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Object oriented approach for computation of two dimensional Hartley transform. (English)
Acharya Nagarjuna Int. J. Math. Inf. Technol. 4, 22-32 (2007).
Summary: Integral transforms play a significant role in many fields of science, Medicine and Engineering. Optical imaging, Electric Power Engineering, Power Electronics, instrumentation and measurement and digital signal processing including the nonlinear filtering and initialization are a few major fields that find the application of the integral transformation. Although the Fourier transforms were the most known and used, the computational complexity lead to the conception of fast Fourier transform and later to the Hartley transforms. This being a real tool, it economizes the computational time and memory. Soon after the Bracewell’s elaboration 1983, the Hartley transform emerged as a powerful tool in Digital Signal Processing and it is universally accepted vice the complex Fourier transform. The Hartley transform can be obtained by replacing the kernel $e^{\#}$ of the Fourier transform $\cos (wx)$. Owing to the real domain representation many valuable properties are derived for the Hartley transform. Despite existence of many fast algorithms that reduce the number of additions and multiplications of computation, the discrete Hartley transform (DHT) gained importance and popularity because of its less computational complexity and implementation cost. Thus, the selection of a suitable DHT algorithm always matters for an effective study. Hence, we are motivated to take up this study using one of the two versions of two dimensional Hartley transform viz., due to Sundararajan in $C^{\#}$ programming language and the validation of the Software is also tested with the property that Hartley transform of Hartley transform is the original function.