Walsh Hadamard Transform (WHT) is an orthogonal, symmetric, involutional, and linear operation used in data encryption, data compression, and quantum computing. The WHT belongs to a generalized class of Fourier transforms, which allows many algorithms developed for the fast Fourier transform (FFT) to work for fast WHT implementations (FWHT). This paper employs this property and uses a well-known parallel-pipeline FFT strategy for VLSI implementation to build parallel-pipeline architectures for FWHT. We apply the FFT parallel-pipeline approach on a Fast WHT and use the High-Level Synthesis (HLS) tool from Xilinx Vitis to generate an FPGA solution.
We also provide an open-source code with the basic blocks to build any model with any parallelization level. The parallel-pipeline proposed solutions achieve a latency reduction of up to 3.57% compared to a pipeline approach on a 256-long signal using 32-bit floating-point numbers.
Fig.1. Fast Walsh-Hadamard Transform dived on a vector of 8 samples.
The black dots perform the sum between the two input arrows. The
dashed lines invert the data sign, and the solid lines keep the data sign
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