# discrete fourier transform - ppt

fourier series to go from f( ) to f(t) substitute to deal with the first basis vector being of length 2 instead of , rewrite as fourier series the coefficients become fourier series alternate forms where complex exponential notation euler's formula euler's formula taylor series expansions even function ( f(x) = f(-x) ) odd function ( A signal f (t) is said to be periodic of period T if f (t) = f (t + T) for all t. Periodic signals can be represented by the Fourier series and non periodic signals can be represented by the Fourier transform. Therefore, the Discrete Fourier Transform of the sequence x[n]. Fourier Transform in Image Processing CS/BIOEN 6640 U of Utah Guido Gerig (slides modified from Marcel Prastawa 2012) Part II. Discrete -Time Fourier Transform Then for uniform convergence of , If x[n] is an absolutely summablesequence, i.e., if for all values of Thus, the absolute summability of x[n]is a sufficient condition for the existence of the DTFT X(ej) lim () ( ) =0 j K j K X e X e < n= x[n] = < . 11.01), one gets: k ikw t k. f t C e 2D Fourier Transform. 26, 28 in Ch. Complex conjugate property 11. Properties Fourier Transform: 2D Discrete Signals Fourier Transform: Properties Fourier Transform: Properties Fourier Transform: Properties Fourier Transform: Properties Fourier .