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With mean-squared error D as a goal, it is well known that one may approach the Rate-Distortion function R(D) of a non-bandlimited, continuous-time Gaussian source by sampling at a sufficiently high rate, applying the Karhunen-Loeve transform to sufficiently long blocks, and then independently coding the transform coefficients of each type. In particular, the coefficients of a given type are ideally encoded with performance attaining a suitably chosen point on the first-order rate-distortion function of that type of coefficient. This paper considers a similar sample-and-transform coding scheme in which ideal coding of coefficients is replaced by coding with some specified family of quantizers, whose operational rate-distortion function is convex.
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