. Numerical experiments are carried out to establish the validity of the proposed method and the results are found to be in close agreement with the exact solutions
Citations
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TL;DR: In this paper, a Walsh operational transfer function (WOTF) is utilized instead of a conventional transfer function to obtain the output response, e.g. average and r.m.s.
Abstract: A new operational technique for the analysis of a continuously pulse-modulated inverter is suggested, where the input pulse wave is expressed by a series combination of Walsh/block pulse functions. A Walsh operational transfer function (WOTF) is utilized instead of a conventional transfer function to obtain the output response, e.g. average and r.m.s. values of load current in the Walsh domain. The transformation from the Walsh to the block pulse domain or vice versa is achieved through a well-known similarity transformation using the Walsh matrix W. Also, a fast algorithm is developed using a single pulse modulation matrix (SPMM). The method is suitable for compuler manipulations and has no restriction on the variation of the modulation delay and the shape or amplitude of the input waveform. Selection of proper time scaling for WOTF gives the solution in the desired time range. Results are found to be in good agreement with the exact solutions.
3 citations
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TL;DR: In this paper, Chen and Chung (1987) showed that the trapezoidal rule is equivalent to evaluating the BPF coefficients of the integrated function by the well known trapezoid rule.
Abstract: It has been shown by Chen and Chung (1987) that the use of the conventional kintegral operational matrix P in block pulse function (BPF) analysis is equivalent to evaluating the BPF coefficients of the integrated function by the well known trapezoidal rule. They have improved upon P by employing a three-point interpolation polynomial in the Lagrange form to develop a new integral operational matrix P 1 (say). In the present paper, it has been established that once a function f(t) is represented by a BPF series, application of P to integrate f(t) in the staircase form is exact. Also, the method proposed by Chen and Chung (1987) is merely an extension of the trapezoidal rule wherein only one term of the remainder has been considered. Consideration of two terms from the remainder improves upon the integral operational matrix P 1 further and this improved operational matrix P 2 (say) has been employed to illustrate its superiority. Inclusion of still further terms from the remainder will improve upon P 2 further, but the rate of improvement will diminish gradually as evident from the illustrative examples.
2 citations
References
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Book•
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01 Jul 1988
TL;DR: This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.
Abstract: The Fast Fourier Transform (FFT) is a mathematical method widely used in signal processing. This book focuses on the application of the FFT in a variety of areas: Biomedical engineering, mechanical analysis, analysis of stock market data, geophysical analysis, and the conventional radar communications field.
1,432 citations
Book•
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01 Jan 1970
TL;DR: This edition features improved treatment of signal analysis, including representations in signal space, as well as a more complete and modern presentation of random variables and random processes.
Abstract: From the Publisher:
Here is a text for the introduction to principles of communications,the introduction to digital communications,and the introduction to data communications. A clear and readable tutorial style is combined with thorough coverage of both basic and advanced concepts. And the second edition acquaints students with the state of the art,including treatment of topics that have only recently become important and which many available texts ignore. This edition features improved treatment of signal analysis,including representations in signal space,as well as a more complete and modern presentation of random variables and random processes,with illustrative examples to teach detection of signals in noise. There is also a complete discussion of modulation techniques and synchronization and error rate calculation.
512 citations
Book•
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01 Jan 1969
TL;DR: When you read more every page of this transmission of information by orthogonal functions, what you will obtain is something great.
Abstract: Read more and get great! That's what the book enPDFd transmission of information by orthogonal functions will give for every reader to read this book. This is an on-line book provided in this website. Even this book becomes a choice of someone to read, many in the world also loves it so much. As what we talk, when you read more every page of this transmission of information by orthogonal functions, what you will obtain is something great.
361 citations
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TL;DR: In this paper, the Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems and a new set of orthogonal functions is derived from Walsh functions.
Abstract: The Walsh operational matrix for performing integration and solving state equations is generalized to fractional calculus for investigating distributed systems. A new set of orthogonal functions is derived from Walsh functions. By using the new functions, the generalized Walsh operational matrices corresponding to √s, √(s2 + 1), e-s and e-√s etc. are established. Several distributed parameter problems are solved by the new approach.
203 citations
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