Introduction

In careful observation of the physics of reverberation, the signal that we hear repeated arrives at our ears at different times due to the different paths the sound waves travel. Take for example you are standing in a church: you clap your hands and hear an immediate 'smack' and reverberating copies of the same 'smack' from different parts of the room. The first 'smack' you heard arrived at your ear through a direct path from your hands. The reverberant copies travelled from your hands to perhaps a distant wall, reflecting back to your ear. As Figure 1 shows, $x_2$ fed straight into the adder corresponds to the direct path of the signal $x_1$. $y_2$, which corresponds to the signal $x_2$ delayed by $M$ samples, corresponds to the same signal but delayed by $M$ samples or in physical terms, traveling a certain longer distance.