Hartley Transform - Relation To Fourier Transform

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.

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