Multidimensional DSP with GPU acceleration: Difference between revisions

Revision as of 23:33, 3 November 2015

Revision as of 23:35, 3 November 2015

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To compute each element in {{math|'''C'''}} takes {{math|''m''}} multiplications and {{math|(''m'' - ''1'')}} additions. Therefore, with a CPU implementation, the time complexity to achieve this computation is ''Θ(n''<sup href="Category:GPGPU">''3''</sup>'')'' in the following C example''.'' However, we have known that elements in {{math|'''C'''}} are independent to each others. Hence, the computation can be fully parallelized by SIMD processors, such as GPGPU devices. With a GPGPU implementation, the time complexity reduces to ''Θ(n)'' in the following OpenCL example''.''

=== Multidimensional Fast Fourier Transform Transform ===

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=== Multidimensional Convolution ===

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<math>y(n_1, n_2)=\sum_{k_1=0}^{m-1}\sum_{k_2=0}^{m-1}x(k_1, k_2)h(n_1-k_1, n_2-k_2)</math>

=== Multidimensional Fast Fourier Transform Transform ===

In addition to convolution, fast Fourier transform is another technique which is often used in signal analysis.

== Real Applications ==