Spectral Analysis: Parametric and Non-Parametric Digital - download pdf or read online

By Francis Castanié

ISBN-10: 1905209053

ISBN-13: 9781905209057

This ebook offers with those parametric tools, first discussing these in accordance with time sequence versions, Capon's procedure and its versions, after which estimators in response to the notions of sub-spaces. although, the booklet additionally offers with the conventional "analog" tools, now referred to as non-parametric equipment, that are nonetheless the main customary in functional spectral research.

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Additional resources for Spectral Analysis: Parametric and Non-Parametric Digital Methods

Example text

15] and the linearity of the Fourier transform. 66] It is equal to N for all integer values of the abscissa. 15]. 68] This means that the Fourier transform of the cisoid of frequency v0 is a comb centered on v0. Using the linearity of the Fourier transform, we obtain the Fourier transform of real sine waves. 24]. 8. Sampling In the majority of applications, the signal studied is a continuous time signal. The spectral analysis, using a digital calculator, requires the sampling of this signal to obtain a discrete time signal.

This spectral “leakage” exists even if the signal processed is not a sine wave. In particular, if the signal consists of two sine waves of very different amplitudes, the secondary lobes coming from the sine wave of large amplitude can mask the main lobe coming from the other sine wave. A solution consists in balancing the signal observed using a smoother truncation window, whose Fourier transform is such that the amplitude of the secondary lobes is much smaller compared to the amplitude of the main lobe, than in the case of the rectangular window.

6] To define the Dirac delta function rigorously, knowledge about the mathematical theory of distributions is required. We will be content here with an intuitive introduction. The Dirac delta function δ can be defined as the limit of the function with unit integral 1 1 2T −T ,T ⎧⎪ δ ( t ) = 0 if ⎨ ⎪⎩ δ ( 0 ) = +∞ when T >G 0 . 9] 40 Spectral Analysis If we multiply the Dirac delta function δ by a number a, we obtain the Dirac ( delta function αδ of weight α αδ ( t ) = 0 if t ≠ 0 , αδ ( 0 ) = ∞ , ∫ +∞ αδ −∞ ( t ) dt = α ).

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Spectral Analysis: Parametric and Non-Parametric Digital Methods by Francis Castanié


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