Date of Award

Spring 1984

Document Type


Degree Name

Doctor of Philosophy (PhD)


Electrical & Computer Engineering

Committee Director

John W. Stoughton

Committee Member

Stephen A. Zahorian

Committee Member

Roland R. Mielke

Committee Member

Frank Allerio


This dissertation addresses the application of non-adaptive transform coding for bit rate reduction of presampled filtered data. Transform coding is examined as an alternative to conventional pulse code modulation (PCM) for multi-source, fixed rate data acquisition systems. Typical bandlimiting presample filters introduce redundancy into the sequence of data samples. Linear transformation of successive N-length blocks of the data sequence and subsequent binary coding of the resulting components is shown to lead to reduced average bit rate for the same less distortion as PCM.

Four Butterworth filters, two corresponding to eight bit PCM systems, and two corresponding to ten bit PCM systems, are considered. The orthonormal transforms (bases) examined are a filter derived Karhunen-Loueve, a discrete cosine, and a discrete Legendre transform. A reference for the previous use of the discrete Legendre basis for transform coding is not known.

Transformation is modeled as a bank of basis dependent FIR filters for analysis. Thus, transform coding is interpreted in terms of spectral energy capture. The magnitude squared transfer function of the presample filter is assumed to define the worst case spectral envelope or power spectral density of the sampled filter output. This is incorporated into the model to establish an upper bound on the average component energy for the various bases. The bases are compared analytically using a bit rate reduction bound, adapted from Zelinski and Noll, and energy packing considerations. The analysis indicates that bit rate reduction is possible and that large block lengths are not required.

The transform coding strategy for N = 16 is implemented on simulated and real data. Bit rate reduction on the order of 25 percent establishes merit for the transform coding strategy. Additionally, transform coding is observed to result in less distortion than PCM for signals having intervals of reduced spectral activity.