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Browsing Paper Publication by Subject "Duality Theorems For Infinite Fourier Cosine And Sine Transforms"

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    Duality Theorems For Infinite Fourier Cosine And Sine Transforms
    (2015-06-18T04:12:14Z) Madhukar, B N; Sanjay, Jain; Satyanarayana, P S
    This paper presents two new properties called Duality Theorems, exclusively each for the Infinite Fourier Cosine and Fourier Sine Transforms respectively, which were hitherto not mentioned or given elsewhere in the literature. These two integral ransforms which are derived from the Fourier Integral and the Infinite Fourier Transform are well known in the mathematical and engineering fraternity and are used in a variety of applications. The Infinite Fourier Cosine and Sine Transforms have their own interesting properties. In this paper, we present formal derivations of the Duality Theorems for these two transforms. The usage of the Duality Theorems help in finding the time – domain function from the Infinite Fourier Cosine and Sine Transforms’ (frequency) domain and vice versa thereby reducing considerable labour and computation time involved in Integration, if a known Infinite Fourier Sine and Cosine Transform pair is known. The usages of the Duality Theorems have been exemplified with suitable illustrative examples.