Abstract
It is well known that only a special class of bandpass signals, called real-zero (RZ) signals can be uniquely represented (up to a scale factor) by their zero crossings, i.e., the time instants at which the signals change their sign. However, it is possible to invertibly map arbitrary bandpass signals into RZ signals, thereby, implicitly represent the bandpass signal using the mapped RZ signal's zero crossings. This mapping is known as real-zero conversion (RZC). In this paper a class of novel signal-adaptive RZC algorithms is proposed. Specifically, algorithms that are analogs of well-known adaptive filtering methods to convert an arbitrary bandpass signal into other signals, whose zero crossings contain sufficient information to represent the bandpass signal's phase and envelope are presented. Since the proposed zero crossings are not those of the original signal, but only indirectly related to it, they are called hidden or covert zero crossings (CoZeCs). The CoZeCs-based representations are developed first for analytic signals, and then extended to real-valued signals. Finally, the proposed algorithms are used to represent synthetic signals and speech signals processed through an analysis filter bank, and it is shown that they can be reconstructed given the CoZeCs. This signal representation has potential in many speech applications.
Highlights
A key issue in sampling theory is the construction of a sequence of samples that unambiguously represent a signal s(t)
In this paper we are primarily concerned with the second approach, i.e., representing bandpass signals by certain time instants
In the proposed signal representation schemes, these timing instants are not the zero-crossing locations of s(t) themselvesas in, for example, Refs. 3, 4͒, but the zero-crossing locations of certain functions that are related to the phase and envelope of the signal s(t)
Summary
A key issue in sampling theory is the construction of a sequence of samples that unambiguously represent a signal s(t). There are two major approaches to constructing such a sequence of samples.[1]. ͑2͒ The second approach is the less familiar notion of representing signals by certain time instants..., Ϫ1 ,0 ,1 , 2 ,. For example, in certain cases the zerocrossings or level-crossing locations of s(t) can be used to represent s(t) to within a scale factor. In this paper we are primarily concerned with the second approach, i.e., representing bandpass signals by certain time instants. In the proposed signal representation schemes, these timing instants are not the zero-crossing locations of s(t) themselvesas in, for example, Refs. 3, 4͒, but the zero-crossing locations of certain functions that are related to the phase and envelope of the signal s(t) In the proposed signal representation schemes, these timing instants are not the zero-crossing locations of s(t) themselvesas in, for example, Refs. 3, 4͒, but the zero-crossing locations of certain functions that are related to the phase and envelope of the signal s(t)
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