Relation To Fourier Transform
This transform differs from the classic Fourier transform in the choice of the kernel. In the Fourier transform, we have the exponential kernel: where i is the imaginary unit.
The two transforms are closely related, however, and the Fourier transform (assuming it uses the same normalization convention) can be computed from the Hartley transform via:
That is, the real and imaginary parts of the Fourier transform are simply given by the even and odd parts of the Hartley transform, respectively.
Conversely, for real-valued functions f(t), the Hartley transform is given from the Fourier transform's real and imaginary parts:
where and denote the real and imaginary parts of the complex Fourier transform.
Read more about this topic: Hartley Transform
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