KERNEL DESIGN FOR REDUCED INTERFERENCE DISTRIBUTIONS

The mixed time-frequency signal representation has received considerable attention as a powerful tool for analyzing a variety of signals. Typical examples of time-frequency energy distributions are the spectrogram and the Wigner distribution. Despite several interesting properties, however, both of them are known to have critical limitations. For the spectrogram, the time and frequency resolutions cannot be simultaneously optimized. The Wigner distribution exhibits negative values and interference terms, which may lead to misinterpretations regarding the signal spectral contents. To overcome these drawbacks, Choi and Williams introduced a new distribution that has an exponential-type kernel. Although retaining high resolution with suppressed interference terms, the exponential distribution (ED, or Choi-Williams distribution) does not completely satisfy the support properties in time and frequency. In this paper, based on desirable distribution properties and associated kernel requirements, we discuss and further define a new class of time-frequency distributions called the reduced interference distribution (RID). Like the ED, the RID suppresses cross terms effectively while retaining high time and frequency resolutions of autoterms. Furthermore, the RID meets most of the desirable kernel requirements, including the time/frequency support properties. A systematic procedure to create RID kernels (or, equivalently, to compute RID's) is proposed. Some aspects and properties of the RID are discussed. It is shown that interpretations in the ambiguity, temporal correlation, spectral correlation, and time-frequency domains are fruitful for conceptualizing the RID. Some experimental results are provided to demonstrate the performance of the RID.