matlab crash course
TRANSCRIPT
!!" ""#$!!"
%&'$""
( % $ " !"& " !" ""$
!
"$ ! %
$ (") !) $
*+ * ! $ $! ,") *-.*/ "
"" $!"$ 0
!"""% *123+% !" 4
$$$#%
) "" $ !" 56
" $ 5 1$" 7 $ !"8
) "9$
!"$%$ "" &
"! """!" $50 "
%$ !$)""""$ )
$ "" ""!:
: "; "") ) & :
:"%&!"%)$"2"!"
"%
!!""" $,"$$
$ / !" " "
0
<"$! "%$ """ $"!$"!"%!%"!
; """ "$"$$
=
!!"#$"$"% "
4%! "
")9 1
1") ""!
%$"! !
!
)!%$ ""
"!&'(("$) (("$"
"!& $ "
%""+*>1$ !"
! )
((" $)
! (("
$""!$)!)
$
. 9
$ ! . !
?@@A
:
!*!*)
% ""%""$!)""
" )>+1
!$"%!(("
B*5!"$ !"$"""
!
9!""$5 !
""" !!,!!/$
"
*!!$"
!"!
+!"$"? A
&+#$",$-*
" " ! $ "
$"
?A%?A%?A% ?!A"π ?A?#A!"√,'/75 $,$/7!"& ""&!"""8
"!'""
C
! ,$"") "
!1 2 / ""!!")
" $
")
@@ & &
@@ . 2 ?."A)$?A""$#!
$
!
@@ ! ""$.D92+1"
@@ + ""$4>292+1"
@@ "! E"! """
"$
@@ E"!!" "!?!"A
; "" ! " " " """%!"; ""!
$#
F
!" &!" $
"" "
.&/0$(1**!*)$"
$!"" !!,@@ /
!*G *2
@@ =:H,CIJ/
;""" !
K
FL
$ "% " ?A
""
$ ",?&A/%!"$$!
@@ &K=:H,CIJ/
;""" !
&K
FL
" " "" $ " &!
""",""$!)"""/
,&/ ,&/ ,&/ ",&/ &!,&/
> ! 2+G1
" ,*-.*/ $(1 ) %$ !!"$
"&"
L
.&2+3*$%"$""1%(($"%$"%"*
, $ ! " 4>2 2G%.%1./%0"$ "&!
0"""?!A
$&
M"NK""!"&!
)$")!
&!% "" )"% ""
)!"
") " !
, "/ ""
""
@@&K
&K
@@&KI&7= !"
&K # " $% &
!&!" ,!/
"" $""""""
$!"" ""
&!"
@@K=O !'( $ $)&& &@@K: *'(
K
:
@@.K,'/H:P'IP
+
.K
L
J
.&4+*!*)$"$"%+$%",*
;"",?&A%?$A?<A/
@@ &K:FLO
@@ $KL=:CO @@ <K'=CO
@@
G" ",O/ ,O/
!$!, !%$$!
" "8/
@@&K:FL
&K
:FLPP
@@$KL=:C
$K
FL=C
@@<K'=C
<K
'=CPP
@@
E ,!/""G!! $&
E
@@&K:FLO
@@$KL=:CO
@@<K'=CO
@@!K<I,&I,$//Q=
!K
'=JHPP:
@@
*(")- *(")1)$"1""&"!" $ !
4&!"%$&RS
P
RSKR='=S
$ "!"$*.E***G $=%
E % ! % RS RS% "!"$RS$RS%RS$
RS%%
1!"$$% I6
9 ""$")
AAA
AAA A
232221
131211
=
BBB
BBB B
232221
131211
=
IK BABABA
BABABA
232322222121
131312121111
K /BA/BA/BA
/BA/BA/BA
232322222121
131312121111
( ) ( ) ( )( ) ( ) ( )
AAAAAA
n ^ A. n23
n22
n21
n13
n12
n11
=
$ "
""",
"!"(G*11
" &0"
&/
$ " "
"
>$ ""!"% "$&$"!
!08
=
!$1)#$*1!"! $
&
,
$$
(?2"A
4)$
$$!".9
"1)!(("#(!$1)#$*
M"!!
M"!"
M".9
:
M"!".9
!%"&!"
$"1)""&!"
")5
-,K!,B !"$
5/
!"!!
G"%$" .9 M$.9
$$ ","0)%$! $
0)/
G , "" "% !
)/"!
,K!,B!!5%55/
B!!5 !"!!$!.9
B5 ""
$ & $! 9 E>( " 0%
"
)1)!(("#(!$1)#$* "" ""$ !"$
& !"$!!$"
$1!,"/
!,B&5/
$1 " "
!"$"!"$&
>"$"$!$$1 "
! % " , "
!"$/!"$
!"$"%&!"%"$
" "" ! $ ("$ $
""!
G
!,B5/
!!$"
C
#1$")#
4!! % #1$")# "" $" $! , /
" ""!"$
")56!,B&!T'="&5%"N/
"'
'=
9 ' K ",!"/ K 4" ,/
1!!"$
= K ,=/
1!!"$"
!
K .,0/
1! !"$
1
*&!"" ,FPJPJLHPP/
* *&!"!!*,FPJPJL*HPP/
4 4&,FPJPJPL/
U *
,"!/
The % sign marks the spot where the number is inserted within the text
Formatting elements (defines the format of the number
The name of the variable whose value is to be displayed
F
" !" " & $ $! T , T "" $ $ "/
!"
$& "")
!,B&6T&T&T65%.
!./
L
& &U!" !"$ ! "
" $ !" !"%
$ "!"
U!$
!",&%$/
")*,)*$") 1
!""$&
!",&%$%B"!5%B!$G5%5!$M"/
9& $"""$!)
/$)"%<)%
")5"""/- "/$
J
$"1!$#$
!!"
$") * 1!$#$
1","/ '
+ ''
+
+' '
$"* 1!$#$
2
U
"
$
;"" $
") )
9
7 1 1!$#$
" H
."
) I
10
+
4'!
!
1&'!
G!
• !" !"• 9!$!$• !!" % """
*&!"
!",&%$/ """! )
!",&%$%55/ ""!
!",&%$%5''$5/ $"" "!
!",&%$%5I5/ !) ,I/7" !
!",&%$%55/ "!)
)
&1) ("&1) *
=P
4!!!""
!$G +! "!$
M"
9,
" /
1!
"
!,"P/
)1<,)</
1!<)
!
)*.",)"/
1!")%
""
"")
."!"%$!
)4.",
)"/
1!"
""""
)
."!
"%$!
-*" 1
5*-*" *-*
"!"&& &""$""
&"",B&5/
$"",B&5/
)$)*!((""!"
",B&5/
)5)!(("
&!"!!
',&%$/&
&,&%$%5&5/
!& !$!$
&,B&5/
9 &% 4 9 !
!!&!"
=
())$"%))5)
& ," !/ !" &!" ""
E"!9 ? & &!A
$ % $!"!$G!$M"
""
$#$ ##!)
V "
V "$"
V G"
VWX 1!
V<W<X 1!<
U) " $ $! 0 4
" "% "" " . 14
!!%"""!!*&!"
!)
$")$"%
7
*))
V"! αV βV γV θV! π
V σV ΦV+" ∆VU ΓV ΛV> ΩV1 Σ
4 & !"$ $ &""% $""% "% &
" $ !" !$G
!$M"""
&$&
&,&%$%B&5%!$G%!$M"/
!$G!M"
$
==
!$G $! % !$M" $!
!!$"!!$" "
!$G +! "!$
M"
2 1!
&
1",/
+"P
4" 1!"
"$"
G"%"
+""
4G 1!
$
""$
41< 1!< 1",!/
+"P
49 1!
%"%"
+""
." 1!"
&
."!
,=/
)'" 1!
)"
,"/
."!
,=/
*." 1!"
"&
&
."!
,=/
9 1!
"&
&
1",!/+"P
5
9 !",&%$/ &% & "
&""&
$ &!!
&
&,R&%&&%$%$&S/ 1"&$&
R&%&&%$%$&S
&0" 1"&
&0 1&0
& 1&"
$
"!"
=
2"
1!$*!$")$#$!%1
$!!"0!"!"
& " , & "/% '" ,
&"%"/%&!"!"
1"$,&%$/ "$& ",P/"$&
"&&
1"&,&%$/ "$& ",P/"&&
"$&
",&%$/ "&$ ",P/&
",%%B"!5/
"!"!,/,
/
*)$1*1*)
1"!!"$!$!
!!"
!",&%$%%%%%/
4&!"%
!",&%$%B'5%%%B''5%%%B5/
"!
>,&$/!" """ !",/!"
"!",/!"
"
=:
6")!)$"$"$#"!&#$"$-*
!' " ;$ $ "$) ",5 $$
$/
((" !$1)$" 5(1*
"1 &!"
@@K
:C
! π,:J=CLJFJ6/ @@!
K:C
! ""<"
@@!
K===P:'PC
(!$ @@K
+0,'/
1 −
,/"$"
@@
KPHPPPP
# 1"?A+0,'/
1 −
G!?A
@@#K
PHPPPP
GG GG
( ""
@@PP
9+$<
K
GG
" 2"""$ @@"@@
."&$< 2"$"&$<$
+!"$"""""$
$
+!"$"""$$< $"
=
$)()$!1)$"$)!*, ""/
""""%
$&, $ /
!$1)$" 5(1*
H H
' 1 '
I "!" I
,/+
Q 2! Q,K=/
0,&/ 10 @@0,L/
K
J
&!,&/ *&!",&/ @@&!,/
K
:L:=
,&/ "","/
@@,'=:/K
=:
",&/ G"""
"
@@",PPP/K
CJPFL
"P,&/ P"
"P
@@"P,PPP/
K
",&/ "&8K,&/,&'/,&'=/6
,&!/
@@",/K
=P
=C
$%"()$!*#"!)$"
!$1)$" 5(1*
! "π :J=CLJFJ
,&/ 1"&
,&/
@@,!C/
KPPPP
,&/ ."&,&/
@@,!C/K
PLCCP
,&/ "&,&/
@@,!C/K
PFF:
,&/ ,!"/
"&,&/
@@,!C/
K=PPPP
,&/ 1,!"/"&
,&/
@@,!C/K
:F
,&/ .,!"
/"&,&/
@@,!C/
KF=
,&/ , "
&Y/
2+G1
@@,P/
KP=C
,&/ ,
"&Y/
2+G1
@@,P/
KP:F=
,&/ ,
"&Y/ 2+G1
@@,P/
KP:CC
=F
1-*$!)$%"()$!*#"!)$"
!$1)$" 5(1*
,&/ E$!",""$
/
2e - e
(x) sinh-xx
=
@@,/
K
F=
,&/ E$!",""$ /
2e e
(x) cosh-xx +=
@@,/K
:@@
,&/ E$!",""$
/
x-x
-xx
e ee e
(x) tanh+−=
@@,/
KPFCC
"$!" %
$&,&/%,&/,&/
U!$!""
=L
()#"!)$"
!$1)$" 5(1*
,&/ 2
@@,F/
K
&,&/ 2 <,
/
@@&,/
K
=
",&/ 2 $,!/
@@",/K
",&/ 2
$,
/
@@",/
K
=@@",'J:/
K'
,&%$/ 2&
$$
@@,%/K
,&/ 12?A&@P
2?'A&ZP
2?PA&KP
@@,/K
@@,P/
KP
@@,'CLJP/
K'
$1* #()
((" !$1)$" 5(1*
4&! : @@=JPF
=J
"!"
PP ≤ ≤PPP> !"$
K
::=LC
" 4&! :
"!"
PP ≤ ≤PP> !"$
@@=JPF
K
::=LF:=LF:
1 :"!"
@@=JPFK
::=JHPP
" 1 "!"
@@=JPFK
::=LF:=LF:HPP
'&
"!
@@=JPF
K::=J
" '&"!
@@=JPFK
::=LF:=LF:
") " @@=JPF
K::
! *"!$"
"" "
!"$
" !$"
,>!!&&/
P
$*)$"#"!)$"#"*$"%
$"'"$
!$1)$" 5(1*
",/ 2
"
@@KRJ=:SO
@@",/
K:
<,/ 2 RS%
<$
@@KRCOLP=S
KC
LP=
@@<,/K=
!,%%/
2&RS "
"
3*
@@KRCOLP=SK
CLP=
@@!,%%=/K
PLC
=
,/ 9%
0& """
@@KRF:=SO
@@K,/KFPP
P:PPP=
,/ 9RS&%
""RS
@@KR=O:COFLJS
K=:C
FLJ
@@K,/
K
J
.&& )$")%")"1*)$",81*)$) clc; N = 1024; n = 0:1:N-1; a = 1; f = 1; y = a*sin(2*pi*f*n/N); figure(1); subplot(2,1,1); plot(n,y); ylim([(min(y)+min(y)*0.1) (max(y)+max(y)*0.1)]); xlim([0 N]); xlabel('sample (n)'); ylabel('amplitude x(n)'); subplot(2,1,2); z = abs(fft(y,N))*2/N; stem(n,z); xlim([0 (N/16)-1]); ylim([-max(z)*0.05 (max(z)+max(z)*0.1)]); xlabel('frequency(Hz)'); ylabel('magnitude');
0 100 200 300 400 500 600 700 800 900 1000-1
-0.5
0
0.5
1
sample (n)
ampl
itude
x(t)
0 10 20 30 40 50 600
0.2
0.4
0.6
0.8
1
frequency(Hz)
mag
nitu
de
=
0 100 200 300 400 500 600 700 800 900 1000-0.2
-0.1
0
0.1
0.2
sample (n)
ampl
itude
x(n
)
0 10 20 30 40 50 600
0.05
0.1
0.15
0.2
frequency(Hz)
mag
nitu
de
)$")1("$!" ")$3, clc; N = 1024; n = 0:1:N-1; Amax = 1; A = Amax; F = 3; fmax = 512; signal = zeros(1,N); for f = F:2*F:fmax A = (Amax*2)/(f*pi); signal = signal + A*sin(2*pi*f*n/N); end y = signal; fig=figure(1); set(fig,'Position',[100 100 800 600]); set(fig,'Color',[1 1 1]); subplot(2,1,1); plot(n,y); ylim([(min(y)+min(y)*0.1) (max(y)+max(y)*0.1)]); xlim([0 N]); xlabel('sample (n)'); ylabel('amplitude x(n)'); subplot(2,1,2); z = abs(fft(y,N))*2/N; stem(n,z); xlim([0 (N/16)-1]); ylim([-max(z)*0.05 (max(z)+max(z)*0.1)]); xlabel('frequency(Hz)'); ylabel('magnitude');
$(1*"")$!$)1"&*))
!"! "" 2. !
""$ $%&!"!
! 75"$8
% *************************************** L = 47e-3; %Use milli Henry range C = 0.1e-6; %Use sub micro Farad range R = 100; %Can be 100 Ohms or more V = 5; % *************************************** clc; fr = 1/(2*pi*sqrt(L*C)); f = 0:10:fr*3; xl = 2*pi*f*L; xc = 1./(2*pi*f*C); q = (1/R)*sqrt(L/C); fr = 1/(2*pi*sqrt(L*C)); z = sqrt((R^2)+ (xl - xc).^2); i = V./z; ph = atan((xl-xc)/R); figure(1); clf; hold off plot(f, R*i,'color','blue'); %VR hold on plot(f,xl.*i,'color','red'); %VL plot(f,xc.*i,'color','green'); %VC text(3*fr/4,max(xc.*i)+ max(xc.*i)*0.1,['fr = ' num2str(fr)]); text(3*2*fr/4,max(xc.*i)+ max(xc.*i)*0.1,['i(max) = ' num2str(max(i))]); text(3*3*fr/4,max(xc.*i)+ max(xc.*i)*0.1,['Q = ' num2str(q)]); xlim([0 fr*3]); ylim([0 max(xc.*i)+ max(xc.*i)*0.2]); xlabel('Frequency (Hz)'); ylabel('Volts'); figure(2) plot(f,ph*180/pi,'color','cyan'); %phase xlim([0 fr*3]); "!"
0 1000 2000 3000 4000 5000 60000
5
10
15
20
25
30
35
40fr = 2321.5134 i(max) = 0.049998 Q = 6.8557
Frequency (Hz)
Vol
ts
0 1000 2000 3000 4000 5000 6000-100
-80
-60
-40
-20
0
20
40
60
80
100
:
*!*)$"%&%(
!!"& ""B"5 )
!"+4 B"5 %Discrete Fourier Transform Routine. clf format long figure(1); %------------------------------- N = 32; n = 0:1:N; Sig_Freq = 3; %-x(n) Signal frequency-- signal=sin(2*pi*n*Sig_Freq/N)+0.2*sin(2*pi*n*Sig_Freq*4/N); %-plot Signal x(n)-------------- subplot(2,1,1); plot (signal,'-g'); hold on; stem (signal); xlim([1 32]); %------------------------------- m=0; for I = 1:N+1 %-Cos+jSin---------------------- real = cos(2*pi*n*m/N); imaj = sin(2*pi*n*m/N); sig_real=signal.*real; sig_imaj=signal.*imaj; %-normalise signals------------- sig1 =sum(sig_real)*2/N; sig2 =sum(sig_imaj)*2/N; %-square signals---------------- sigdft =(sig1)*(sig1); sigdft2=(sig2)*(sig2); %-square root sum of signals---- sig3 = (sigdft+sigdft2)^0.5; %-plot magnitude of harmonics--- subplot (2,1,2); hold on; stem (m,sig3);
m = m+1; end; xlim([0 33]);
5 10 15 20 25 30-1.5
-1
-0.5
0
0.5
1
1.5
0 5 10 15 20 25 300
0.5
1
1.5
0 100 200 300 400 500 600 700 800 900 1000-1
-0.5
0
0.5
1
time (t)
ampl
itude
x(t)
0 100 200 300 400 500 600 700 800 900 1000-1
-0.5
0
0.5
1
time (t)
ampl
itude
x(t)
0 5 10 15 20 25 300
0.5
1
frequency(Hz)
mag
nitu
de
3, ")$)$"
!$0
E%!"& !!"
clc; clear all; N = 1024; n = 0:1:N-1; fmax = 1; nH = 14; fig = figure(1); clf; set(fig,'Position',[100 100 800 600]); set(fig,'Color',[1 1 1]); subplot(3,1,1); hold on; y=0; for f = 1:2:nH; plot(sin(2*pi*f*n/N)/f, 'color', [1-f/nH 0.5 f/nH]); y = y + (sin(2*pi*f*n/N)/f); end ylim([-1.1 1.1]); xlim([0 N]); xlabel('time (t)'); ylabel('amplitude x(t)'); Box on; subplot(3,1,2); plot(n,y); ylim([(min(y)+min(y)*0.1) (max(y)+max(y)*0.1)]); xlim([0 N]); xlabel('time (t)'); ylabel('amplitude x(t)'); subplot(3,1,3); z = abs(fft(y,N))*2/N; stem(n,z,'-r'); ylim([-max(z)*0.05 (max(z)+max(z)*0.1)]); xlim([0 (N/32)-1]); xlabel('frequency(Hz)'); ylabel('magnitude');