ABSTRACT

Among the important applications of the Fourier transform are analytically representing nonperiodic functions, solving differential equations, aiding in the analysis of linear time-invariant systems, and analyzing and processing signals in engineering, medical, optical, metallographic, and seismic problems. It is the use of the fast Fourier transform, a computational algorithm that reduces the number of calculations in the use of the discrete Fourier transform that makes the discrete Fourier transform a viable and indispensable procedure. In the amplitude-modulated system, the carrier signal is produced by a stable oscillator with power amplifiers to establish the desired power level. While such modulation does save energy of the carrier in the transmitted signal and the carrier component carries no information, subsequent extraction of the information component is rather difficult. The ability to shift the frequency spectrum of the information-carrying signal by means of amplitude modulation allows us to transmit many different signals simultaneously through a given channel, such as transmission line, and telephone line.