Some Discrete Fourier Transform Pairs
Note | ||
---|---|---|
Shift theorem | ||
Real DFT | ||
from the geometric progression formula | ||
from the binomial theorem | ||
is a rectangular window function of W points centered on n=0, where W is an odd integer, and is a sinc-like function (specifically, is a Dirichlet kernel) | ||
Discretization and periodic summation of the scaled Gaussian functions for . Since either or is larger than one and thus warrants fast convergence of one of the two series, for large you may choose to compute the frequency spectrum and convert to the time domain using the discrete Fourier transform. |
Read more about this topic: Discrete Fourier Transform
Famous quotes containing the words discrete and/or transform:
“We have good reason to believe that memories of early childhood do not persist in consciousness because of the absence or fragmentary character of language covering this period. Words serve as fixatives for mental images. . . . Even at the end of the second year of life when word tags exist for a number of objects in the childs life, these words are discrete and do not yet bind together the parts of an experience or organize them in a way that can produce a coherent memory.”
—Selma H. Fraiberg (20th century)
“The lullaby is the spell whereby the mother attempts to transform herself back from an ogre to a saint.”
—James Fenton (b. 1949)
Related Phrases
Related Words