By E.S. Gopi


The Algorithms similar to SVD, Eigen decomposition, Gaussian blend version, HMM and so forth. are almost immediately scattered in numerous fields. There continues to be a necessity to assemble all such algorithms for fast reference. additionally there's the necessity to view such algorithms in program perspective. This ebook makes an attempt to meet the above requirement. The algorithms are made transparent utilizing MATLAB courses.


The Algorithms reminiscent of SVD, Eigen decomposition, Gaussian mix version, HMM and so on. are scattered in numerous fields. there's the necessity to acquire all such algorithms for fast reference. additionally there's the necessity to view such algorithms in software viewpoint. set of rules Collections for electronic sign Processing purposes utilizing MATLAB makes an attempt to fulfill the above requirement. additionally the algorithms are made transparent utilizing MATLAB courses.

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The fuzzy base rule is as given in the table 1-1. 2 are assumed as mentioned in the table 1-2. Table 1-2. 2 Figure 1-20. Relationship between crisp value and fuzzy membership for the Input variable X in the example 1. 4 ___________________________________________________________ fuzzygv . m posx=[0 3 5 7 10]; maxx=max(posx); posx=posx/max(posx); posy=[0 20 45 65 100]; maxy=max(posy); posy=posy/max(posy); posz=[0 35 70 90 100]; maxz=max(posz); posz=posz/max(posz); i=posx(1):1/999:posx(2); j=(posx(2)):(1/999):posx(3); k=(posx(3)):(1/999):posx(4); l=(posx(4)):(1/999):posx(5); xsmall=[1/posx(2)*i (-1/(posx(3)-posx(2))*(j-posx(3))) zeros(1,length([k l]))]; xmedium =[zeros(1,length([i])) (1/(posx(3)-posx(2))*(j-posx(2))) (-1/(posx(4)posx(3))*(k-posx(4))) zeros(1,length([l]))]; xlarge=[zeros(1,length([i j])) (1/(posx(4)-posx(3))*(k-posx(3))) (-1/(posx(5)-posx(4))*(lposx(5))) ]; figure plot([i j k l]*maxx,xsmall,':'); hold plot([i j k l]*maxx,xmedium,'-'); plot([i j k l]*maxx,xlarge,'--'); xlabel('crisp value') ylabel('fuzzy value') title('XINPUT') i=posy(1):1/999:posy(2); j=(posy(2)):(1/999):posy(3); k=(posy(3)):(1/999):posy(4); l=(posy(4)):(1/999):posy(5); ysmall=[1/posy(2)*i (-1/(posy(3)-posy(2))*(j-posy(3))) zeros(1,length([k l]))]; 42 Chapter 1 ymedium =[zeros(1,length([i])) (1/(posy(3)-posy(2))*(j-posy(2))) (-1/(posy(4)posy(3))*(k-posy(4))) zeros(1,length([l]))]; ylarge=[zeros(1,length([i j])) (1/(posy(4)-posy(3))*(k-posy(3))) (-1/(posy(5)-posy(4))*(lposy(5))) ]; figure plot([i j k l]*maxy,ysmall,':'); hold plot([i j k l]*maxy,ymedium,'-'); plot([i j k l]*maxy,ylarge,'--'); xlabel('crisp value') ylabel('fuzzy value') title('YINPUT') i=posz(1):1/999:posz(2); j=(posz(2)):(1/999):posz(3); k=(posz(3)):(1/999):posz(4); l=(posz(4)):(1/999):posz(5); zsmall=[1/posz(2)*i (-1/(posz(3)-posz(2))*(j-posz(3))) zeros(1,length([k l]))]; zmedium =[zeros(1,length([i])) (1/(posz(3)-posz(2))*(j-posz(2))) (-1/(posz(4)posz(3))*(k-posz(4))) zeros(1,length([l]))]; zlarge=[zeros(1,length([i j])) (1/(posz(4)-posz(3))*(k-posz(3))) (-1/(posz(5)-posz(4))*(lposz(5))) ]; figure plot([i j k l]*maxz,zsmall,':'); hold plot([i j k l]*maxz,zmedium,'-'); plot([i j k l]*maxz,zlarge,'--'); xlabel('crisp value') ylabel('fuzzy value') title('ZOUTPUT') xinput=[6]; xinput=round(((xinput/maxx)*1000)) yinput=[50]; yinput=round(((yinput/maxy)*1000)) %fuzzy values xfuzzy=[xsmall(xinput) xmedium(xinput) xlarge(xinput)]; yfuzzy=[ysmall(yinput) ymedium(yinput) ylarge(yinput)]; 1.

Suppose if q3 is the lowest among the values in the vector, the number 3 is assigned to the variable u8. This is called one iteration. Step 4: • The updating pheromone matrix for the second iteration is computed as described in the step 2 using the set of orders selected by the five ants in the first iteration. This is called as Updating pheromone matrix (2). • Pheromone matrix used in the 2nd iteration is computed as Pheromone matrix (2) = Pheromone matrix (1) +Updating Pheromone matrix (2) Step 5: Next set of orders selected by the five ants are computed as described in the step 3.

The orders selected by the four ants after 50 Iterations are displayed below. ANT1: ANT2: ANT3: ANT4: 1 1 3 4 2 2 2 2 3 3 7 3 4 4 4 7 5 5 1 1 6 6 6 6 7 7 5 5 8 8 8 8 Note that ANT1 and ANT2 found the best order as expected using Ant colony technique. Initially the cost values are having more changes. After 40th iteration, cost value gradually increases and reaches maximum which is the optimum cost corresponding the optimum order selected using Ant colony technique. 1. *Q(max(i,A(i)),min(i,A(i))); end Chapter 2 PROBABILITY AND RANDOM PROCESS Algorithm Collections 1.

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Algorithm Collections for Digital Signal Processing by E.S. Gopi
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