01_CM0340Tut_Frequency_Space

01_CM0340Tut_Frequency_Space - CM0340 Tutorial 1: Frequency...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
1 JJ II J I Back Close CM0340 Tutorial 1: Frequency Space Refer to Lecture notes for main point of reference (also recapped during this tutorial) Some additional explanation here: DCT revisited and practical computation explained (MATLAB) Demo MATLAB JPEG implementation discussed.
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 JJ II J I Back Close DCT Revisited DCT (Discrete Cosine Transform) is actually a cut-down version of the Fourier Transform or the Fast Fourier Transform (FFT): For N data items 1D DCT is defined by: F ( u ) = ± 2 N ² 1 2 . Λ( u ) N - 1 X i =0 cos h π.u 2 .N (2 i + 1) i f ( i ) where Λ( ξ ) = ³ 1 2 for ξ = 0 1 otherwise
Background image of page 2
3 JJ II J I Back Close DCT Example Let’s consider a DC signal that is a constant 100, i.e f ( i ) = 100 for i = 0 ... 7 (see DCT1Deg.m ): So the domain is [0 , 7] for both i and u We therefore have N = 8 samples and will need to work 8 values for u = 0 ... 7 . We can now see how we work out F ( u ) : As u varies we work can work for each u a component or a basis . F ( u ) . Within each F ( u ) , we cam work out the value for each F i ( u ) to define a basis function Basis function can be pre-computed and simply looked up in DCT computation.
Background image of page 3

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

View Full DocumentRight Arrow Icon
4 JJ II J I Back Close f ( i ) and F ( U ) Plots 1 2 3 4 5 6 7 8 0 10 20 30 40 50 60 70 80 90 100 1 2 3 4 5 6 7 8 0 50 100 150 200 250 300 f ( i ) = 100 for i = 0 ... 7 F ( u ) : F (0) 283 , F (1 ... 7) = 0
Background image of page 4
JJ II J I Back Close DCT Example: F (0) So for u = 0 : Note: Λ(0) = 1 2 and cos(0) = 1 So F (0) is computed as: F (0) = 1 2 2 (1 . 100 + 1 . 100 + 1 . 100 + 1 . 100 + 1 . 100 +1 . 100 + 1 . 100 + 1 . 100) 283 Here the values F i (0) = 1 2 2 ( i = 0 ... 7 ). These are a bases of
Background image of page 5

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

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/26/2012 for the course CM 0340 taught by Professor Davidmarshall during the Fall '09 term at Cardiff University.

Page1 / 21

01_CM0340Tut_Frequency_Space - CM0340 Tutorial 1: Frequency...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online