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Discrete-Time Signals and Circuits Fundamentals

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Fundamentals of Adaptive Signal Processing

Part of the book series: Signals and Communication Technology ((SCT))

Abstract

In all real physical situations, in the communication processes, and in the wider meaning terms, it is usual to think the signals as variable physical quantity or symbols, to which is associated a certain information. A signal that carries information is variable and, in general, we are interested in the time (or other)-domain variation: signal ⟺ function of time or, more generally, signal ⟺ function of several variables.

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Notes

  1. 1.

    For nonstationary signal, for instance, may be considered a signal generated by a nonstationary system such as, for example, a sine wave oscillator that continuously varies the amplitude, phase, and frequency such that its statistical characteristics (mean value, rms value, etc.) are not constant.

  2. 2.

    Given a \( x\left[n\right] \) sequence, with \( 0\le n\le N-1 \), there are more ways to extend it as a periodic sequence depending on the aggregation of the segments and the type of, odd or even, chosen symmetry.

  3. 3.

    In electrical circuits a reactive element is defined by a constitutive relationship in which there is a time-dependence explicit by a differential of an electrical variable (e.g., current or voltage). For example, the constitutive relationship that defines the electrical element capacitance C [farad] is

    $$ i(t)=C\left(dv(t)/dt\right). $$
  4. 4.

    Later, it was discovered that the two authors had independently reinvented an algorithm of Carl Friedrich Gauss in 1805 (and subsequently rediscovered in many other limited forms).

  5. 5.

    It seems that the term pole is derived from the pole of the circus that underlies the tarp. The cusp shape assumed by the tensed canvas from the pole recalls the plot of the TF module \( {\left|H(z)\right|}_{z\to {p}_k} \) for \( z\to {p}_k \).

  6. 6.

    The TF’s plots were evaluated with the program Matlab FDAtool.

  7. 7.

    A stable circuit is said to be minimum phase if the zeros make a positive contribution to the phase or in the case of analog circuits are to the left of the imaginary axis or, in the case of DT circuits, are inside the unit circle.

References

  1. Oppenheim AV, Schafer RW, Buck JR (1999) Discrete-time signal processing, 2nd edn. Prentice Hall, Englewood Cliffs, NJ

    Google Scholar 

  2. Rabiner LR, Gold B (1975) Theory and application of digital signal processing. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  3. Ahmed N, Natarajan T, Rao KR (1974) Discrete cosine transform. IEEE Trans Comput 23(1):90–93

    Article  MathSciNet  MATH  Google Scholar 

  4. Martucci SA (1994) Symmetric convolution and the discrete sine and cosine transforms. IEEE Trans Signal Process SP-42(5):1038–1051

    Article  Google Scholar 

  5. Haar A (1910) Zur Theorie der Orthogonalen Funktionensysteme. Math Ann 69:331–371

    Article  MathSciNet  MATH  Google Scholar 

  6. Mallat SG (1998) A wavelet tour of signal processing. Academic, San Diego, CA. ISBN 0-12-466605-1

    MATH  Google Scholar 

  7. Vetterli M, Kovačević J (2007) Wavelets and subband coding. Open-Access Edition, http://www.waveletsandsubbandcoding.org/

  8. Vetterli M, Kovačević J, Goyal VK (2013) Foundations of signal processing. Free version, http://www.fourierandwavelets.org

  9. Feig E, Winograd S (1992) Fast algorithms for the discrete cosine transform. IEEE Trans Signal Process 40(9):2174–2193

    Article  MATH  Google Scholar 

  10. Frigo M, Johnson SG (2005) The design and implementation of FFTW3. Proc IEEE 93(2):216–231

    Article  Google Scholar 

  11. Cooley JW, Tukey J (1965) An algorithm for the machine calculation of complex Fourier Series. Math Comput 19:297–301

    Article  MathSciNet  MATH  Google Scholar 

  12. Brigam EO (1998) The fast fourier transform and its application. Prentice-Hall, Englewood Cliffs, NJ

    Google Scholar 

  13. Antoniou A (1979) Digital filters: analysis and design. MacGraw-Hill, New York

    Google Scholar 

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Authors and Affiliations

  1. DIET, Sapienza University of Rome, Rome, Italy

    Aurelio Uncini

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  1. Aurelio Uncini
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Uncini, A. (2015). Discrete-Time Signals and Circuits Fundamentals. In: Fundamentals of Adaptive Signal Processing. Signals and Communication Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-02807-1_1

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  • DOI: https://doi.org/10.1007/978-3-319-02807-1_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02806-4

  • Online ISBN: 978-3-319-02807-1

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