skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Chirp Z-transform spectral zoom optimization with MATLAB.

Abstract

The MATLAB language has become a standard for rapid prototyping throughout all disciplines of engineering because the environment is easy to understand and use. Many of the basic functions included in MATLAB are those operations that are necessary to carry out larger algorithms such as the chirp z-transform spectral zoom. These functions include, but are not limited to mathematical operators, logical operators, array indexing, and the Fast Fourier Transform (FFT). However, despite its ease of use, MATLAB's technical computing language is interpreted and thus is not always capable of the memory management and performance of a compiled language. There are however, several optimizations that can be made within the chirp z-transform spectral zoom algorithm itself, and also to the MATLAB implementation in order to take full advantage of the computing environment and lower processing time and improve memory usage. To that end, this document's purpose is two-fold. The first demonstrates how to perform a chirp z-transform spectral zoom as well as an optimization within the algorithm that improves performance and memory usage. The second demonstrates a minor MATLAB language usage technique that can reduce overhead memory costs and improve performance.

Authors:
Publication Date:
Research Org.:
Sandia National Laboratories
Sponsoring Org.:
USDOE
OSTI Identifier:
1004350
Report Number(s):
SAND2005-7084
TRN: US201104%%963
DOE Contract Number:
AC04-94AL85000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; IMPLEMENTATION; MATHEMATICAL OPERATORS; MEMORY MANAGEMENT; OPTIMIZATION; PERFORMANCE; PROCESSING

Citation Formats

Martin, Grant D. Chirp Z-transform spectral zoom optimization with MATLAB.. United States: N. p., 2005. Web. doi:10.2172/1004350.
Martin, Grant D. Chirp Z-transform spectral zoom optimization with MATLAB.. United States. doi:10.2172/1004350.
Martin, Grant D. 2005. "Chirp Z-transform spectral zoom optimization with MATLAB.". United States. doi:10.2172/1004350. https://www.osti.gov/servlets/purl/1004350.
@article{osti_1004350,
title = {Chirp Z-transform spectral zoom optimization with MATLAB.},
author = {Martin, Grant D.},
abstractNote = {The MATLAB language has become a standard for rapid prototyping throughout all disciplines of engineering because the environment is easy to understand and use. Many of the basic functions included in MATLAB are those operations that are necessary to carry out larger algorithms such as the chirp z-transform spectral zoom. These functions include, but are not limited to mathematical operators, logical operators, array indexing, and the Fast Fourier Transform (FFT). However, despite its ease of use, MATLAB's technical computing language is interpreted and thus is not always capable of the memory management and performance of a compiled language. There are however, several optimizations that can be made within the chirp z-transform spectral zoom algorithm itself, and also to the MATLAB implementation in order to take full advantage of the computing environment and lower processing time and improve memory usage. To that end, this document's purpose is two-fold. The first demonstrates how to perform a chirp z-transform spectral zoom as well as an optimization within the algorithm that improves performance and memory usage. The second demonstrates a minor MATLAB language usage technique that can reduce overhead memory costs and improve performance.},
doi = {10.2172/1004350},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2005,
month =
}

Technical Report:

Save / Share:
  • The PARET algorithm for extracting mode or singularity parameters from a sampled record of transient experimental data has difficulty with data containing modes that are closely spaced in frequency relative to their absolute frequencies. It was felt that preprocessing the data with the so-called Zoom Transform might improve the performance of the PARET algorithm in such cases. This report describes a study carried out to determine the benefits of zooming to mode parameter estimation. The results suggest that zooming can greatly enhance the power of the PARET algorithm for certain types of data and should be implemented as a usermore » option. 7 figures, 4 tables.« less
  • Spectral analysis over an instantaneous bandwidth of 2.4 GHz was demonstrated, utilizing superconductive dispersive delay lines in a chirp-transform configuration. Two-tone resolution of 43 MHz and + or - 1.2 dB amplitude uniformity was achieved.
  • This report analyzes the effects of finite-precision arithmetic on discrete Fourier transforms (DFTs) calculated using the chirp-z transform algorithm. An introduction to the chirp-z transform is given together with a description of how the chirp-z transform is implemented in hardware. Equations for the effects of chirp rate errors, starting frequency errors, and starting phase errors on the frequency spectrum of the chirp-z transform are derived. Finally, the maximum possible errors in the chirp rate, the starting frequencies, and starting phases are calculated and used to compute the worst case effects on the amplitude and phase spectrums of the chirp-z transform.more » 1 ref., 6 figs.« less
  • We present Poblano v1.0, a Matlab toolbox for solving gradient-based unconstrained optimization problems. Poblano implements three optimization methods (nonlinear conjugate gradients, limited-memory BFGS, and truncated Newton) that require only first order derivative information. In this paper, we describe the Poblano methods, provide numerous examples on how to use Poblano, and present results of Poblano used in solving problems from a standard test collection of unconstrained optimization problems.
  • The dissertation examines spectral transform algorithms for the solution of the shallow water equations on the sphere and studies their implementation and performance on shared memory vector multiprocessors. Beginning with the standard spectral transform algorithm in vorticity divergence form and its implementation in the Fortran based parallel programming language Force, two modifications are researched. First, the transforms and matrices associated with the meridional derivatives of the associated Legendre functions are replaced by corresponding operations with the spherical harmonic coefficients. Second, based on the fast Fourier transform and the fast multipole method, a lower complexity algorithm is derived that uses fastmore » transformations between Legendre and interior Fourier nodes, fast surface spherical truncation and a fast spherical Helmholz solver. Because the global shallow water equations are similar to the horizontal dynamical component of general circulation models, the results can be applied to spectral transform numerical weather prediction and climate models. In general, the derived algorithms may speed up the solution of time dependent partial differential equations in spherical geometry.« less