PULSE SHAPING BY MANIPULATING TRANSFORM ZEROS.
Abstract
The Fourier transform of a pulse, a time-limited function of bounded amplitude, is characterized by an infinite set of zeros in the complex frequency plane. The possibility of a transform zero canceling a system function pole, was used by Gerst and Diamond to design signal inputs to a system to yield pulse outputs for the elimination of intersymbol interference. Gerst and Diamond also pointed to the value of differentiable pulses as design tools. The feasibility of shifting complex zeros to their conjugate positions in the frequency plane, was used by Hofstetter and Walther to find a set of pulses with an identical autocorrelation function. This paper reviews certain transform properties, and explores operations on transform zeros for the purpose of pulse shaping. In particular, zero manipulations for the following purposes are discussed. (1) By removing transform zeros, a pulse is shaped to have more derivatives. The zero removal process is extended to yield an infinitely-differentiable pulse. (2) By zero deletion and shifting, a pulse is made to approximate a chosen waveform. (3) By zero deletion and shifting, a pulse is shaped to have: (a) a specified amplitude density spectrum (e.g., rectangular-pulse-like); or (b) a specified energy density spectrum (e.g., complementary to 'colored' noise of the 1/f type). (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 29, 1964
- Accession Number
- AD0617403
Entities
People
- Denis W. Fermental
- Jane B. Campbell
- Nelson T. Tsao-wu
- Sze-hou Chang
Organizations
- Northeastern University