Computing a DCT using an FFT, Signal analysis 
Computing a DCT using an FFT, Signal analysis 
Dec 9 2005, 06:40
Post
#1


Group: Members Posts: 35 Joined: 15April 04 From: Australia Member No.: 13509 
I am trying to make sense of the output of the FFT when used to calculate a type2 DCT (DCTII). I managed to scrape together enough documentation that infomed me that, if I wanted to perform a DCTII using an FFT algorithm, then the data should be arranged to be real even symmetric, with every even indexed data element set to zero.
No problem there. In addition, the outputs are correct, but half the expected value (I can see the output needs scaling by 2 to compensate for the fact that every second sample of the input is zero). However, I am tyring to figure out how the output comes to be what it is? In particular, where the zero comes from (term 4 & term 12) [counting from 0]. Input Real : 0 x0 0 x1 0 x2 0 x3 0 x3 0 x2 0 x1 0 x0 Imag : 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Output Real : ya yb yc yd 0 yd yc yb ya yb yc yd 0 yd yc yb Imag : 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 [grumble: looks good in fixed width font, but spaces are not turning out here] In my real application, I am using a 16 point DCT, which equates to a 64 point FFT, but the above is representative. Any hints? PS: I know there are better ways of doing DCTs, but in my implementation, I only have access to an FFT routine. Cheers,Owen. 


Jan 13 2006, 06:49
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#2


Group: Members Posts: 1593 Joined: 24March 02 From: Revere, MA Member No.: 1607 
http://www.ee.columbia.edu/~marios/courses...%20(Thesis).pdf
Here is another paper for reference describing faster way's to compute a DCT using an FFT.  College student/IT Assistant



Jan 13 2006, 10:03
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#3


Mad Scientist Group: Developer (Donating) Posts: 4890 Joined: 24September 01 Member No.: 13 
QUOTE (HotshotGG @ Jan 13 2006, 07:49 AM) http://www.ee.columbia.edu/~marios/courses...%20(Thesis).pdf Here is another paper for reference describing faster way's to compute a DCT using an FFT. The paper is about the MDCT, not the DCT. And the MDCT is based on a type 4 DCT, while he needs a type 2 DCT. This post has been edited by Garf: Jan 13 2006, 10:04 


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