Spectral Invariance of $$*$$-Representations of Twisted Convolution Algebras with Applications in Gabor Analysis

We show spectral invariance for faithful $$*$$ ∗ -representations for a class of twisted convolution algebras. More precisely, if G is a locally compact group with a continuous 2-cocycle c for which the corresponding Mackey group $$G_c$$ G c is $$C^*$$ C ∗ -unique and symmetric, then the twisted convolution algebra $$L^1 (G,c)$$ L 1 ( G , c ) is spectrally invariant in $${\mathbb {B}}({\mathcal {H}})$$ B ( H ) for any faithful $$*$$ ∗ -representation of $$L^1 (G,c)$$ L 1 ( G , c ) as bounded operators on a Hilbert space $${\mathcal {H}}$$ H . As an application of this result we give a proof of the statement that if $$\Delta $$ Δ is a closed cocompact subgroup of the phase space of a locally compact abelian group $$G'$$ G ′ , and if g is some function in the Feichtinger algebra $$S_0 (G')$$ S 0 ( G ′ ) that generates a Gabor frame for $$L^2 (G')$$ L 2 ( G ′ ) over $$\Delta $$ Δ , then both the canonical dual atom and the canonical tight atom associated to g are also in $$S_0 (G')$$ S 0 ( G ′ ) . We do this without the use of periodization techniques from Gabor analysis.

The Psychoacoustics of Automatic Speech Recognition

Automatic speech recognition (ASR) software has been suggested as a candidate model of the human auditory system thanks to dramatic improvements in performance in recent years. To test this hypothesis, we compared several state-of-the-art ASR systems to results from humans on a barrage of standard psychoacoustic experiments. While some systems showed qualitative agreement with humans in some tests, in others all tested systems diverged markedly from humans. In particular, none of the models used spectral invariance, temporal fine structure or speech periodicity in a similar way to humans. We conclude that none of the tested ASR systems are yet ready to act as a strong proxy for human speech recognition. However, we note that the more recent systems with better performance also tend to better match human results, suggesting that continued cross-fertilisation of ideas between human and automatic speech recognition may be fruitful. Our software is released as an open-source toolbox to allow researchers to assess future ASR systems or add additional psychoacoustic measures.

Can The Spectra Of Hermitian Operator Be Invariant Under x ⇀ ↽ p ? :Case Study :1D General

We address an intriguing question on spectral invariance in quantum mechanics onexchange of co-ordinate and momentum x ⇀ ↽ p considering general oscillator as anexample.Key words:exchange of co-ordinate and momentum , spectral invariance , generaloscillator .