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24] D. M. Kodek and M. Krisper, "Telescopic rounding for suboptimal finite wordlength FIR digital filter design," Digit.Abstract-In this correspondence, reconstruction of a uniformly sampled sequence from a nonuniformly sampled transient sequence using symmetric extension is described. First, a relationship between the discrete Fourier transform (DFT) of a uniformly sampled sequence and the DFT of a nonuniformly sampled sequence is obtained. From the relationship, the formula to reconstruct the DFT of a uniformly sampled sequence from the DFT of a nonuniformly sampled sequence is derived when the nonuniform sampling ratios are known. Second, a symmetric extension of the nonuniformly sampled sequence is described to avoid discontinuity that adds highfrequency content in the DFT. Finally, experimental results are presented.

Modulating the electric dipole field with ultrasound pulse, ultrasound current source density imaging (UCSDI) can detect current direction and form spatial 3D imaging of dipole changing in one period of treatment. As ultrasound pulse passes through the conductive media, it convolves/correlates with the inner product of the electric field of a dipole and lead field of a pair of detectors, making the shifting frequency of polarity lower than the center frequency of the ultrasound pulse. After acoustoelectric (AE) signal is shifted to base band, the AE voltage is positive at anode and negative at cathode. In the simulation, the lead fields of detectors and electric field of dipole were calculated by the finite element (FE) method; the convolution and correlation in the computation of AE signal were accelerated using 3-D fast Fourier transforms. The current direction and amplitude are encoded in the phase and amplitude of the AE signal. Based on the analysis of polarity algorithms on the simulated and in-vitro ultrasound current source density images, it is concluded that the cross-correlation method is significantly better than the autocorrelation method to extract the frequency shift for high pulse bandwidth.

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