Juan Miguel Medina

On the Prediction of a Class of Wide-Sense Stationary Random Processes

We prove that under suitable conditions, a multi-band wide sense stationary stochastic process can be linearly predicted at time with arbitrarily small error using past samples taken at uniform rate. This result generalizes previous similar results for band-limited signals. Moreover we prove that the prediction problem from uniform past samples is equivalent to a disjoint translates condition on the spectrum together with the divergence of a logarithmic integral. We also show that, for the band-limited case, under similar conditions, non uniform samples can be taken.

Wide Sense Stationary Processes Forming Frames

In this paper, we study the question of the representation of random variables by means of frames or Riesz basis generated by stationary sequences. This concerns the representation of continuous time wide sense stationary random processes by means of discrete samples.

Equivalence Between Representations for Samplable Stochastic Processes and its Relationship With Riesz Bases

We characterize random signals which can be linearly determined by their samples. This problem is related to the question of the representation of random variables by means of a countable Riesz basis. We study different representations for processes which are linearly determined by a countable Riesz basis. This concerns the representation of continuous time processes by means of discrete samples.

A synthesis of a 1/f process via Sobolev spaces and fractional integration

We provide an almost-sure convergent expansion of a process with power law of fractional order by means of some known theorems from harmonic analysis and rather simple probability theory results.

Some Localization Properties of the Lp Continuous Wavelet Transform

ABSTRACT We shall prove some simultaneous localization or concentration inequalities for the continuous wavelet transform. We will also show that simultaneous localization in the scale-time(space) is impossible, in the sense that the scale sections of the support of wavelet transform of a nonnull Lp-function can not have finite Lebesgue measure. Finally, some properties of the support of continuous wavelet transform of band-limited functions are studied.

Frame sequences and representations for samplable random processes

In this work characterize random signals which can be linearly determined by its discrete time samples, this problem is related to the question of the representation of random variables by means of a frame sequence. We study different representations for processes which are linearly determined by a frame sequence. This concerns the stable representation of continuous time processes by means of discrete samples. Finally, we study how these can be applied in reducing the effects of reconstructing a random signal from corrupted samples by additive noise.

A convergence result for unconditional series in Lp(ì)

We give sufficient conditions for the convergence almost everywhere of the expansion with respect to an unconditional basis for functions in Lp p > 2. This result extends the classical theorem of Menchoff and Rademacher for orthogonal series in L2.

Correction to "On the Prediction of a Class of Wide-Sense Stationary Random Processes" [Jan 11 70-77]

In the above titled papers (ibid., vol. 59, no. 1, pp. 70-77, Jan. 2011), there were several errors made during production. The corrections are presented here.

Stationary sequences and stable sampling

In this paper we study the question of the representation of random variables by means of frames or Riesz basis generated by stationary sequences. This concerns to the possible representation of continuous time processes by means of discrete samples.

Stationary random processes forming frames and basis: Some applications

We will give necessary and sufficient conditions for the samples taken at uniform rate from a w.s.s. processes (or of an “observed” process) to form a frame or a Riesz basis of its span. In some way this is an analogue problem to that of finding conditions for frames of a shift invariant subspace of L2(ℝ) with a finite number of generators. We will give also related results and applications.