On Minimum Sampling Rates for Signals in Shift Invariant Spaces
نویسندگان
چکیده
This paper is focus on to design a sampling system with minimum sampling rate for signals in the shift invariant Hilbert space. To achieve this goal, we propose a method to calculate the Rate of Innovation (RI) of signals in the Hilbert space. The RI is then used to identify a suitable sampling kernel as well as the sampling rate for a specific signal. We show that the RI of the kernel should be greater or equal to the RI of the signal for the signal to be perfectly reconstructible. The minimum sampling rate depends on the RI of the signal. Examples are included to demonstrate how our method is applied to calculate the RI. Some known sampling theories can also be fitted into the framework of sampling system with minimum sampling rate.
منابع مشابه
Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups
We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...
متن کاملTranslation Invariant Approach for Measuring Similarity of Signals
In many signal processing applications, an appropriate measure to compare two signals plays a fundamental role in both implementing the algorithm and evaluating its performance. Several techniques have been introduced in literature as similarity measures. However, the existing measures are often either impractical for some applications or they have unsatisfactory results in some other applicati...
متن کاملPhaseless Sampling and Reconstruction of Real-Valued Signals in Shift-Invariant Spaces
Sampling in shift-invariant spaces is a realistic model for signals with smooth spectrum. In this paper, we consider phaseless sampling and reconstruction of real-valued signals in a shift-invariant space from their magnitude measurements on the whole Euclidean space and from their phaseless samples taken on a discrete set with finite sampling density. We introduce an undirected graph to a sign...
متن کاملTranslation Invariant Approach for Measuring Similarity of Signals
In many signal processing applications, an appropriate measure to compare two signals plays a fundamental role in both implementing the algorithm and evaluating its performance. Several techniques have been introduced in literature as similarity measures. However, the existing measures are often either impractical for some applications or they have unsatisfactory results in some other applicati...
متن کاملLocal reconstruction for sampling in shift-invariant spaces
The local reconstruction from samples is one of most desirable properties for many applications in signal processing, but it has not been given as much attention. In this paper, we will consider the local reconstruction problem for signals in a shiftinvariant space. In particular, we consider finding sampling sets X such that signals in a shift-invariant space can be locally reconstructed from ...
متن کامل