Principal Component Filter Bank (PCFB) is considered optimal in terms of coding gain for specific conditions. P P Vaidyanathan stated that coding gain does not necessarily always increase with the increase in the number of bands. However, very few attempts are made in the literature to go beyond the confines of work done by P P Vaidyanathan. We present the analytic proofs for the monotonicity of specific shapes of PSDs. This papers also derives properties of coding gain of PCFBs, which brings the new insights on the coding gain of Principal Component Filter Banks.