  Pulse Compression (PC) active sonar waveforms provide a significant
improvement in range resolution over single frequency sinusoidal waveforms also
known as Continuous Wave (CW) waveforms. Since their inception in the 1940's, a
wide variety of PC waveforms have been designed using either Frequency
Modulation (FM), phase coding, or frequency hopping to suite particular sonar
applications. The Sinusoidal FM (SFM) waveform modulates its Instantaneous
Frequency (IF) by a single frequency sinusoid to achieve high Doppler
sensitivity which also aids in suppressing reverberation. This allows the SFM
waveform to resolve target velocities. While the SFM's resolution in range is
inversely proportional to its bandwidth, the SFM's Auto-Correlation Function
(ACF) contains many large sidelobes. The periodicity of the SFM's IF creates
these sidelobes and impairs the SFM's ability to clearly distinguish multiple
targets in range. This dissertation describes a generalization of the SFM
waveform, referred to as the Generalized SFM (GSFM) waveform, that modifies the
IF to resemble the time/voltage characteristic of a FM chirp waveform. As a
result of this modification, the Doppler sensitivity of the SFM is preserved
while substantially reducing the high range sidelobes producing a waveform
whose Ambiguity Function (AF) approaches a thumbtack shape. This dissertation
describes the properties of the GSFM's thumbtack AF shape, compares it to other
well known waveforms with a similar AF shape, and additionally considers some
of the practical considerations of active sonar systems including transmitting
the GSFM on piezoelectric transducers and the GSFM's ability to suppress
reverberation. Lastly, this dissertation also describes designing a family of
in-band nearly orthogonal waveforms with potential applications to Continuous
Active Sonar (CAS).
