Doctoral Dissertations

Mukta Lal Kar

Date of Award

6-1981

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Engineering Science

Major Professor

Lewis J. Pinson, E. C. Huebschmann

Committee Members

R. D. Joseph, K. C. Reddy, R. L. Young, K. E. Harwell

Abstract

Application of the popular Fast Fourier Transform (FFT) algorithm is limited to equi-spaced data. A literature survey of spectrum analyses using randomly sampled I records shows that most are not suitable for real time applications and require considerable high speed storage. For these reasons they are not suitable for small system applications.

A simple approach to spectrum estimation for randomly sampled data was investigated. This approach is based on the Fourier series and the method of modified least squares fit to estimate the Fourier coefficients. The estimator is algebraically very simple and produces an alias-free spectrum if a sufficient number of data points are available. This is true even if the mean sampling rate is less than the Nyquist rate required for spectral computation when using equi-spaced data samples.

Detailed statistical and error analyses are presented for the estimator. A statistical analysis shows the estimator to be asymptotically unbiased and consistent. Also, a number of simulation experiments were conducted using both computer generated data and the data acquired in practical laboratory setups. For some cases the same data were input to other algorithms for comparison. The experimental results verify the analytic solutions in the majority of the cases.

Finally, stepwise procedures to use this algorithm are stated and the implementation in small computer systems is discussed.

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