We revisit AM stereo systems in detail from an academic standpoint, even when the trend of the AM stereo broadcasting is currently in decline. L. R. Kahn played a crucial role in promoting the AM stereo broadcasting from the second half of the twentieth century. However, his system was never set as the standard in the USA. In this study, the performance of Kahn’s system is first examined using Matlab. As a result, a problem caused by a “pseudo-Hilbert transform” is found in the setting of modulation index. Then, a truly ISB-based AM stereo system is studied and found to perform comparable or superior to that of the C-Quam, which was adopted as the standard. Next, we pursue how to asynchronously demodulate the truly ISB-based AM stereo signal with taking into account both the digital signal processing technology including the Hilbert transform and the recent stability of oscillators. Finally, we show that the present rigorous demodulation method can be easily applied to the C-Quam, paving the way for developing a compatible receiver for both systems.