07_dftx

# 07_dftx - Discrete Fourier Transform COMP344 COMP344...

This preview shows pages 1–5. Sign up to view the full content.

Discrete Fourier Transform COMP344 COMP344 Discrete Fourier Transform

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Discrete Signals Discretize a continuous function f ( x ) into a sequence { f ( x 0 ) , f ( x 0 + Δ x ) , f ( x 0 +2Δ x ) , f ( x 0 +3Δ x ) . . . f ( x 0 +[ N - 1]Δ x ) } N samples, Δ x units apart Sequence f (0) , f (1) , f (2) , . . . , f ( N - 1) f ( x ) = f ( x 0 + x Δ x ) , x = 0 , 1 , 2 , . . . , N - 1 COMP344 Discrete Fourier Transform
Discrete Fourier Transform (DFT) F ( u ) = R -∞ f ( x ) e - j 2 π ux dx f ( x ) = R -∞ F ( u ) e j 2 π ux du The discrete Fourier transform of the sampled f ( x ) is: F ( u ) = 1 N N - 1 x =0 f ( x ) e - j 2 π xu / N , u = 0 , 1 , 2 , . . . , N - 1 Inverse DFT: f ( x ) = N - 1 u =0 F ( u ) e j 2 π xu / N COMP344 Discrete Fourier Transform

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Diﬀerent Notations F ( u ) = 1 N N - 1 x =0 f ( x ) e - j 2 π xu / N , f ( x ) = N - 1 u =0 F ( u ) e j 2 π xu / N Sometimes this is written with the (1 / N ) switched F ( u ) = N - 1 X x =0 f ( x ) e - j 2 π xu / N f ( x ) = 1 N
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 09/24/2010 for the course COMP 344 taught by Professor Albertk.wong during the Fall '09 term at HKUST.

### Page1 / 16

07_dftx - Discrete Fourier Transform COMP344 COMP344...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online