Uas Roni Kurniawan Fft Dan Dekomposisi.docx

NAMA : RONI KURNIAWAN NPM

: 41187003170030

UAS

: KOMPUTASI NUMERIK

SOAL

: JAWABAN NOMOR 2 DAN 1

JAWABAN SOAL NO 2 PLOTING SIGNAL

AMPLITUDE SPECTRUM X(t) DAN S(t)

SYNTAXS Fs = 1000; % Sampling frequency T = 1/Fs; % Sampling period L = 1000; % Length of signal t = (0:L-1)*T; % Time vector s=100; %INTI JAWABAN PERUBAHAN SYANTAXS S = 1*sin(2*pi*50*t)+2*sin(2*pi*100*t)+3*sin(2*pi*150*t)+4*sin(2*pi*200*t)+4.5*si n(2*pi*250*t)+5*sin(2*pi*300*t)+5.5*sin(2*pi*350*t)+6*sin(2*pi*400*t)+6.5*sin (2*pi*450*t); X = S + 10*randn(size(t)); N = 10*randn(size(t)); figure(4) plot(1000*t(1:s),S(1:s)) title('Original signals') xlabel('t(milis)') ylabel('s(t)') X=S+2*randn(size(t)); figure(5) plot(1000*t(1:s),N(1:s)) title('nois signals') xlabel('t(milis)') ylabel('s(t)') X=S+2*randn(size(t)); figure(1) plot(1000*t(1:s),X(1:s)) title('Signal Corrupted with Zero-Mean Random Noise') xlabel('t (milliseconds)') ylabel('X(t)') Y = fft(X); P2 = abs(Y/L); P1 = P2(1:L/2+1); P1(2:end-1) = 2*P1(2:end-1); f = Fs*(0:(L/2))/L; figure(2) plot(f,P1) title('Single-Sided Amplitude Spectrum of X(t)') xlabel('f (Hz)') ylabel('|P1(f)|') Y = fft(S); P2 = abs(Y/L); P1 = P2(1:L/2+1); P1(2:end-1) = 2*P1(2:end-1); figure(3)

plot(f,P1) title('Single-Sided Amplitude Spectrum of S(t)') xlabel('f (Hz)') ylabel('|P1(f)|')

JAWABAN SOAL NO 1 Matrix hasildekomposisiterkeciladalah xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx NAMA : RONI KURNIAWAN NPM

: 41187003170030

UAS

: KOMPUTASI NUMERIK

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx A=U x S x V NILAI TERKECIL YANG MASIH DAPAT MENGINFORMASIKAN NILAI[A] NILAI AWAL A=[6,6]

A=

17 18

5

5 45

1

42 28 30 15 115

3

10 10 10 21 51

2

28

5 65 39 132

5

24 26 45 21 116

4

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx A=U x S x V U=U(:,:)

A

17.0000 18.0000 5.0000 5.0000 45.0000 1.0000 42.0000 28.0000 30.0000 15.0000 115.0000 3.0000 10.0000 10.0000 10.0000 21.0000 51.0000 2.0000 28.0000 5.0000 65.0000 39.0000 132.0000 5.0000 24.0000 26.0000 45.0000 21.0000 116.0000 4.0000

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx A=U x S x V U=U(:,1:5)

A=

17.0000 18.0000 5.0000 5.0000 45.0000 1.0000 42.0000 28.0000 30.0000 15.0000 115.0000 3.0000 10.0000 10.0000 10.0000 21.0000 51.0000 2.0000 28.0000 5.0000 65.0000 39.0000 132.0000 5.0000 24.0000 26.0000 45.0000 21.0000 116.0000 4.0000

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx A=U x S x V U=U(:,1:3)

A=

16.8091 17.7625 4.7985 4.7971 45.2056 1.0673 42.0809 28.1007 30.0854 15.0860 114.9128 2.9715 10.0532 10.0662 10.0562 21.0566 50.9427 1.9812 27.9458 4.9325 64.9428 38.9424 132.0584 5.0191 24.0326 26.0405 45.0344 21.0346 115.9649 3.9885

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx A=U x S x V U=U(:,1:2)

A=

17.1086 17.5301 4.7263 4.8353 45.1861 1.0554 37.7113 31.4911 31.1382 14.5287 115.1974 3.1455 10.5830 9.6552 9.9286 21.1242 50.9081 1.9601 25.1887 7.0717 65.6070 38.5907 132.2380 5.1289 31.1968 20.4818 43.3083 21.9484 115.4983 3.7032

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx A=U x S x V U=U(:,1:2) Hasil compress terkecilberdasaekan matrix A

A=

17.5401 17.4388 5.9580 3.1170 45.0105 1.0006 37.1250 31.6151 29.4646 16.8635 115.4360 3.2200 13.2862 9.0835 17.6447 10.3598 49.8079 1.6167 25.0770 7.0954 65.2880 39.0357 132.2835 5.1431 30.5782 20.6126 41.5427 24.4115 115.7501 3.7818

>> SYNTAXS clc; clear; disp ('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx') disp ('NAMA : RONI KURNIAWAN') disp ('NPM : 41187003170030') disp ('MATA KULIAH: KOMPUTASI NUMERIK') disp ('TUGAS UAS : TAKE HOME') disp ('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx') disp ('A=U x S x V') disp ('NILAI TERKECIL YANG MASIH DAPAT MENGINFORMASIKAN NILAI[A]') disp ('NILAI AWAL A=[6,6]') A=[17 18 5 5 45 1;42 28 30 15 115 3;10 10 10 21 51 2;28 5 65 39 132 5;24 26 45 21 116 4] [U,S,V]=svd(A); VT=V'; disp ('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx') disp ('A=U x S x V') disp ('U=U(:,:)') A=U*S*VT U=U(:,1:5); S=S(1:5,1:5); VT=VT(1:5,1:6); disp ('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx') disp ('A=U x S x V') disp ('U=U(:,1:5)') A=U*S*VT U=U(:,1:4); S=S(1:4,1:4); VT=VT(1:4,1:6);

disp ('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx') disp ('A=U x S x V') disp ('U=U(:,1:3)') A=U*S*VT U=U(:,1:3); S=S(1:3,1:3); VT=VT(1:3,1:6); disp ('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx') disp ('A=U x S x V') disp ('U=U(:,1:2)') A=U*S*VT U=U(:,1:2); S=S(1:2,1:2); VT=VT(1:2,1:6); disp ('xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxx') disp ('A=U x S x V') disp ('U=U(:,1:2)') A=U*S*VT