The generalized sinusoidal FM (GSFM) waveform modifies the sinusoidal FM (SFM) waveform to use an instantaneous frequency (IF) function that resembles a FM chirp waveform and as a result of this the GSFM possesses a thumbtack ambiguity function (AF) [Hague, Buck, Asilomar (2012)]. This is a drastic improvement over the SFM, which suffers from poor range resolution as its AF contains many ambiguous peaks generated by the periodicity of the SFM's IF. Analyzing the Taylor Series expansion of the GSFM's AF near the origin proves that the GSFM achieves minimal range-Doppler coupling for single target measurements. This minimizes the error in jointly estimating target range and velocity. The GSFM's AF Peak Sidelobe Level (PSL) and Integrated Sidelobe Ratio (ISLR) are comparable to or better than that of other waveforms with a thumbtack AF. Consequently, the target masking effect experienced in multi-target environments is less severe for the GSFM than other thumbtack waveforms. Lastly, test tank experiments demonstrate that the GSFM's desirable AF properties are robust to the signal conditioning necessary for transmission on practical piezoelectric transducers. [Work supported by ONR and the SMART Scholarship Program.]