Analog Least Mean Square (ALMS) loop is a promising method to cancel self-interference (SI) in in-band fullduplex (IBFD) systems. In this paper, the steady state analyses of the residual SI powers in both analog and digital domains are firstly derived. Eigenvalue decomposition is then utilized to investigate the frequency domain characteristics of the ALMS loop. Our frequency domain analyses prove that the ALMS loop has an effect of amplifying the frequency components of the residual SI at the edges of the signal spectrum in the analog domain. However, the matched filter in the receiver chain will reduce this effect, resulting in a significant improvement of the interference suppression ratio (ISR). It means that the SI will be significantly suppressed in the digital domain before information data detection. This paper also derives the lower bounds of ISRs given by the ALMS loop in both analog and digital domains. These lower bounds are joint effects of the loop gain, tap delay, number of taps, and transmitted signal properties. The discovered relationship among these parameters allows the flexibility in choosing appropriate parameters when designing the IBFD systems under given constraints.