Electrical and Computer Engineering ETDs

Publication Date



The discrete Laguerre transform (DLT) belongs to the family of unitary transforms known as Gauss-Jacobi transforms. Using classical methodology, the DLT is derived from the orthonormal set of Laguerre functions. Moreover, using recursion relationships common to all sets of orthonormal polynomials, generalized systolic arrays for forward and inverse unitary transform operations are derived and applied to the DLT. By examining the basis vectors of the transform matrix, the types of signals that can be best represented by the DLT are determined, namely oscillatory and damped oscillatory signals. Applications are demonstrated in the area of frequency domain adaptive filters, where the DLT compares favorably with the most popular real-coefficient transform, the discrete cosine transform (DOT). In particular, the DLT performs well in echo cancellation and sinusoidal signal enhancement examples. Data compression simulations demonstrate that the DLT outperforms the DOT in the compression of damped sinusoidal signals and speech data.


NASA Microelectronics Research Center at UNM

Document Type




Degree Name

Electrical Engineering

Level of Degree


Department Name

Electrical and Computer Engineering

First Committee Member (Chair)

Nasir Ahmed

Second Committee Member

Mo Jamshidi

Third Committee Member

Samuel D. Stearns

Fourth Committee Member

Gary Maki

Fifth Committee Member

Neeraj Magotra