Assignment :1. 1 Arithmetic Operations : Compute the following quantities ) -1. and compare with (1-

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1 1 Arithmetic Operations : Compute the following quantities and compare with ( ) -1 Assignment : The square root x can be calculated as sqrt(x) or 3 ( 5+1) 2 x^0.5. Area=πr 2 with r=π ⅓ 1 (π is pi in Matlab) Command Result 2^5/{2^5-1) 3*(sqrt(5)-1)/(sqrt(5)+1^2-1 area=pi*(pi^(1/3)-1)^ Exponential and logarithms: The mathematical quantities ex, lnx, and logx are calculated with exp(x), log(x), and log10(x), respectively. Calculate the following quantities. e x, ln(e 3 ), log10(e 3 ), and log 10 (10 5 ). e π 163. Solve 3 x =17 for x and check the result. ( The solution is x=(ln17)/(ln3). You can verify the result by direct substitution.). Command Result exp(3) log(exp(3)) log10(exp(3)) log10(10^5)) exp(pi*sqrt(163)) x=log(17)/log(3) e nd Semister M. Tech in VLSI & Microelectronics Page :1

2 3. Trigonometry: The basic MATLAB trigonometric functions are sin, cos, tan, cot, sec, and csc. The inverses, e.g., arcsin, arctan etc. The same is true for hyperbolic functions. The inverse function atan2 takes 2 arguments, y and x, and gives the four -quardrant inverse tangent. The argument of these functions must be in radians. Calculate the followings. Sin π/6, cos π and tan π/2. Sin 2 π/6 + cos 2 π/6. (Typing sin^2(x) for sin2x will produce an error.) y=cosh2x sinh2x, with x=32π. Command sin(pi/6) cos(pi) tan(pi/2) (sin(pi/6))^2+(cos(pi/6))^2 x=32*pi;y=(cosh(x)^2-(sinh(x))^2 Result e Complex Numbers: Matlab recognizes the letters i and j as imaginery number (-1). A complex number 2+5i may be input as 2+5i or 2+5*i in MATLAB. The former case is always interpreted as a complex number whereas the later case is taken as complex only if i had not been assigned any local value. The same is true for j. This kind of context dependence, for better or worse, pervades MATLAB. Compute the following quantities. (1+3i)/(1-3i). Can you check the result by Hand Calculation? e i π /4. Check the Euler's formula e ix = cos x + isinx by computing the right hand side, too. Executes the commands exp(pi/2*i) and exp(pi/2i). Can you explain the difference between the two results. Command (1+3i)/(1-3i) exp(i*pi/4) exp(pi/2*i) exp(pi/2i) Result i i i i 2 nd Semister M. Tech in VLSI & Microelectronics Page :2

3 Assignment : 2 * Check the output of the following program segment Sl No Program Output 1.) x=[1 2 3]; subplot(3,1,1); stem(x); y=[1 2 3]; subplot(3,1,2); stem (y); z=x.*y; subplot (3,1,3); stem (z); 2.) a=[1 2 3; 4 5 6; 7 8 9]; b=a(2,3); stem (b); 3.) a=[1 2 3; 4 5 6; 7 8 9]; b= a(1,:); subplot (2,1,1); stem(x); 4.) a=[4 7 9; 2 3 1; 4 4 5]; b=a(2,:); stem (b); 2 nd Semister M. Tech in VLSI & Microelectronics Page :3

4 Sl No Program Output 5). x=[1 2 3]; subplot(3,1,1); stem (x); ylabel ('x'); xlabel('n'); y=[1 2 3;4 5 6; 7 8 9]; subplot(3,1,2); stem (y); xlabel ('n'); ylabel('y'); z=x*y; subplot(3,1,3); stem (z); xlabel ('n'); ylabel('z'); 6). x=[1 2 3;4 5 6; 7 8 9]; y= x^-1; stem (y); 7) x=0:0.01:20; y=sin(x); stem (y); 2 nd Semister M. Tech in VLSI & Microelectronics Page :4

5 Sl No Program Output 8) x=0:pi/20:4*pi; y=sin(x); stem(x,y); 9) x=input('enter the value of x'); y=2^2 + log(pi)*sin(x); disp('answer'); disp(y); plot(x,y); stem (x,y); 10) x=linspace(0,10,8); y=sin(x); plot(x,y); disp(y); Value given 5 11) t=linspace(0,10,5); x=t.*sin(t); stem (t,x); disp(x); 2 nd Semister M. Tech in VLSI & Microelectronics Page :5

6 Sl No Program Output 12) t=linspace(0,20,10); y=(t-1)./(t+1); stem(t,y); 13) t=linspace(0,2*pi,5); x=2*cos(t); y=2*sin(t); n=x.^2+y.^2).^0.5; stem (t,n); 14) a=[ ]; b=exp(a); plot(a,b); 2 nd Semister M. Tech in VLSI & Microelectronics Page :6

7 Sl No Program Output 15) x=0:10:20; y=exp(-0.4*x).*sin(x); plot(x,y); grid; 16) x=linspace(-10,10,21); y=exp(x); stem(x,y); 17) n=input('enter the Length'); i=-n:2:n; y=exp(i); stem(i,y); 2 nd Semister M. Tech in VLSI & Microelectronics Page :7

8 Sl No Program Output 18) n=('enter the length of exp sequence'); i=0:n; m=input('enter the exp value'); y=exp(m*i); plot(i,y); xlabel('n'); ylabel('y'); 19) x=0:1:14; y=[ ]; stem(x,y,'*'); ## ('Length of the matrics should be match'); 20) n=8; i=0:1:n-1; y=i; stem(i,y); 21) n=('enter Seq Length'); m=('enter Ramp Slope'); i=0:n; grid on; y=m*i; stem(i,y); xlabel('n'); ylabel('n'); 2 nd Semister M. Tech in VLSI & Microelectronics Page :8

9 Assignment :3 1. A simple sine plot: Plot y=sinx, 0 x 2π, taking 100 linearly spaced points in the given interval. Label the axes and put 'Plot created by yourname' in the title. x=linspace (0,2*pi, 100); plot (x,sin(x)) xlabel ('x'), ylabel ('sin(x)'); title ('Plot created by Kalyan'); 2. Line styles: Make the same plot as above, but rather than displaying the graph as a curve, show the unconnected data points. To display the data points with small circles, use plot(x,y.'o'). [Hint: You may peep into section 6.1 on page 145 if you wish.] Now combine the two plots with the command plot (x,y,x,y,'o') to show the line through the data points as well as the distinct data points. plot (x,sin(x), x, sin(x),'o') xlabel ('x'), ylabel ('sin(x)') 2 nd Semister M. Tech in VLSI & Microelectronics Page :9

10 3. An exponentially decaying sine plot: Plot y=e -0.4x sinx, 0 x 4π, taking 10, 50 and 100 points in the interval. x=linspace (0,4*pi*10); %with 10 points y=exp(-.4*x).*sin(x); plot(x,y) x=linspace(0,4*pi,50); % with 50 points y=exp(-.4*x).*sin(x); plot(x,y) x=linspace(0,4*pi,100); %with100 points y=exp(-.4*x).*sin(x); plot (x,y) 4. Space curve: Use the command plot3(x,y,z) to plot the circular helix x(t)=sin t, y(t)=cost, z(t) = t, 0 t 20 t=linspace(0,20,100); plot3(sin(t), cos(t),t) 5. Log scale plots: The plot commands semilogx, semilogy and loglog, plot the x-values, the y-values, and both x- and y-values on a log- scale respectively. Create a vector x=0:10:1000. Plot x vs. x 3 using the three log scale plot commands. [Hint: First, compute y=x.^3 and then use semilogx (x,y) etc.] x=0:10:1000; y=x.^3; semilogx(x,y) semilogy(x,y) loglog(x,y) 2 nd Semister M. Tech in VLSI & Microelectronics Page :10

11 Assignment : 4 Write a Program to show the output response of Impulse Response. N=21; n=-10:10; y=[zeros(1,10),ones(1,1),zeros(1,10)]; plot (x,y); stem (x,y); Write a Program to show the Ramp function in Matlab. n=input ('Enter value'); m= input ('Enter ramp slope'); i=0:n; y=i*m; stem(i,y); Write a Program to show folding in Matlab n=0:.1:.2; x=[1 2 3]; subplot (3,1,1); stem(n,x); n=-n; subplot(3,1,2); stem(n,x); Write a Program to show Shifting in Matlab. n=0:.1:.2; x=[5 8 2]; subplot (3,1,1); stem(n,x); n=n+2; y=x; subplot(3,1,2); stem(n,x); 2 nd Semister M. Tech in VLSI & Microelectronics Page :11

12 Write a Program to show Fliping in Matlab. n=0:.1:.2; x=[3 8 1]; subplot (3,1,1); stem(n,x); y=fliplr(x); subplot(3,1,2); stem(n,y); Write a Program to show Element to element multiplication x=[ ]; subplot(3,1,1); stem(x); grid on; y=[4 40 7]; subplot (3,1,2); stem(y); grid on; z=x.*y; subplot (3,1,3); stem(z); grid on; Write a Program to show Convolution x=[1,2,1,1]; n1=length(n); subplot(3,1,1); stem(x); h=[1,1,1,1]; n2=length(h); subplot(3,1,2); stem (h); n=0:n1+n2-2; y=conv(x,h); subplot(3,1,3) ]stem(x,y); disp(y); disp('answer'); 2 nd Semister M. Tech in VLSI & Microelectronics Page :12