Abstract: A method for performing channel shortening equalization with frequency notch mitigation is provided, where the method is applied to an electronic device. The method includes: obtaining channel response information from channel estimation to determine a relaxed channel convolution matrix corresponding to the channel response information, with the relaxed channel convolution matrix being a partial matrix of a channel convolution matrix corresponding to the channel response information, wherein the relaxed channel convolution matrix is obtained from omitting a portion of matrix elements of the channel convolution matrix; and based upon the relaxed channel convolution matrix, jointly performing time domain channel shortening control and frequency domain flatness control over the TEQ to perform channel shortening equalization with frequency notch mitigation by utilizing the TEQ. In particular, the portion of matrix elements includes a plurality of rows of matrix elements within the channel convolution matrix.

Abstract: A low complexity motion compensating beamforming system utilizes a probe array to fire for beamforming by synthetic apertures. The beamforming range of each firing is a region of interest (ROI), and the common area of adjacent ROI's forms the common ROI. The central image beam of the common ROI is used to generate image beam vectors, in order to analyze the cross-correlation for the corresponding low resolution images (LRI's). The analysis result is used to compute an offset for sequentially compensating and combining the LRI's to form a high resolution image (HRI). The mechanism helps improve the quality of ultrasonic beamforming and the frame rate.

Abstract: A method for performing channel shortening equalization with frequency notch mitigation is provided, where the method is applied to an electronic device. The method includes: obtaining channel response information from channel estimation to determine a relaxed channel convolution matrix corresponding to the channel response information, with the relaxed channel convolution matrix being a partial matrix of a channel convolution matrix corresponding to the channel response information, wherein the relaxed channel convolution matrix is obtained from omitting a portion of matrix elements of the channel convolution matrix; and based upon the relaxed channel convolution matrix, jointly performing time domain channel shortening control and frequency domain flatness control over the TEQ to perform channel shortening equalization with frequency notch mitigation by utilizing the TEQ. In particular, the portion of matrix elements includes a plurality of rows of matrix elements within the channel convolution matrix.

Abstract: A method for performing a singular value decomposition (SVD) upon a matrix. The method includes the steps of: (a) simplifying the matrix to derive a simplified matrix; (b) performing an iterative matrix multiplication upon the simplified matrix to generate an iterated matrix; (c) extracting a vector of the iterated matrix according to an iteration number of the iterative matrix multiplication; (d) de-correlating the simplified matrix from the vector to update the simplified matrix; (e) repeating steps (b), (c), and (d) until a predetermined number of vectors have been derived; and (f) storing a first unitary matrix determined according to the predetermined number of vectors in the singular value decomposition.

Abstract: A method for performing a singular value decomposition (SVD) upon a matrix. The method includes the steps of: (a) simplifying the matrix to derive a simplified matrix; (b) performing an iterative matrix multiplication upon the simplified matrix to generate an iterated matrix; (c) extracting a vector of the iterated matrix according to an iteration number of the iterative matrix multiplication; (d) de-correlating the simplified matrix from the vector to update the simplified matrix; (e) repeating steps (b), (c), and (d) until a predetermined number of vectors have been derived; and (f) storing a first unitary matrix determined according to the predetermined number of vectors in the singular value decomposition.