Approximating Smooth Step Functions Using Partial Fourier Series Sums

Abstract

This report documents several continuous functions that can approximate a discrete step function. The functions considered include the cosine, cubic polynomial, bezier polynomial, and hyperbolic tangent. Based on the error condition used, the Hyperbolic Tangent (Tanh) and Cosine functions provide the "best" approximations depending on the degree of smoothness desired.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2012
Accession Number
ADA567759

Entities

People

  • Wesley Bylsma

Organizations

  • United States Army Tank Automotive Research, Development and Engineering Center

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Amplitude
  • Coefficients
  • Complex Numbers
  • Computations
  • Department Of Defense
  • Engineering
  • Errors
  • Fourier Series
  • Governments
  • Numbers
  • Numerical Integration
  • Polynomials
  • Step Functions
  • Transitions
  • United States
  • United States Government

Readers

  • Approximation Theory.