We have developed several methods of designing sparse periodic arrays based upon the polynomial factorization method. In these methods, transmit and receive aperture polynomials are selected such that their product results in a polynomial representing the desired combined transmit/receive (T/R) effective aperture function. A desired combined T/R effective aperture is simply an aperture with an appropriate width exhibiting a spectrum that corresponds to the desired two-way radiation pattern. At least one of the two aperture functions that constitute the combined T/R effective aperture function will be a sparse polynomial. A measure of sparsity of the designed array is defined in terms of the element reduction factor. We show that elements of a linear array can be reduced with varying degrees of beam mainlobe width to sidelobe reduction properties.

For arbitrary matrix dilation M whose determinant is odd or equal to ±2, we describe all symmetric interpolatory masks generating dual compactly supported wavelet systems with vanishing moments up to arbitrary order n. For each such mask, we give explicit formulas for a dual refinable mask and for wavelet masks such that the corresponding wavelet functions are real and symmetric/antisymmetric. We proved that an interpolatory mask whose center of symmetry is different from the origin cannot generate wavelets with vanishing moments of order n > 0. For matrix dilations M with |det M | = 2, we also give an explicit method for construction of masks (non-interpolatory) m 0 symmetric with respect to a semi-integer point and providing vanishing moments up to arbitrary order n. It is proved that for some matrix dilations (in particular, for the quincunx matrix) such a mask does not have a dual mask. Some of the constructed masks were successfully applied for signal processes.

In this paper we analyze the most used measures for the assessment of spectral similarity of reflectance and radiance signals. First of all we divide them in five groups on the basis of the type of errors they measure. We proceed analyzing their mathematical definition to identify unintended behaviors and types of errors they are blind to. Then exploiting the Munsell atlas we analyze the correlation between metrics in terms of both Pearson's Linear Correlation Coefficient (PLCC) and Spearman's Rank Order Correlation Coefficient (SROCC). Finally we analyze the behaviour of the selected metrics with respect to two different color properties: the Chroma and the Lightness computed in the CIE L* a* b* color space. The source code of the spectral measures considered is available at the following link: <ext-link ext-link-type="url" xlink:href="https://celuigi.github.io/spectral-similarity-metrics-comparison/">https://celuigi.github.io/spectral-similarity-metrics-comparison/</ext-link>.

This paper outlines a general method for the factorization of a polynomial with unity coefficients into a product of sparse polynomials with fewer nonzero coefficients with unity values. The factorization method is then used to design sparse antenna arrays with uniform and linearly tapered effective aperture functions.

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