Fourier efficiency using analytic translation and Hilbert samples

The discrete Fourier transform (DFT) inherently accepts complex data; yet signals to be processed are usually real. This necessitates special accommodations if efficient computation is to be achieved. Further accommodation is necessary for efficiency when processing bandpass data. Both accommodations can be made by generating analytic signals using Hilbert transforms. The generation of such signals around zero frequency can be accomplished by analytic band translation where the bandpass can afterwards be defined at baseband by a pair of matched filters. After baseband processing, the spectrum can be translated back up to an arbitrary frequency or can enter after Hilbert sampling directly into the complex DFT for the most efficient spectrum analysis. The analytic translation to the zero‐centered baseband frequencies provides the most conveniently normalized spectrum and facilitates the most efficient use of computational resources. The analytic band translator applies to either digital or analog implementa...