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).