An alternate presentation of the development of the Fourier transform from the complex exponential Fourier series is presented. It uses spectral concepts to aid the mathematical development and a redefined spectral form for the spectral information obtained with the Fourier series. It has been used a number of times in the classroom and has been found to aid the students' understanding of the Fourier transform and the spectra of an aperiodic signal.
G. E. Carlson, "ALTERNATE PRESENTATION OF FOURIER TRANSFORM DEVELOPMENT FROM FOURIER SERIES.," IEEE Transactions on Education, vol. E thru 29, no. 4, pp. 201 - 203, Institute of Electrical and Electronics Engineers, Jan 1986.
The definitive version is available at https://doi.org/10.1109/TE.1986.5570566
Electrical and Computer Engineering
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01 Jan 1986