We use a white noise approach to Malliavin calculus to prove the following white noise generalization of the Clark-Haussmann-Ocone formula F (ω) = E[F ] + T 0 E[D t F |F t ] ⋄ W (t)dt Here E[F ] denotes the generalized expectation, D t F (ω) = dF dω is the (generalized) Malliavin derivative,⋄ is the Wick product and W (t) is 1-dimensional Gaussian white noise. The formula holds for all f ∈ G * ...

We consider Gaussian, Poissonian, fractional Gaussian and fractional Poissonian white noise spaces, all represented through the corresponding orthogonal basis of the Hilbert space of random variables with finite second moments, given by the Hermite and the Charlier polynomials. There exist unitary mappings between the Gaussian and Poissonian white noise spaces. We investigate the relationship o...

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ABSTRACT On the base of the estimator variance analysis we present a classification for a number digital chaos communication schemes and conventional spread spectrum techniques, which allows the qualitative comparison of the behaviour of the systems under the presence of additive white Gaussian noise on the channel. The classification results in a ranking and shows that the conventional stored-...

• The direct part (i.e., achievablity of transmission at rates approaching 1 2 log2(1+ P σ z )) however does not rely on the noise being AWGN and the theorem holds for a much broader class of channels. In fact, the proof below requires only that the noise have average power σ2 z and that it is empirically uncorrelated with the input signal. Thus, the noise may be non-Gaussian, and does not even...

We consider binary communication over the additive white Gaussian noise channel with no bandwidth constraint on the channel input signals, assuming the availability of a noiseless delayless feedback link. Although the signals at time t can depend on the noise at times 7 < t and are therefore random functions, we require that the signal energy never exceed a fixed level. We show that the optimal...

Many musical instruments’ sounds can be represented by harmonic and additive noise signals. We are interested in separating these two elements of the sound. We fit a local harmonic model that tracks changes in pitch and of the amplitude of the harmonics. Deterministic changes in the signal suggest that different window sizes should be considered. Various ways to choose appropriate window sizes ...