DCT Definition
xEn a DCT I s day 27XEN us Tff htt K o
N
I
1
2 3
XI2N Upsampling1 zero stuffing 4N length signal
4N length DTT 4N length transformed signal
4 Extraprob
in
HW6
Fgm FengaoNI metrically extend fun t n n N 2N I
Retain the first samples of
this
04 dLkf dtnox nsospyftlntkhd
n A0 inI given
c Hoss cos CA
LKJ 2E.IEcos IntIl and IEnt XINt 2 EN I n GSP Int’s
change of variable
NI
2 E XEN as P
NEO
oxen’SHMOs t u In’t
c yk z oxen cos uIn’t’z
INI n’t’s XEN’Tostffy ni 1
y
oscotak
cosC A
2 a
dug i.d kfthkd.IT
I
n NIn
25
Givenyen fkn o en N
dad 2 xEnJbse nt
XINtn NEN 2N
cat YIK yEDe N
relate Yadto dad Iz¦Ì nye 5274412N
change of variable n 2N l n n 2NI
YIK
xEnte N 2n
0
1 2
2N length signalfrom YIK withYEN
E’x
Intoxmje JMKYN qnoxnye.PH 2N
A N 2N n
AO LnjeJMKY2N.gl
N i
e 522k 2N l n
n oxznyet522kn2NeJ2N42ND
n N I
n O
eJ2H4Il2N Enge 52214M 2N I nye jaunt E kN ethkfzlknfqfjxnyfeJEhkln IKN e.phKent’s 2N
205121kt n 1k
e.PK Y2NztnEoxnzcsslTtkTvlntIi eJ 42NdLkJ
We can also verify YENKI YIK YENI0 then retain the first N coefficients
b How to insert the DCT I csefs
KI
YIK
YID
Construct a
IDFT
Retain onlythe first half
2N
length
NI
0
ZEKIfYEK OIK 2N YINKI NEk N
i YINKO yude.ITn 2N
22nF IN fjEoyLkJeFWn2N
yzNyge0221412N
DEN feeK NK
4214 7 yage527442N nm I
IN ly t yEkJeJ
yLH.us f Iun1
Haft 2 tuTzYEItYETyEM4uI.n
o
in
I