Bounds for Truncation Error in Sampling Expansions of Finite Energy Band-Limited Signals.
Abstract
An upper bound is established for the magnitude of the truncation error incurred when a real-valued, finite energy signal which is band-limited to -pi(r) < or = omega < or = pi(r) (o <r<1) is approximated by 2N+1 terms from its Shannon sampling series expansion. The sampling expansion is associated with the band (-pi, pi), and consequently involves samples taken at the integer points. The bound is of the form K(r,t)/N (Square root of E) where E is the signal energy. This bound is of the same asymptotic form as the bounds derived by Yao and Thomas and Brown. The bound derived here is tighter than the Yao-Thomas bound for values of r near unity, and is tighter than the bound obtained by Brown for all value of r.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 18, 1974
- Accession Number
- ADA031916
Entities
People
- H. S. Piper Jr
Organizations
- Pennsylvania State University