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
Famous quotes containing the words relation to, relation and/or transform:
“You see, I am alive, I am alive
I stand in good relation to the earth
I stand in good relation to the gods
I stand in good relation to all that is beautiful
I stand in good relation to the daughter of Tsen-tainte
You see, I am alive, I am alive”
—N. Scott Momaday (b. 1934)
“A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.”
—Lionel Trilling (1905–1975)
“God defend me from that Welsh fairy,
Lest he transform me to a piece of cheese!”
—William Shakespeare (1564–1616)