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An algebraic integer (AI) based time-multiplexed row-parallel architecture and two final-reconstruction step (FRS) algorithms are proposed for the implementation of bivariate AI-encoded 2-D discrete cosine transform (DCT). The architecture directly realizes an error-free 2-D DCT without using FRSs between row-column transforms, leading to an 8×8 2-D DCT which is entirely free of quantization errors in AI basis. As a result, the user-selectable accuracy for each of the coefficients in the FRS facilitates each of the 64 coefficients to have its precision set independently of others, avoiding the leakage of quantization noise between channels as is the case for published DCT designs. The proposed FRS uses two approaches based on (i) optimized Dempster-Macleod multipliers and (ii) expansion factor scaling. This architecture enables low-noise high-dynamic range applications in digital video processing that requires full control of the finite-precision computation of the 2-D DCT. The proposed architectures and FRS techniques are experimentally verified and validated using hardware implementations that are physically realized and verified on FPGA chip. Six designs, for 4-and 8-bit input word sizes, using the two proposed FRS schemes, have been designed, simulated, physically implemented and measured. The maximum clock rate and block-rate achieved among 8-bit input designs are 307.787 MHz and 38.47 MHz, respectively, implying a pixel rate of 8×307.787≈2.462 GHz if eventually embedded in a real-time video-processing system. The equivalent frame rate is about 1187.35 Hz for the image size of 1920×1080. All implementations are functional on a Xilinx Virtex-6 XC6VLX240T FPGA device.

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Three dimensional (3-D) narrow cone-shaped filter passbands are ideally required for the selective filtering of sampled broad-band 3-D plane waves on the basis of their directions of arrival. A method is proposed for approximating narrow 3-D cone-shaped passbands using a 3-D cone-filter-bank structure in which the subbands consist of band limited 3-D narrow-band infinite impulse response (IIR) beam filters having 3-D uniform bandwidths that are approximately proportional to their distance from the origin in the 3-D frequency space. The 3-D beam filters may be realized from a cascade of 3-D IIR frequency-planar filters. It is shown that the proposed 3-D cone filter bank achieves low distortion of broad-band passband 3-D plane waves, and significant attenuation of broad stopband plane waves.

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Abstract-We propose an algorithm-independent framework for rigorously comparing digital watermarking algorithms with respect to bit rate, perceptual quality, computational complexity, and robustness to signal processing. The framework is used to evaluate five audio watermarking algorithms from the literature, revealing that frequency domain techniques perform well under the criteria.