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 1940s, 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 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 autocorrelation 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 paper describes a generalization of the SFM waveform, referred to as the generalized SFM (GSFM) waveform, which modifies the SFM's IF to resemble the time/voltage characteristic of an 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 paper focuses primarily on the properties of the GSFM's thumbtack AF shape and compares it to other well-known waveforms with a similar AF shape. The GSFM waveform achieves zero range-Doppler coupling for single target measurements which in turn minimizes the variance in jointly estimating target range and velocity and optimizes resolution of multiple point targets in range and velocity. The GSFM's AF peak sidelobe levels, which determine the waveform's ability to detect weak targets in the presence of strong ones, are comparable to other well-established thumbtack AF waveforms such as Costas or phase-coded waveforms over a wide range of time-bandwidth product (TBP) values.