Digital measurement of the analog acoustical parameters of a music performance hall is difficult. The aim of such work is to create a digital acoustical derivation that is an accurate numerical representation of the complex analog characteristics of the hall. The present study describes the exponential sine sweep (ESS) measurement process in the derivation of an acoustical impulse response function (AIRF) of three music performance halls in Canada. It examines specific difficulties of the process, such as preventing the external effects of the measurement transducers from corrupting the derivation, and provides solutions, such as the use of filtering techniques in order to remove such unwanted effects. In addition, the book presents a novel method of numerical verification through mean-squared error (MSE) analysis in order to determine how accurately the derived AIRF represents the acoustical behavior of the actual hall.