The most direct scope of Fourier Transform (FT) is to give an alternative representation of a signal: from the original domain to the corresponding frequency domain. The original domain can be time, space or any other independent variable that can be used as the domain of the function. This subject has been treated in Part 1 [1]. In particular, the FT of a signal, also referred to as the frequency spectrum of a signal, has been used to calculate the lowest sampling frequency that provides a correct representation of the signal itself. At the beginning of this contribution, it is illustrated how to implement the so-called windowing process to periodic sequences. Then, the meaning of the operations denominated convolution and deconvolution is discussed. It is shown how FT provides a very effective path to the execution of these operations in the alternative domain by employing the convolution theorem. Finally, the application of convolution and deconvolution operations to experimental signals associated with the 'spontaneous' convolution of two concurrent events is analysed by different examples.

Analog and digital worlds: Part 2. Fourier analysis in signals and data treatment / Seeber, Renato; Ulrici, Alessandro. - In: CHEMTEXTS. - ISSN 2199-3793. - 3:2(2017), pp. 1-15. [10.1007/s40828-017-0044-x]

### Analog and digital worlds: Part 2. Fourier analysis in signals and data treatment

#### Abstract

The most direct scope of Fourier Transform (FT) is to give an alternative representation of a signal: from the original domain to the corresponding frequency domain. The original domain can be time, space or any other independent variable that can be used as the domain of the function. This subject has been treated in Part 1 [1]. In particular, the FT of a signal, also referred to as the frequency spectrum of a signal, has been used to calculate the lowest sampling frequency that provides a correct representation of the signal itself. At the beginning of this contribution, it is illustrated how to implement the so-called windowing process to periodic sequences. Then, the meaning of the operations denominated convolution and deconvolution is discussed. It is shown how FT provides a very effective path to the execution of these operations in the alternative domain by employing the convolution theorem. Finally, the application of convolution and deconvolution operations to experimental signals associated with the 'spontaneous' convolution of two concurrent events is analysed by different examples.
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Analog and digital worlds: Part 2. Fourier analysis in signals and data treatment / Seeber, Renato; Ulrici, Alessandro. - In: CHEMTEXTS. - ISSN 2199-3793. - 3:2(2017), pp. 1-15. [10.1007/s40828-017-0044-x]
Seeber, Renato; Ulrici, Alessandro
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/1152466`