# Accession Number:

## AD0411224

# Title:

## DESIGN OF INPUT WAVEFORMS TO YIELD TIME-LIMITED ORTHOGONAL OUTPUTS,

# Descriptive Note:

# Corporate Author:

## NORTHEASTERN UNIV BOSTON MASS

# Personal Author(s):

# Report Date:

## 1963-03-01

# Pagination or Media Count:

## 61.0

# Abstract:

Given a time-invariant, linear system, with impulse response ht, system function Hs, is there a set of input signals which results in a set of output signals that are orthogonal on a given interval of time. A solution to the pro blem is discussed. Restraints are imposed on in put and output sets to evolve problems of prac tical engineering interest. A feasibility study is made of the solution proposed. For this pur pose a rational system function Hs NsDs is assumed. Restraints imposed on both input and output sets are that the functions be real-val ued, of finite energy and time-limited. It is shown that the proposed solution involves finding a set of real-valued, finite-energy pkt which are sufficiently differentiable for the ra tional system function and which have the prop erty that the set N pkt is orthogonal, N being the polynomial of differentiation equivalent to the polynomial Ns. Techniques for determining members of a set pkt are described. It is demonstrated that many such sets can be found for a given rational Hs. Author