From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001
From: priyanka
Date: Wed, 24 Jun 2015 15:03:17 +0530
Subject: initial commit / add all books

---
 1202/CH17/EX17.1/17_1.sce  | 168 +++++++++++++++++++++++++++++++++++++++++++++
 1202/CH17/EX17.1/17_1a.png | Bin 0 -> 15493 bytes
 1202/CH17/EX17.1/17_1b.png | Bin 0 -> 16771 bytes
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 create mode 100755 1202/CH17/EX17.1/17_1.sce
 create mode 100755 1202/CH17/EX17.1/17_1a.png
 create mode 100755 1202/CH17/EX17.1/17_1b.png

(limited to '1202/CH17/EX17.1')

diff --git a/1202/CH17/EX17.1/17_1.sce b/1202/CH17/EX17.1/17_1.sce
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+clear
+clc
+
+//Example 17.1
+disp('Example 17.1')
+
+//In this solution we assume that a sampled signal is given to us at a very fast
+//sampling rate and then we resample from it for our computations
+//This depicts how data is in practical situations. 
+//Since computers are digital data is always discrete
+//A more kiddish way of writing this code would have been to make a function
+//which takes time as input and gives signal value as output ie generate a 
+//continuous signal definition. Then no matter what our sampling time is 
+//we can always get the desired values by calling the function say func(Ts*k)
+//where Ts denotes sampling time and k is the index no.(ie deltaT*k)
+//In principle this will also work fine and will reduce the length of the code
+//but this will not lead to learning for coding in practical situations
+
+Ts=0.001 //sampling time for analog
+t=0:Ts:5;
+n=length(t);
+square_base=0.5*squarewave((t-0.5)*2*%pi/3)+0.5;
+ym=square_base+0.25*sin(t*2*%pi*9);
+subplot(2,2,1)
+plot(t,[square_base' ym'])
+xtitle('Fig 17.6 (a)','Time(min)','Output');
+ 
+
+//Analog Filter
+tauf1=0.1;tauf2=0.4;
+s=%s;
+F1=syslin('c',1/(tauf1*s+1));
+F2=syslin('c',1/(tauf2*s+1));
+yf1=csim(ym,t,F1);
+yf2=csim(ym,t,F2);
+subplot(2,2,2);
+plot(t,[yf1' yf2' square_base'])
+legend("$\tau_F=0.1\ min$","$\tau_F=0.4\ min$",position=3);
+xtitle('Fig 17.6 (b)','Time(min)','Output');
+ 
+ //Note that analog filtering can also be achieved by perfect sampling in EWMA digital filter
+ //Since Exponentially weighted digital filter is an exact discretization of analog
+ //filter if we take Ts=0.001 ie the perfect sampling of data we get identical answers
+ //from digital or analog filter. You can try this by chaning Ts1 or Ts2 to 0.001
+
+//Digital filtering
+Ts1=0.05;Ts2=0.1;
+alpha1=exp(-Ts1/tauf1);
+alpha2=exp(-Ts2/tauf1);
+samples1=1:Ts1/Ts:n;
+samples2=1:Ts2/Ts:n;
+yf1=zeros(length(samples1),1);
+yf2=zeros(length(samples2),1);
+
+for k=1:length(samples1)-1
+    yf1(k+1)=alpha1*yf1(k)+(1-alpha1)*ym(samples1(k));
+end
+for k=1:length(samples2)-1
+    yf2(k+1)=alpha2*yf2(k)+(1-alpha2)*ym(samples2(k));
+end
+
+subplot(2,2,3);
+plot(t(samples1)',[yf1],color='blue');
+plot(t(samples2)',yf2,color='red');
+plot(t,square_base,color='black');
+legend("$\Delta t=0.05 \ min$","$\Delta t=0.1\  min$",position=3);
+xtitle('Fig 17.6 (c)','Time(min)','Output');
+ 
+
+
+//Moving Filter
+N1=3;
+N2=7;
+yf1=zeros(1,length(samples1))
+yf2=zeros(1,length(samples1))
+for k=N1+1:length(samples1)
+    yf1(k)=yf1(k-1)+1/N1*(ym(samples1(k))-ym(samples1(k-N1)));
+end
+for k=N2+1:length(samples1)
+    yf2(k)=yf2(k-1)+1/N2*(ym(samples1(k))-ym(samples1(k-N2)));
+end
+//for k=N2+1:n
+//    yf2(k)=yf2(k-1)+1/N2*(ym(k)-ym(k-N2));
+//end
+subplot(2,2,4);
+plot(t(samples1),[yf1' yf2'])
+plot(t,square_base,color='black');
+legend("$N^*=3$","$N^*=7$",position=4);
+xtitle('Fig 17.6 (d)','Time(min)','Output');
+ 
+
+
+//Now for the gaussian noise
+scf();
+Ts=0.001 //sampling time for analog
+t=0:Ts:5;
+n=length(t);
+square_base=0.5*squarewave((t-0.5)*2*%pi/3)+0.5;
+ym=square_base+grand(1,length(t),"nor", 0, sqrt(0.1));//0.1 is for setting variance=0.1
+subplot(2,2,1)
+plot(t,[square_base' ym'])
+xtitle('Fig 17.6 (a)','Time(min)','Output');
+ 
+
+//Analog Filter
+tauf1=0.1;tauf2=0.4;
+s=%s;
+F1=syslin('c',1/(tauf1*s+1));
+F2=syslin('c',1/(tauf2*s+1));
+yf1=csim(ym,t,F1);
+yf2=csim(ym,t,F2);
+subplot(2,2,2);
+plot(t,[yf1' yf2' square_base'])
+legend("$\tau_F=0.1\ min$","$\tau_F=0.4\ min$",position=3);
+xtitle('Fig 17.6 (b)','Time(min)','Output');
+ 
+
+//Digital filtering
+Ts1=0.05;Ts2=0.1;
+alpha1=exp(-Ts1/tauf1);
+alpha2=exp(-Ts2/tauf1);
+samples1=1:Ts1/Ts:n;
+samples2=1:Ts2/Ts:n;
+yf1=zeros(length(samples1),1);
+yf2=zeros(length(samples2),1);
+
+for k=1:length(samples1)-1
+    yf1(k+1)=alpha1*yf1(k)+(1-alpha1)*ym(samples1(k));
+end
+for k=1:length(samples2)-1
+    yf2(k+1)=alpha2*yf2(k)+(1-alpha2)*ym(samples2(k));
+end
+
+subplot(2,2,3);
+plot(t(samples1)',[yf1],color='blue');
+plot(t(samples2)',yf2,color='red');
+plot(t,square_base,color='black');
+legend("$\Delta t=0.05 \ min$","$\Delta t=0.1\  min$",position=3);
+xtitle('Fig 17.6 (c)','Time(min)','Output');
+ 
+
+
+//Moving Filter
+N1=3;
+N2=7;
+yf1=zeros(1,length(samples1))
+yf2=zeros(1,length(samples1))
+for k=N1+1:length(samples1)
+    yf1(k)=yf1(k-1)+1/N1*(ym(samples1(k))-ym(samples1(k-N1)));
+end
+for k=N2+1:length(samples1)
+    yf2(k)=yf2(k-1)+1/N2*(ym(samples1(k))-ym(samples1(k-N2)));
+end
+//for k=N2+1:n
+//    yf2(k)=yf2(k-1)+1/N2*(ym(k)-ym(k-N2));
+//end
+subplot(2,2,4);
+plot(t(samples1),[yf1' yf2'])
+plot(t,square_base,color='black');
+legend("$N^*=3$","$N^*=7$",position=4);
+xtitle('Fig 17.6 (d)','Time(min)','Output');
+ 
+
+
+mprintf("Please note that for guassian noise\n results...
+    will be different from book owing to randomness\n...
+    we do not know the seed for the random noise")
+
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cgit