Time domain

x[n]

Frequency domain

X2π(ω)Remarks

integer M

    

odd M

     even M

integer M > 0

The 

 

term must be

interpreted as

a distribution in

the sense of

a Cauchy

principal

value around

its poles at ω =

2πk.

     -π ≤ a < π

real number a

     -π < a < π real number a

real number a

integer M

real number a

real number W

0 < W ≤ 0.5

real numbers W

0 < W ≤ 1

it works as

a differentiator fil

ter

real

numbers W, a

0 < W ≤ 1

Hilbert transform

real

numbers A, B

complex C

http://en.wikipedia.org/wiki/Discrete-time_Fourier_transform