Convolution Quadrature (CQ) is a method for numerical approximation of convolution integrals [1,2]. It has been widely used in the context of boundary integral equations.
What are the advantages of CQ with respect to simple (Nyquist-satisfying) sampling followed by discrete convolution?
I come from a digital signal processing background and I still haven't grasped why one would use such a complex method like CQ if simple sampling would do.
[1] C. Lubich. Convolution quadrature and discretized operational calculus. I. Numerische Math- ematik, 52(2):129–145, 1988.
[2] C. Lubich. Convolution quadrature and discretized operational calculus. II. Numerische Math- ematik, 52(4):413–425, 1988.