Abstract
In the previous chapter, the Dirac distribution has been introduced as a sum of exponentials with all possible frequencies and amplitude as one. Using this result as a start, we introduce naturally the notion of impulse response of an LTI system. The impulse response appears to be the inverse Fourier transform of the frequency response of the system. This leads to the general definition of the inverse and direct Fourier transforms. We examine in this chapter the first main results given by Fourier transformation. The Parseval–Plancherel energy theorem is demonstrated. The important Poisson’s summation formula is given. Finally, we present in this chapter the elements of the two-dimensional Fourier transform.
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© 2016 Springer International Publishing Switzerland
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Cohen Tenoudji, F. (2016). Fourier Transform. In: Analog and Digital Signal Analysis. Modern Acoustics and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-42382-1_5
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DOI: https://doi.org/10.1007/978-3-319-42382-1_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42380-7
Online ISBN: 978-3-319-42382-1
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