Angular Spread and Density Function of Spherical Waves

Field sensors and actuators such as loudspeakers, microphones and antennas have their response functions, or patterns, expressed in spherical coordinates. The patterns lead to basic parameters such as directivity, radiation efficiency, and even bandwidth. Such patterns are also used for describing the incoming wave distribution. The angular mean, variance and density functions are presented here for the spherical wave modes. These foster a better understanding of the signal processing associated with patterns.