An Alternate Presentation of Fourier Transform Development from Fourier Series

Students often have difficulty understanding the Fourier transform concept and its relation to Fourier series concepts and signal spectrum concepts. Conceptual problems occur for the student in understanding the transition from the line spectra obtained with Fourier series to the continuous frequency spectra obtained with Fourier transforms and in understanding the reason that the resulting amplitude spectrum is in fact an amplitude density spectrum. An alternate presentation of the development of the Fourier transform from the complex exponential Fourier series is presented. This presentation has been found to improve students' understanding of the nature of the spectral information obtained for an aperiodic signal with the Fourier transform.