Transition of Signals from Time Sampled Form to Frequency Sampled Form using Transformation Methods

Abstract

This research paper deals with the transformation of digital signals from time domain representation to the frequency domain representation. This transformation is completed in three phases, the first phase is transformation from digitally time domain represented signal to sampled stripe set based signal through time sampling procedure and the second phase is transformation from time sampled stripe set based signal to frequency domain represented signal with certain angular frequency and the third phase is from frequency domain represented signal to sampled stripe set formed frequency domain based signal through frequency sampling procedure. The necessity for signal transformation is the industry need for utilization of digital signal processing based devices in wireless communication systems. The models of transformation of digital signals from time domain representation to frequency domain in sampled form are proposed systematically with using classical digital signal processing models. After using and evaluating the mathematical models I got that for odd and fractional values of k, the Fourier transforms of digital signals have real and imaginary part whereas for even values of k, the Fourier transforms of digital signals have only real form.