H∞ Design of Periodically Nonuniform Interpolation and Decimation for Non-Band-Limited Signals

Abstract

: In this paper, we consider signal interpolation of discrete-time signals which are decimated nonuniformly. A conventional interpolation method is based on the sampling theorem, and the resulting system consists of an ideal filter with complex-valued coefficients. While the conventional method assumes band limitation of signals, we propose a new method by sampled-data H ∞ optimization. By this method, we can remove the band-limiting assumption and the optimal filter can be with real-valued coefficients. Moreover, we show that without band-limited assumption, there can be the optimal decimation patterns among ones with the same ratio. By examples, we show the effectiveness of our method.

Optimal discretization of analog filters via sampled-data H^∞ control theory

“…of an input u. A positive delay time l may improve the approximation performance when l is large enough as discussed in e.g., [7,12]. We here assume l is an integer multiple of h, that is, l = mh, where m is a nonnegative integer.…”

“…Then, to avoid a trivial solution (i.e., K(z) = 0), we should assume some a priori information for the inputs. As used in [7,12], we adopt the following signal subspace of L 2 [0, ∞) to which the inputs belong:…”

“…Although these methods are widely used, there may lead considerable discretization errors for unexpected signals such as signals that contains highfrequency components. To solve this, we apply the sampled-data H ∞ -optimal filter design [5,7,12,13] to the discretization problem. The proposed design procedure is summarized as follows:…”