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Cosine modulated filter banks have gained popularity for their ability to provide perfect reconstruction (PR) while maintaining an efficient design and implementation. However, this effectiveness is hindered if the filter bank is implemented in the fixed-point domain where quantization, rounding, and overflow occur, and result in reconstruction errors. In this article we demonstrate how to maintain PR of the filter bank when implementing it in fixed-point number format with constant wordlength. We explore how the frequency selectivity of the analysis and synthesis filters changes from the floating point ones due to fixed-point errors and present new design criteria for filter banks that will be implemented in fixed-point number format.Index Terms-Cosine modulated filter banks, fixed-point implementation, perfect reconstruction (PR).

Most high resolution medical images such as X-ray radiographic images require enormous storage space and considerable time for transmission and viewing. We propose a wavelet design that creates the optimal filter taps for any class of images adaptively for high fidelity image reconstruction using an energy compacted section of the wavelet decomposed original image with considerable reduction in memory requirement as well as in execution, transmission, and viewing time. This optimal filter tap design is based on two-channel perfect reconstruction quadrature mirror filter (PR-QMF) banks using an interior-point-based optimization algorithm. The algorithm finds wavelet filter taps that allows the smallest amount of energy in the detail sections of the wavelet decomposition of an image in real time. Once the filter taps have been created and a one level wavelet transform has been performed, the energy compacted component of the image containing one fourth of the number of elements in the original image, is retained without any significant loss in the information content. This energy compacted section of the image is then used for any chosen advanced compression algorithm. This technique provides a significant reduction in execution time without an appreciable increase in distortion for advanced lossy image compression algorithms.

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Compressive sampling has a rich theoretical background in a number of fields from image processing to medical imaging to geophysical data analysis. In this paper we explore compressive sampling from the perspective of classic array processing. We derive a basis appropriate for reconstructing multichannel data which is sparsely sampled from a uniform linear array. Here we reconstruct both time and spatial components of the signal using randomly sampled time series. We present both theoretical and experimental evidence that compressive sampling can be successful for traditional array processing applications.