Hadamard transforms on multiply/add architectures

Coppersmith, Don; Feig, Ephraim; Linzer, Elliot

doi:10.1109/78.285664

Cited by 20 publications

(9 citation statements)

References 2 publications

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“…So, the 4-point Walsh-Hadamard transform can be computed by 7 addition and 3 one-bit shift operations (two operations to calculate z 0 , one for z 1 , and four for y 0 , y 1 , y 2 , y 3 , and three one-bit shift operations) [7]. Step 1.…”

Section: Fast Hadamard Transform On Shift/add Architecturesmentioning

confidence: 99%

“…We recall that an N = 2 k -point fast Hadamard transform algorithm with shift operation has the complexity [7] C(N ) = 7k2 k−3 , k is even, (7k + 1)2 k−3 , k is odd, C s (N ) = 3k2 k−3 , k is even, 3(k − 1)2 k−3 , k is odd,…”

Section: Complexity Of the General Algorithm With Shiftsmentioning

confidence: 99%

“…Many of the current advanced workstations and signal processors are designed for efficient fused multiply-add operations [7], [9], [10], where the primitive operation is a multiply-add ±a ± bc operation, where a, b, and c are real numbers. In [10] a decimation-in-time "radix-4" Hadamard transform which supports a multiply/add instruction was developed.…”

Section: Introductionmentioning

confidence: 99%

“…In [10] a decimation-in-time "radix-4" Hadamard transform which supports a multiply/add instruction was developed. The authors have shown that this "radix-4" algorithm is 5.6%-7.4% faster than a regular "radix-4" algorithm [7].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Decomposition of Binary Matrices and Fast Hadamard Transforms

Sarukhanyan

Agaian

Astola

et al. 2005

Circuits Syst Signal Process

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Binary matrices or (±1)-matrices have numerous applications in coding, signal processing, and communications. In this paper, a general and efficient algorithm for decomposition of binary matrices and the corresponding fast transform is developed. As a special case, Hadamard matrices are considered. The difficulties of the construction of 4n-point Hadamard transforms are related to the Hadamard problem: the question of the existence of Hadamard matrices. (It is not known whether for every integer n, there is an orthogonal 4n × 4n matrix with elements ±1.) In the derived fast algorithms, the number of real operations is reduced from O(N 2 ) to O(N log N ) compared to direct computation. The proposed scheme requires no zero padding of the input data. Comparisions revealing the efficiency of the proposed algorithms with respect to the known ones are given. In particular, it is demonstrated that, in typical applications, the proposed algorithm is significantly more efficient than the conventional Walsh-Hadamard transform. Note that for Hadamard matrices of orders ≥ 96 the general algorithm is more efficient than the classical Walsh-Hadamard transform whose order is a power of 2. The algorithm has a simple and symmetric structure. The results of numerical examples are presented.

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Section: Fast Hadamard Transform On Shift/add Architecturesmentioning

confidence: 99%

Section: Complexity Of the General Algorithm With Shiftsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Decomposition of Binary Matrices and Fast Hadamard Transforms

Sarukhanyan

Agaian

Astola

et al. 2005

Circuits Syst Signal Process

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“…Some of them operate either in the transform domain [16], the pixel values are transformed into another domain by applying appropriate transform like OCT [1], [7], [8], OFT [9] ,DHT [13], [14], [15] and DWT [10], [11] and embedding technique done by modifying these coefficients, or in the spatial domain [12], [16], provides algorithm that directly operate on the pixel values of the host image such as the Least Significant Bit (LSB) substitution [17], Information bit hiding in spatial domain for JPEG image is described in [18]. But it was seen that the spatial domain watermarks are weaker than the frequency domain [17].…”

Section: Introductionmentioning

confidence: 99%

Hardware realization of DC embedding video watermarking technique based on FPGA

Elaraby

Madian

Ashour

et al. 2010

2010 International Conference on Microelectronics

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In this paper, a video watermark technique is proposed. The proposed technique depends on inserting invisible watermark in Low Frequency DCT domain using pseudo random number (PN) sequence generator for the video frames instead of high or mid band frequency components. This technique has been realized using Matlab and VHDL. The system has been implemented on Xilinx chip XC5VLX330T. The result of implementation shows that maximum frequency 13.61 MHZ. The experimental and implementation results has been demonstrated and discussed.

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