\(\newcommand{\sfT}{\mathsf T}\newcommand{\rank}{\operatorname{rank}}\) 为了避免歧义, 我们这里约定 \[H = \begin{bmatrix}1 & 1 \\ 1 & -1\end{bmatrix}, \]以及
Hadamardmatrix;walshfunction;walsh-Hadamardtransformation;transformcoding Hadamard矩阵D~s3是线性代数[6卅中非常重 要的概念.因为这类矩阵具有正交性和元素二元性, 它在信号处理等方面应用正引起越来越多的人的重 视和兴趣[。州‘。 .1993年12月,Hadamard矩阵专家 ...
This is achieved by an (N N) transformation matrix (H transform matrix) which is orthonormal and has a block-diagonal structure. As such, it results in substantial saving in the number of multiplications required to obtain the DHT, relative to direct computation. Its total operation is almost...
"Abstract -- The matrix form of the Walsh functions . . . can be generated by the modulo-2 product of two generating matrices: the natural binary code, and the transpose of the bit-reversed form of the first. As a result, the coefficients of the Walsh transform occur in bit-reversed o...
The rows (or columns) of the symmetric hadamardMatrix contain the Walsh functions. The Walsh functions in the matrix are not arranged in increasing order of their sequences or number of zero-crossings (i.e. 'sequency order') but are arranged in 'Hadamard order'. The Walsh matrix, which co...
We identify a family of dual periodic optical superlattices from vairous columns of the Walsh–Hadamard transform matrix. We provide closed form expressions for the second harmonic spectral response of the designed optical superlattices, by explicitly performing the Fourier sum corresponding to finite ...
This is achieved by first expressing the Hadamard matrix as a power of a matrix, which allows for efficient CTD implementation. These results are then used in CTD implementation of fast Fourier transforms. The errors which accrue on using CTDs for implementing the Walsh-Hadamard transform are ...
5.4.1 C-matrix transform An integer approximation of DCT-II computed via the Walsh-Hadamard transform (WHT), called C-matrix transform (CMT) [19, 22–24], is the first attempt to approximate the real-valued discrete trigonometric transform in the integer domain. At first, Hein and Ahmed [...
If the fastwht function receives a matrix input, it applies the fast Walsh-Hadamard transform to each column in the matrix. This operation can be performed in parallel. If you have access to a mex compiler (with openMP), this part of the code can be easily parallelised (in the MATLAB ...
This chapter is devoted to the study of the Walsh-Hadamard transform (WHT), which is perhaps the most well-known of the nonsinusoidal orthogonal transforms. The WHT has gained prominence in various digital signal processing applications, since it can ess