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We propose a robust algorithm to detect the arrival of a vehicle of arbitrary type when other noises are present. It is done via analysis of its acoustic signature against an existing database of recorded and processed acoustic signals. To achieve it with minimum number of false alarms, we combine a construction of a training database of acoustic signatures signals emitted by vehicles using the distribution of the energies among blocks of wavelet packet coefficients with a procedure of random search for a near-optimal footprint (RSNOFP). The number of false alarms in the detection is minimized even under severe conditions such as: the signals emitted by vehicles of different types differ from each other, whereas the set of non-vehicle recordings (the training database) contains signals emitted by planes, helicopters, wind, speech, steps, etc. The proposed algorithm is robust even when the tested conditions are completely different from the conditions where the training signals were recorded. The proposed technique has many algorithmic variations. For example, it can be used to distinguish among different types of vehicles. The proposed algorithm is a generic solution for process control that is based on a learning phase (training) followed by an automatic real time detection.

We present a new family of frames, which are generated by perfect reconstruction filter banks of linear phased filters. The filter banks are based on discrete interpolatory splines and are related to Butterworth filters. Each filter bank contains one interpolatory symmetric low-pass filter and two high-pass filters, one of which is also interpolatory and symmetric. The second high-pass filter is either symmetric or antisymmetric. These filter banks generate the analysis and synthesis scaling functions and pairs of framelets. We introduce the concept of semi-tight frame. All the analysis waveforms in a tight frame coincide with their synthesis counterparts. In the semi-tight frame we can trade properties of smoothness and number of vanishing moments between the synthesis and the analysis framelets. We construct dual pairs of frames, where all the waveforms are symmetric and all the framelets have the same number of vanishing moments. Although most of the designed filters are IIR, they allow fast implementation via recursive procedures. The waveforms are well localized in time domain despite their infinite support. The frequency response of the designed filters is flat.

Abstract-In this paper. we design a new family of biorthogonal wavelet transforms and describe their applications to still image compression. The wavelet transforms are constructed from various types of interpolatory and quasiinterpolatory splines. The transforms use finite impulse response and infinite impulse response filters that are implemented in a fast lifting mode.

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We present a new family of biorthogonal wavelet and wavelet packet transforms for discrete periodic signals and a related library of biorthogonal periodic symmetric waveforms. The construction is based on the superconvergence property of the interpolatory polynomial splines of even degrees. The construction of the transforms is performed in a "lifting" manner that allows more efficient implementation and provides tools for custom design of the filters and wavelets. As is common in lifting schemes, the computations can be carried out "in place" and the inverse transform is performed in a reverse order. The difference with the conventional lifting scheme is that all the transforms are implemented in the frequency domain with the use of the fast Fourier transform. Our algorithm allows a stable construction of filters with many vanishing moments. The computational complexity of the algorithm is comparable with the complexity of the standard wavelet transform. Our scheme is based on interpolation and, as such, it involves only samples of signals and it does not require any use of quadrature formulas. In addition, these filters yield perfect frequency resolution.  2002 Elsevier Science

In the paper we present a new family of biorthogonal wavelet transforms and the related library of biorthogonal symmetric waveforms. For the construction we used the interpolatory discrete splines which enabled us to design a library of perfect reconstruction ÿlter banks. These ÿlter banks are related to Butterworth ÿlters. The construction is performed in a "lifting" manner. The di erence from the conventional lifting scheme is that the transforms of a signal are performed via recursive ÿltering with the use of IIR ÿlters. These ÿlters have linear phase property and the basic waveforms are symmetric. The ÿlters allow fast cascade or parallel implementation. We present explicit formulas for construction of wavelets with arbitrary number of vanishing moments. In addition, these ÿlters yield perfect frequency resolution. The proposed scheme is based on interpolation and, as such, it involves only samples of signals and it does not require any use of quadrature formulas. ?

In this paper we consider equidistant discrete splines S( j ), j # Z, which may grow as O(| j | s ) as | j | Ä . Such splines are relevant for the purposes of digital signal processing. We give the definition of the discrete B-splines and describe their properties. Discrete splines are defined as linear combinations of shifts of the B-splines. We present a solution to the problem of discrete spline cardinal interpolation of the sequences of power growth and prove that the solution is unique within the class of discrete splines of a given order. Academic Press