final dsp lab manual
TRANSCRIPT
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DSP Laboratory Manual
EXPERIMENT No. 1
ARCHITECTURE AND INSTRUCTION SET OF
DSPCHIP-TMS3!C"#13
FEATURES OF HI$HEST-PERFORMANCE FLOATIN$-POINT
DI$ITAL SI$NAL PROCESSOR TMS3!C"#13
Enhanced Harvard Architecture
VLIW Parallel Architecture
Rich Addressing modes
Two general purpose Register files(A!A"# $ %!%"#&
')*+! %it ,ata Word
Rich Instruction set
Eight '!%it Instructions)-.cle
')*+!%it ,ata Word
,epartment of E-E -/R Institute of Technolog.
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+0+!1 *02!ns Instruction -.cle Time
"3 /IP4)"'# /5L6P4
Rich Peripheral 4et1 6ptimi7ed for Audio
Highl. 6ptimi7ed -)-88 -ompiler
TMS3!C"#13 ARCHITECTURE
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INSTRUCTION SET FEATURES
9 4ingle! and ,ou:le!Precision Instructions
9%.te!Addressa:le (3!1 "*!1 '!%it ,ata&93!%it 6verflow Protection
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94aturation; %it!5ield E
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TMS3!C"#13 DSP FEATURES
Highest!Performance 5loating!Point ,igital 4ignal Processor (,4P&>
Eight '!%it Instructions)-.cle
')*+!%it ,ata Word
'!1 %!1 !/H7 (?,P&1 and %-1 !1 "*2!/H7 (P@P& -loc Rates
'0'!1 +0+!1 #!1 *!Instruction -.cle Times
+)"31 "3)"'#1 "*)"1 and "''*)" /IP4 )/5L6P4
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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Rich Peripheral 4et1 6ptimi7ed for Audio
Highl. 6ptimi7ed -)-88 -ompiler
E HPI1 3!1 "*!1 '!%it R6/ %oot
Endianness> Little Endian1 %ig Endian
'!%it E
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Enhanced ,irect!/emor.!Access (E,/A& -ontroller ("* Independent
-hannels&
"*!%it Host!Port Interface (HPI&
Two /ultichannel Audio 4erial Ports (/cA4Ps&
Two Independent -loc Fones Each (" TG and " RG&
Eight 4erial ,ata Pins Per Port>
Individuall. Assigna:le to an. of the -loc Fones
Each -loc Fone Includes>
Programma:le -loc ?enerator
Programma:le 5rame 4.nc ?enerator
T,/ 4treams 5rom !' Time 4lots 4upport for 4lot 4i7e>
31 "1 "*1 1 +1 31 ' %its
,ata 5ormatter for %it /anipulation
Wide Variet. of I4 and 4imilar %it 4tream 5ormats
Integrated ,igital Audio Interface Transmitter (,IT& 4upports>
4)P,I51 IE-*#3!"1 AE4!'1 -P!+' 5ormats
Cp to "* transmit pins
Enhanced -hannel 4tatus)Cser ,ata
E
4erial!Peripheral!Interface (4PI&
High!4peed T,/ Interface
A-2 Interface
Two '!%it ?eneral!Purpose Timers
,edicated ?PI6 /odule With "* pins (E
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Pacage 6ptions>
3!Pin PowerPA,B Plastic (Low!Profile& uad 5latpac (P@P&
2!%?A Pacages (?,P and F,P& 0"'!Jm)*!Level -opper /etal Process
-/64 Technolog.
'0'!V I)6s1 "0 !V Internal (?,P $ P@P&
'0'!V I)6s1 "0+!V Internal (?,P&(' /H7 onl.&
&LOC' DIA$RAM
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TMS3!C"#13 DS' O()r(*)+ &lo, D*ara/
INTRODUCTION TO CODE COMPOSER STUDIO
-ode -omposer is the ,4P industr.Ks first full. integrated development
environment (I,E& with ,4P!specific functionalit.0 With a familiar
environment lied /4!:ased -88T/1 -ode -omposer lets .ou edit1 :uild1
de:ug1 profile and manage proects from a single unified environment0 6ther
uniMue features include graphical signal anal.sis1 inection)e
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Host (P-& with windows (#)3)/e)GP)=T)&0
T/4'-*2"' ,4P 4tarter Dit (,4D).
INTRODUCTION0
Linear -onvolution involves the following operations0
"0 5olding
0 /ultiplication
'0 Addition
+0 4hifting
These operations can be represented by a Mathematical
Expression as follows:
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Where> n+1 +0 ;Values of n $ should :e a multiple of +0
If n $ are not multiples of +1 pad with 7eroSs to mae multiples of +
r n8!" ; 4i7e of output seMuence0
+8+!"
20
r " ' + # *
n UtiUm.proects& with name lconv0pt0
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Add the source files conv0asm0
to the proect using Proectadd files to proectS pull down menu0
Add the liner command file hello0cmd0
(Path> c>UtiUtutorialUds*2"'Uhello"Uhello0cmd&
Add the run time support li:rar. file rts*20li:0
(Path> c>UtiUc*UcgtoolsUli:Urts*20li:&
-ompile the program using the Proect!compileS pull down menu or :.
clicing the shortcut icon on the left side of program window0
%uild the program using the Proect!%uildS pull down menu or :.
clicing the shortcut icon on the left side of program window0
Load the program (lconv0out& in program memor. of ,4P chip using the
5ile!load programS pull down menu0
To View output graphicall.
4elect view graph time and freMuenc.0
PRO$RAMMIN$ FOR LINEAR CONOLUTION IN 4C5 LAN$UA$E0
includestdio0hX
main(&
Q int m+; )9Lenght of i)p samples seMuence9)
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int n+; )9Lenght of impulse response -o!efficients 9)
int i1;
int
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Note:
"0 To e
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20 What us the length of linear convolution if length of input $ impulse
responses
are ="$ =respectivel.]30 What is the difference :etween continuous and discrete convolution]
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EXPERIMENT No. 3
AIM0
To verif. the circular convolution operation Csing ,4D -ode composer
studio0
EUIPMENTS NEEDED0
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Host (P-& with windows (#)3)/e)GP)=T)&0
T/4'-*2"' ,4P 4tarter Dit (,4D&0 -R61 5unction ?enerators1 -onnecting wires
INTRODUCTION:
Steps for circular Convolution
4teps for circular convolution are the same as the usual convolution1 e Y4pinY hN^mOntimes Anti -loc Wise (counter!clocwise& to get hNn!
mO
(i0e0 4impl. rotate the seMuence1 hNnO1 clocwise :. nsteps&
5igure > 4tep
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4tep '> Point wise multipl. thefNmO wheel and the hNn^mO wheel0 sumyNnO
4tep +> Repeat for all _n_N "
E Two discrete!time signals to :e convolved0
hN^mO
5igure +
/ultipl.fNmO and sum to .ield>yNO '
hN"^mO
5igure #
/ultipl.fNmO and sum to .ield>yN"O #
hN^mO
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,epartment of E-E -/R Institute of Technolog.
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5igure *
/ultipl.fNmO and sum to .ield>yNO '
hN'^mO
5igure 2
/ultipl.fNmO and sum to .ield>yN'O "
PROCEDURE0
6pen -ode -omposer 4tudio; mae sure the ,4P it is turned on0
4tart a new proect using Proect!new pull down menu1 save it in a
separate director.(c>UtiUm.proects& with name ,*r,on(.26t.
Add the source files C*r,ular Con(olut*on.C.
to the proect using Proectadd files to proectS pull down menu0
Add the liner command file 7)llo.,/80
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(Path> c>UtiUtutorialUds*2"'Uhello"Uhello0cmd&
Add the run time support li:rar. file rt9"#!!.l*b
(Path> c>UtiUc*UcgtoolsUli:Urts*20li:&
-ompile the program using the Proect!compileS pull down menu or :.
clicing the shortcut icon on the left side of program window0
%uild the program using the Proect!%uildS pull down menu or :.
clicing the shortcut icon on the left side of program window0
Load the program(lconv0out& in program memor. of ,4P chip using the
5ile!load programS pull down menu0
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PRO$RAMMIN$ FOR CIRCULAR CONOLUTION IN 4C5 LAN$UA$E0
:*n,lu8);9t8*o.7?3!@=7?3!@=y?3!@=*=6=t)/2?3!@==>?3!@=a?3!@
(o*8 /a*nB
2r*ntB )nt)r t7) l)nt7 o t7) *r9t 9)Gu)n,)n
9,anB8=J/
2r*ntB )nt)r t7) l)nt7 o t7) 9),on8 9)Gu)n,)n
9,anB8=Jn
2r*ntB )nt)r t7) *r9t 9)Gu)n,)n
orB*K!*;/*
9,anB8=J>?*@
2r*ntB )nt)r t7) 9),on8 9)Gu)n,)n
orB6K!6;n6
9,anB8=J7?6@
*B/-nK! I l)nt7 o bot7 9)Gu)n,)9 ar) not )Gual
,epartment of E-E -/R Institute of Technolog.
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*B/?*@K!
/Kn
Q
y?!@K!
a?!@K7?!@
orB6K16;n6 ol8*n 7Bn to 7B-n
a?6@K7?n-6@
C*r,ular ,on(olut*on
orB*K!*;n*
y?!@K>?*@a?*@
orBK1;n
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y?@K!
,*r,ular 97*t
orB6K16;n6
>?6@Ka?6-1@
>?!@Ka?n-1@
orB*K!*;n*
a?*@K>?*@
y?@K>?*@>?*@
Q
Q
8*92lay*n t7) r)9ult
2r*ntB t7) ,*r,ular ,on(olut*on *9n
orB*K!*;n*
2r*ntB8 t=y?*@
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RE4CLT>
IN PUT0
E0 >?@K3= = 1=!Q
7?@K1= 1= !=!Q
OUT PUT0 y?@K3= %= 3=!Q
CE4TI6=4
"0 Wh. we need circular convolution]
0 What is the difference :etween circular $ linear convolution]
'0 What is the length of output seMuence after circular convolution if the lengths of
input $ impulse responses are /" $ / respectivel.]
+0 4tate the circular convolution propert. of ,5T]
#0 Where we reMuired convolution propert.]
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*0 What does 7ero padding mean] Where we reMuired this concept]
20 What is difference :etween linear shifting $ circular shifting of signal] 4howwith e
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EXPERIMENT No.
AIM0
,esign 5IR filter(LP)HP&and verif. with different cutoff freMuencies usingmatla: software0
EUIPMENTS0
Host (P-& with windows (#)3)/e)GP)=T)&1 matla: software
AL$ORITHM0
". $)t t7) 2a99 ban8 an8 9to2 ban8 r*22l)9.
. $)t t7) 2a99 ban8 an8 9to2 ban8 )8) r)Gu)n,*)9.
3. $)t t7) 9a/2l*n r)Gu)n,y.. Cal,ulat) t7) or8)r o t7) *lt)r.
%. F*n8 t7) +*n8o+ ,o)*,*)nt9.
". Dra+ t7) /an*tu8) an8 27a9) r)92on9)9.
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PRO$RAMME0
Prora/ or FIR LPF u9*n bla,/an +*n8o+nK!
2K!!
GK3!!
9K1!!!
nK29
+*n8o+Kbla,/anBn1
bK*r1Bn=n=+*n8o+
?H @Kr)GBb=1=1
9ub2lotB=1=1
2lotB2*=ab9BH
t*tl)B/an*tu8) r)92on9) o l2
ylab)lBa*n *n 8b--------lab)lBnor/al*)8 r)Gu)n,y------
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+*n8o+ K
-!.!!!! !.!!V !.!! !.1!1 !.!! !.3!! !.%!V !."V
!.V
!.V"! 1.!!!! !.V"! !.V !."V !.%!V !.3!! !.!!
!.1!1
!.!! !.!!V -!.!!!!
b K !.!!!! -!.!!!3 -!.!!!V !.!!# !.!1!1
-!.!!!! -!.!3" -!.!3! !.!#V !.V!"
!.3VVV !.V!" !.!#V -!.!3! -!.!3"
-!.!!!! !.!1!1 !.!!# -!.!!!V -!.!!!3
!.!!!!
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FIR LO PASS FILTER DESI$N USIN$ RECTAN$LE INDO0
Prora/ or FIR LPF u9*n r),tanular +*n8o+
nK!
2K!!
GK3!!
9K1!!!
nK29
+*n8o+Kr),t+*nBn1
bK*r1Bn=n=+*n8o+
?H @Kr)GBb=1=1
9ub2lotB=1=1
2lotB2*=ab9BHt*tl)B/an*tu8) r)92on9) o l2
ylab)lBa*n *n 8b--------lab)lBnor/al*)8 r)Gu)n,y------
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RESULT0-
+*n8o+ K
-!.!!!! !.!!V !.!! !.1!1 !.!! !.3!! !.%!V !."V
!.V!.V"! 1.!!!! !.V"! !.V !."V !.%!V !.3!! !.!!
!.1!1
!.!! !.!!V -!.!!!!
b K
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,epartment of E-E -/R Institute of Technolog.
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!.!!!! -!.!!!3 -!.!!!V !.!!# !.!1!1
-!.!!!! -!.!3" -!.!3! !.!#V !.V!"
!.3VVV !.V!" !.!#V -!.!3! -!.!3"
-!.!!!! !.!1!1 !.!!# -!.!!!V -!.!!!3
!.!!!!
FIR LO PASS FILTER DESI$N USIN$ TRIAN$LEINDO0
2rora/ or FIR LPF u9*n tr*anular +*n8o+
nK!
2K!!
GK3!!
9K1!!!nK29
+*n8o+Ktr*anBn1
bK*r1Bn=n=+*n8o+
?H @Kr)GBb=1=1
9ub2lotB=1=1
2lotB2*=ab9BH
t*tl)B/an*tu8) r)92on9) o l2
ylab)lBa*n *n 8b--------lab)lBnor/al*)8 r)Gu)n,y------
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2lotB2*=anl)BH
t*tl)B27a9) r)92on9) o l2
ylab)lBanl)--------lab)lBnor/al*)8 r)Gu)n,y------
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+*n8o+ K
-!.!!!! !.!!V !.!! !.1!1 !.!! !.3!! !.%!V !."V
!.V
!.V"! 1.!!!! !.V"! !.V !."V !.%!V !.3!! !.!!
!.1!1
!.!! !.!!V -!.!!!!
b K
!.!!!! -!.!!!3 -!.!!!V !.!!# !.!1!1
-!.!!!! -!.!3" -!.!3! !.!#V !.V!"
!.3VVV !.V!" !.!#V -!.!3! -!.!3"
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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-!.!!!! !.!1!1 !.!!# -!.!!!V -!.!!!3
!.!!!!
EXPERIMENT No. %
AIM0
To verif. the IIR filter Csing ,4D -ode composer studio with T/4'-*2"'
it0
EUIPMENTS0
Host (P-& with windows (#)3)/e)GP)=T)&0
T/4'-*2"' ,4P 4tarter Dit (,4D).
PROCEDURE0
6pen -ode -omposer 4tudio; mae sure the ,4P it is turned on0 -reate a new proect
Initiali7e on :oard codec0
Add the given a:ove -S source file to the current proect(remove codec0c
source file from the proect if .ou have alread. added&
%uild the program
Load the generated o:ect file (90out& on to target :oard0
Run the program using 5#1
6:serve the waveform on the -R6 screen0
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PRO$RAME FOR IIR FILTER0
#include "filtercfg.h"
#include "dsk6713.h"#include "dsk6713_aic23.h"
const signed int filter_Coeff[] ={ 1273!1273!1273!27671$32%21137 &'( 2)!! & 3123123123276727*%32%367 &+( $!! & 1%))1%))1%))32767231%!2173) &+( 2)!! & *26$*26$*26$3276773*)1$367 &'( %!!!& 721)721)721)32767)!3*6171 &'( 7!!!&, -
& Codec configuration settings &/06713_C23_Config config = { !4!!17 & ! /06713_C23_+589:+ +eft line in;ut channel?'89:+ >ight line in;ut channel
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/06713_C23_Codec'andle hCodec-
int l_in;ut r_in;ut l_out;ut r_out;ut-
& nitialiEe the Goard su;;ort liGrarH ust Ge called first & /06713_initD-
& /tart the codec & hCodec = /06713_C23_o;enCodec! IconfigD-
/06713_C23_setreJhCodec 3D-
Ahile1D { & >ead a sa;le to the left channel &
Ahile K/06713_C23_readhCodec Il_in;utDD-
& >ead a sa;le to the right channel &
Ahile K/06713_C23_readhCodec Ir_in;utDD-
l_out;ut=>_+5>Ifilter_Coeff l_in;utD- r_out;ut=l_out;ut-
& /end a sa;le to the left channel & Ahile K/06713_C23_AritehCodec l_out;utDD-
& /end a sa;le to the right channel & Ahile K/06713_C23_AritehCodec r_out;utDD- ,
& Close the codec &
/06713_C23_closeCodechCodecD-,
signed int >_+5>const signed int & h signed int 41D{
static signed int 4[6] = { ! ! ! ! ! ! ,- & 4nD 4n1D4n2D. Bust Ge static & static signed int H[6] = { ! ! ! ! ! ! ,- & HnD Hn1DHn2D. Bust Ge static &
int te;=!-
te; = short intD41- & Co;H in;ut to te; &
4[!] = signed intD te;- & Co;H in;ut to 4[stages][!] &
te; = intDh[!] & 4[!]D - & F! & 4nD &
te; L= intDh[1] & 4[1]D- & F12 & 4n1D &te; L= intDh[1] & 4[1]D- & F12 & 4n1D &
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te; L= intDh[2] & 4[2]D- & F2 & 4n2D &
te; = intDh[%] & H[1]D- & 12 & Hn1D & te; = intDh[%] & H[1]D- & 12 & Hn1D &
te; = intDh[)] & H[2]D- & 2 & Hn2D && i
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EXPERIMENT No. "
AIM0
To find the ,5T of a seMuence using =!Point 55Talgorithm usingT/4'-*2"' ,4P processor0
EUIPMENTS NEEDED0
Host (P-& with windows (#)3)/e)GP)=T)&0
T/4'-*2"' ,4P 4tarter Dit (,4D&06scilloscope and 5unction generator0
INTRODUCTION0
The ,5T EMuation
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Twiddle Factor
In the ,efinition of the ,5T1 there is a factor called the Twiddle Factor
where = num:er of samples0
If we tae an 3 :it sample seMuence we can represent the twiddle factor as a
vector in the unit
circle0 e0g0
0
PROCEDURE0
6pen -ode -omposer 4tudio1 mae sure the ,4P it is turned on0
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,epartment of E-E -/R Institute of Technolog.
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4tart a new proect using Proect!new pull down menu1 save it in a
separate director.(c>UtiUm.proects& with name [FFT.26tW.
Add the source files [FFT%".,[ and FFT.CW in the proect using
Proectadd files to proectS pull down menu0
Add the liner command file [7)llo.,/8W.
Add the rts file rt9"#!!.l*bW .
-ompile the program using the Proect!compileS pull down menu or :.
clicing the shortcut icon on the left side of program window0
Load the program in program memor. of ,4P chip using the 5ile!load
programS pull down menu0
Run the program and o:serve output using graph utilit.0
PRO$RAM FOR IMPLEMENTATION0
/ain0c (fft #*0c&>
include math0hX
define PT4 *+ )) of points for 55T
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define PI '0"+"#*#'#32
t.pedef struct Qfloat real1imag; -6/PLEG;
void 55T(-6/PLEG 9@1 int n&; ))55T protot.pe
float io:ufferNPT4O; ))as input and output :uffer
float
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samplesNiO0real0;
samplesNiO0imag0;
for (i ; i PT4 ; i88& ))swap :uffers
Q
samplesNiO0realio:ufferNiO; )):uffer with new data
for (i ; i PT4 ; i88&
samplesNiO0imag 0; ))imag components
55T(samples1PT4&; ))call function 55T0c
for (i ; i PT4 ; i88& ))compute magnitude
Q
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void 55T(-6/PLEG 9@1 int =& ))input sample arra.1 of points
Q-6/PLEG temp"1temp; ))temporar. storage varia:les
int i11; ))loop counter varia:les
int upper`leg1 lower`leg; ))inde< of upper)lower :utterfl. leg
int leg`diff; ))difference :etween upper)lower leg
int num`stages ; ))num:er of 55T stages (iterations&
int inde
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temp0real (@Nupper`legO&0real ! (@Nlower`legO&0real;
temp0imag (@Nupper`legO&0imag ! (@Nlower`legO&0imag;
(@Nlower`legO&0real temp0real9(wNinde
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temp"0imag (@NO&0imag;
(@NO&0real (@NiO&0real;
(@NO&0imag (@NiO&0imag; (@NiO&0real temp"0real;
(@NiO&0imag temp"0imag;
return;
RESULT0
In2ut0
6CTPCT>
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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+#
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UESTION
"0 What is the difference :etween continuous time $ discrete time 5ourier
transform]
0 What is the condition for convergence of 5ourier transform]
'0 What is the difference :etween discrete Time 5ourier Transform
(,T5T&$ ,5T]+0 What is the difference :etween F transform $ ,5T]
#0 4tate convolution propert. of the ,5T] Where we could use the
convolution propert.]
*0 4tate ParsevalSs theorem0]
20 4tate correlation propert. of the ,5T0]
EXPERIMENT No. #
AIM0
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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+*
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?enerate sum of sinusoidal seMuences
EUIPMENTS0
Host (P-& with windows (#)3)/e)GP)=T)&0matla: software0
PRO$RAME0
2rora/ to )n)rat) 9*nu9o*8al 9*nal9 +*t7 8*)r)nt a/2l*tu8)9
t*tl)B9*n) +a()9
tK!0.%02*
yK9*nBt
y1K%9*nBt
yK1!9*nBt
y3K1%9*nBt
9ub2lotB==1
2lotBy
>lab)lBt*/)
ylab)lBa/2l*tu8)
9ub2lotB==
9t)/By>lab)lBn----lab)lBt*/)
ylab)lBa/2l*tu8)
9ub2lotB==
9t)/By1
>lab)lBn----
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9ub2lotB==%
2lotBy
>lab)lBt*/)ylab)lBa/2l*tu8)
9ub2lotB=="
9t)/By
>lab)lBn---lab)lBt*/)
ylab)lBa/2l*tu8)
9ub2lotB==
9t)/By3
>lab)lBn-- ?E=ERATI6= 65 4I=C46I,AL 4I?=AL
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,epartment of E-E -/R Institute of Technolog.
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+3
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2rora/ to )n)rat) 9u/ o 9*n) 9)Gu)n,)9
t*tl)B9u/ o 9*n +a()9
tK!0.%02*
>K9*nBt
9ub2lotB==1
9t)/B>
>lab)lBn----
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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>lab)lBn----lab)lBn----lab)lBn----lab)lBn----
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9t)/By3
>lab)lBn----lab)lBn----
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UESTIONS0
"0 what is the difference :etween sin $ cos signals]
0 What is meant :. signal]
'0 What is the difference :etween time domain $ freMuenc. domain signal]
+0 What is the difference :etween periodic $ a periodic signal0
#0 What is the difference :etween orthogonal and orthonormal signals]
*0 What is the need for 5ourier series $ 5ourier transform]
20 What is the difference :etween discrete $ digital signals]
30 What is the difference :etween even signal $ odd signal]
0 What is the difference :etween power signal $ energ. signal]
"0What is the difference :etween amplitude scaling $ time scaling of a signal]
""0What is the difference :etween deterministic $ random signal]
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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#
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EXPERIMENT No.
AIM0
Verif. 5IR low pass filter)High pass using matla: software0
ECIP/E=T4>
Host (P-& with windows (#)3)/e)GP)=T)&0
T/4'-*2"' ,4P 4tarter Dit (,4D&0
-R61 5unction ?enerators1 -onnecting wires
AL$ORITHM0
". $)t t7) 2a99 ban8 an8 9to2 ban8 r*22l)9.
. $)t t7) 2a99 ban8 an8 9to2 ban8 )8) r)Gu)n,*)9.
3. $)t t7) 9a/2l*n r)Gu)n,y.
. Cal,ulat) t7) or8)r o t7) *lt)r.
%. F*n8 t7) +*n8o+ ,o)*,*)nt9.
". Dra+ t7) /an*tu8) an8 27a9) r)92on9)9.
PRO$RAME0
&UTTERORTH IIR ANALO$ LO PASS FILTER 0
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
#'
#'
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2rora/ or butt)r +ort7 analo IIR LPF
+1K*n2utB)nt)r 2a99 ban8 ,uto r)Gu)n,y0
+K*n2utB)nt)r 9to2 ban8 ,uto r)Gu)n,y0r2K*n2utB)nt)r 2a99 ban8 r*22l) *n 8b
r9K*n2utB)nt)r 9to2 ban8 r*22l) *n 8b
9K*n2utB)nt)r t7) 9a/2l*n r)Gu)n,y
+1K+29
+K+99
?N=+n@Kbuttor8B+1=+=r2=r9=9
?=2=@Kbutt)rBN=+n
?b=a@K2tB=2=
?b=a@Kbutt)rBN=+n=9
+K!0!.!102*
?7=o/)a@Kr)G9Bb=a=+
a*nK!lo1!Bab9B7
anKanl)B7
9ub2lotB=1=1
t*tl)B/a r)9 o l2
2lotBo/)a2*=a*n
ylab)lBa*n *n 8b--------lab)lBnor/al*)8 r)Gu)n,y------lab)lBnor/al*)8 r)Gu)n,y----
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RESULT0-
)nt)r 2a99 ban8 ,uto r)Gu)n,y01%!!
)nt)r 9to2 ban8 ,uto r)Gu)n,y03!!!
)nt)r 2a99 ban8 r*22l) *n 8b1!
)nt)r 9to2 ban8 r*22l) *n 8b!
)nt)r t7) 9a/2l*n r)G)n,y#!!!
b K ! ! ! ! ! ! !.!!!
a K 1.!!!! 1.%3# 1.11% !.%#%# !.1#! !.!3% !.!!!
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,epartment of E-E -/R Institute of Technolog.
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EXPERIMENT No. V
AIM0
-ompute Power ,ensit. 4pectrum of a seMuence using matla: software0
EUIPMENTS0
Host (P-& with windows (#)3)/e)GP)=T)&0 /atla: software
AL$ORITHM0
1. $)t t7) 9*nal >Bn o l)nt7 N *n /atr*> or/.
. T7) ,orr)lat)8 9*nal *9 8)not)8 a9 yBn.
3. yBn *9 *()n by t7) or/ula.
yBn K
=
k
nkxkx &(&(
+7)r) n K - BN-1 to BN-1
. PSD K FFT B Auto-,orr)lat*on un,t*on yBn .
PRO$RAM0
2rora/ or auto J 298
>K*n2utB)nt)r t7) 9)Gu)n,)
yK>,orrB>=>
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
#2
#2
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9ub2lotB3=1=1
9t)/B>
ylab)lBA/2l*tu8)---lab)lB n-----lab)lBn----
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)nt)r t7) 9)Gu)n,) ?1 3 @
Auto ,orr)lat*on un,t*on
y K 3 1 1 1 3
Po+)r 92),tral 8)n9*ty un,t*on
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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#
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2 K ? ".!!!! -1."11 -1!.1* 1.3#" 1.%%1V* -1.11"% -
.V1#*
-1.11"% .V1#* 1.3#" - 1.%%1V* -1."11 1!.1* @
UESTIONS0
"0 What is spectrum]
0 What are the applications]
'0 What is auto correlation]
+0 How to define power spectral densit.0
#0 What is :andwidth]
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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*
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EXPERIMENT No. 1!
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
*"
*"
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AI/>
To find the 5ast 5ourier transform of given "!, signal 0
EUIPMENTS0
Host (P-& with windows (#)3)/e)GP)=T)&0
T/4'-*2"' ,4P 4tarter Dit (,4D&0
6scilloscope and 5unction generator0
INTRODUCTION0
Why the FFT
If .ou loo at the eMuation for theDiscrete Fourier Transform.ou will see that
it is Muite complicated to wor out as it involves man. additions and
multiplications involving comple< num:ers0 Even a simple eight sample signal
would reMuire + comple< multiplications and #* comple< additions to wor
out the ,5T0 At this level it is still managea:le1 however a realistic signal could
have "+ samples which reMuires over 11 comple< multiplications
and additions0 As .ou can see the num:er of calculations reMuired soon mounts
up to unmanagea:le proportions0
http>))www0spd0eee0strath0ac0u)binteract)fourier)images)fft"0
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seMuence0 It is an ingenious wa. of achieving rather than the ,5TKs clums. P
timing0
The idea :ehind the 55T is the divide and conquerapproach1 to :rea up the
original = point sample into two (= ) & seMuences0 This is :ecause a series of
smaller pro:lems is easier to solve than one large one0 The ,5T reMuires (=!
"& comple< multiplications and =(=!"& comple< additions as opposed to the
55TKs approach of :reaing it down into a series of point samples which onl.
reMuire " multiplication and additions and the recom:ination of the points
which is minimal0
5or e
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S7ul)8 In2ut9
The process of decimating the signal in the time domain has caused the I=PCTsamples to :e re!ordered0 5or an 3 point signal the original order of the samples
is
! ! #! $! %! &! '! (
%ut after decimation the order is
! %! #! '! ! &! $! (
At first it ma. loo as if there is no order to this new seMuence1 %CT if the
num:ers are represented as :inar. a patter soon :ecomes apparent0
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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What has happened is that the :it patterns representing the sample num:er has
:een reversed0 This new seMuence is the order that the samples enter the 55T0
AL$ORITHM TO IMPLEMENT FFT0
St)2 1 - 4elect no0 of points for 55T(Eg> *+&0
St)2 Y ?enerate a sine wave of freMuenc. f (eg> " H7 with a sampling
rate =o0 of Points of 55T(eg0 *+&& using /at7 l*brary un,t*on0
St)2 3 - Tae sampled data and appl. 55T algorithm 0
St)2 Y Cse ?raph option to view the Input $ 6utput0
St)2 % - Repeat St)2-1 to for different no0 of points $ freMuencies0
PROCEDURE0
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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*#
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6pen -ode -omposer 4tudio1 mae sure the ,4P it is turned on0
4tart a new proect using Proect!new pull down menu1 save it in aseparate director.(c>UtiUm.proects& with name [FFT.26tW.
Add the source files [FFT%".,[ and FFT.CW in the proect using
Proectadd files to proectS pull down menu0
Add the liner command file [7)llo.,/8W.
Add the rts file rt9"#!!.l*bW .
-ompile the program using the Proect!compileS pull down menu or :.
clicing the shortcut icon on the left side of program window0
Load the program in program memor. of ,4P chip using the 5ile!load
programS pull down menu0
Run the program and o:serve output using graph utilit.0
PR6?RA/ 56R I/PLE/E=TATI6= 65 55T I= -S >
/ain0c (fft #*0c&>
include math0hX
define PT4 *+ )) of points for 55T
define PI '0"+"#*#'#32
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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t.pedef struct Qfloat real1imag; -6/PLEG;
void 55T(-6/PLEG 9@1 int n&; ))55T protot.pe
float io:ufferNPT4O; ))as input and output :uffer
float
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samplesNiO0imag0;
for (i ; i PT4 ; i88& ))swap :uffers
Q
samplesNiO0realio:ufferNiO; )):uffer with new data
for (i ; i PT4 ; i88&
samplesNiO0imag 0; ))imag components
55T(samples1PT4&; ))call function 55T0c
for (i ; i PT4 ; i88& ))compute magnitude
Q
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Q
-6/PLEG temp"1temp; ))temporar. storage varia:les
int i11; ))loop counter varia:lesint upper`leg1 lower`leg; ))inde< of upper)lower :utterfl. leg
int leg`diff; ))difference :etween upper)lower leg
int num`stages ; ))num:er of 55T stages (iterations&
int inde
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(@Nlower`legO&0real temp0real9(wNinde
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(@NO&0imag (@NiO&0imag;
(@NiO&0real temp"0real;
(@NiO&0imag temp"0imag;
return;
RESULT0
In2ut0
Out2ut0
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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2"
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UESTIONS
"0 What is the difference :etween radi< $ radi
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FOR PRACTICE
Program 1.
(>:?>BB8? :> +85> C:89:+O:8 8atlaG.
x=[1,2]andh=[1,2,4]
clc; clear all; close all;
x=input('enter the 1st sequence');
h=input('enter the 2nd sequence');
y=conv(x,h);
subplot (,1,1);
ste!(x);
ylabel ('a!plitude""#');
xlabel('(a) n ""#');
subplot (,1,2);
ste!(h);
ylabel ('a!plitude""#');
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
2'
2'
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xlabel('(b) n ""#');
ste!(y);
ylabel ('a!plitude""#');
xlabel ('(c) n ""#');
$disp('the resultant si%nal is');y
Program 2.
PRO$RAMMIN$ FOR CIRCULAR CONOLUTION IN /atlab0
clc; clear all; close all;
ginput(Kenter the "st seMuenceK&;
hinput(Kenter the nd seMuenceK&;
n"length(g&;
nlength(h&;nma
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else
gNg17eros("1!n'&O;
end
Z computation of circular convolved seMuencefor i">n;
.(i&;
i;
for ">n;
.(i&.(i&8g(&9h(&;
!";
if(&
n;
end
end
end.la:el(Kamplitude!!XK&;
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r2K*n2utB)nt)r 2a99 ban8 r*22l) *n 8b
r9K*n2utB)nt)r 9to2 ban8 r*22l) *n 8b
9K*n2utB)nt)r t7) 9a/2l*n r)Gu)n,y+1K+29
+K+99
?n=+n@Kbuttor8B+1=+=r2=r9=9
?=2=@Kbutt)rBn=+n
?b=a@K2tB=2=
?b=a@Kbutt)rBn=+n=9
?b1=a1@K*/2*n(arBb=a
+K!0!.!102*
?7=o/@Kr)GBb1=a1=+
/K!lo1!Bab9B7
anKanl)B7
9ub2lotB=1=1
2lotBo/2*=/
ylab)lBa*n *n 8b--------lab)lBnor/al*)8 r)Gu)n,y------lab)lBnor/al*)8 r)Gu)n,y----
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)nt)r 2a99 ban8 ,uto r)Gu)n,y01%!!
)nt)r 9to2 ban8 ,uto r)Gu)n,y03!!!
)nt)r 2a99 ban8 r*22l) *n 8b1!
)nt)r 9to2 ban8 r*22l) *n 8b!
)nt)r t7) 9a/2l*n r)G)n,y#!!!
b K ! ! ! ! ! ! !.!!!
a K 1.!!!! 1.%3# 1.11% !.%#%# !.1#! !.!3% !.!!!
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
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22
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Prora/ .
&UTTERORTH IIR DI$ITALHI$H PASS FILTER 0
Prora/ or 8**tal IIR HPF
+2K*n2utB)nt)r 2a99 ban8 )8) r)G
+9K*n2utB)nt)r 9to2 ban8 )8) r)G
r2K*n2utB)nt)r 2a99ban8 r*22l)
r9K*n2utB)nt)r 9to2ban8 r*22l)
?N=+n@Kbuttor8B+2=+9=r2=r9
?b=a@Kbutt)rBN=+n=7*7
?7=o/)a@Kr)GBb=a
a*nK!lo1!Bab9B7
anKanl)B7
9ub2lotB=1=1
2lotBo/)a2*=a*n
t*tl)B/a r)9 o 8**tal 72
>lab)lBnor/al*)8 r)G-----
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ylab)lBa*n *n 8b-----lab)lBnor/al*)8 r)G-------
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)nt)r 9to2 ban8 )8) r)G .
)nt)r 2a99 ban8 r*22l) 1!
)nt)r 9to2 ban8 r*22l) !
b K
!.!VV -!.3V"# !.%V%! -!.3V"# !.!VV
a K
1.!!!! -!.!"# !.#% -!.!11 !.!1#
Prora/ %.
FIR LO PASS FILTER DESI$N USIN$ HAMMIN$
INDO0
2rora/ or FIR LPF u9*n Ha//*n +*n8o+
,epartment of E-E -/R Institute of Technolog.
,epartment of E-E -/R Institute of Technolog.
3
3
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nK!
2K!!
GK3!!9K1!!!
nK29
+*n8o+K7a//*nBn1
bK*r1Bn=n=+*n8o+
?H @Kr)GBb=1=1
9ub2lotB=1=1
2lotB2*=ab9BH
t*tl)B/an*tu8) r)92on9) o l2
ylab)lBa*n *n 8b--------lab)lBnor/al*)8 r)Gu)n,y------
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DSP Laboratory Manual
DSP Laboratory Manual
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