Convolution and Filtering

Abstract

DSP has led to both increased efficiency and increased difficulty in measuring the AIRF of a music performance hall. The efficiency of DSP produces an environment of increased detailed analysis but also produces greater difficulty in achieving accurate numerical quantification. An initial difficulty is the necessary conversion of an analog signal in continuous time to that of a digitally sampled representation in discrete time. This is called analog-to-digital (A/D) conversion. Convolution and filtering are also important in signal processing and the derivation of an AIRF. In order to achieve an accurate numerical AIRF representation, it is necessary to understand the numerical processing involved in the execution of a particular convolution or filtering algorithm. This is first accomplished through a deeper understanding of signal processing basics, such as the discrete-time or digital representation of continuous-time signals. Other basics include the advantages of the Fourier transform and processing in the frequency domain as compared to processing in the time domain. It is then important to look at some of the different traditional convolution methods, such as overlap-save, and to develop an understanding of some of the corresponding convolution algorithms and techniques available for both implementation and optimization.