MATLAB: SIGNAL PROCESSING

Transcription

1 MATLAB: SIGNAL PROCESSING P a g e

2 CONTENT Chapter No. Title Page No. Chapter 1 Introduction 3 Chapter 2 Arithmetic Operations 4-6 Chapter 3 Trigonometric Calculations 7-9 Chapter 4 Matrices Chapter 5 Features of Matrices Chapter 6 2-D Plot Chapter 7 2-D Plot Designing Chapter 8 2-D Plot Fig. & Subplot Chapter 9 3-D Plot Chapter 10 Input Values P a g e

3 CHAPTER 1 INTRODUCTION 1.1 MATLAB an Introduction MATLAB is a language of technical computing. MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and fourth-generation programming language. A proprietary programming language developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, Fortran and Python. In 2004, MATLAB had around one million users across industry and academia. MATLAB users come from various backgrounds of engineering, science, and economics. Millions of engineers and scientists worldwide use MATLAB to analyze and design the systems and products transforming our world. MATLAB is in automobile active safety systems, interplanetary spacecraft, health monitoring devices, smart power grids, and LTE cellular networks. It is used for machine learning, signal processing, image processing, computer vision, communications, computational finance, control design, robotics, and much more. The MATLAB platform is optimized for solving engineering and scientific problems. The matrix-based MATLAB language is the world s most natural way to express computational mathematics. Built-in graphics make it easy to visualize and gain insights from data. A vast library of prebuilt toolboxes lets you get started right away with algorithms essential to your domain. The desktop environment invites experimentation, exploration, and discovery. These MATLAB tools and capabilities are all rigorously tested and designed to work together. MATLAB helps you take your ideas beyond the desktop. You can run your analyses on larger data sets and scale up to clusters and clouds P a g e

4 CHAPTER 2 ARITHMETIC OPERATION Variable Assignment In MATLAB we need to simply assign the variable with the corresponding values and calculate the results. For example let s take a=1 >> a=1 a = 1 For example let s take b=2 >> b=2 b = 2 So we can easily calculate c=a+b >> c=a+b c = 3 Note: we don t need to specify data type or put traditional header files to assign a value to variable in MATLAB. Practice set 1 Question 1: If a=2000, b=3000 find (a^2)+2*a*b+(b^2). Solution : >> a=2000 a = P a g e

5 >> b=3000 b = 3000 >> (a^2)+2*a*b+(b^2) ans = Practice set 2 Question 2: If a= , b=7.14 find c=(a^3)+3*a*b+(b^3). Solution: >> a= a = >> b=7.14 b = >> c=(a^3)+3*a*b+(b^3) c = e P a g e

6 Practice set 3 Question 3: If a=12596, b=9.1463, c=1000 find c=(a+b+c)^3. Solution: >> a=12596 a = >> b= b = >> c=1000 c = 1000 >> c=(a+b+c)^3 c = e+12 Assignments If a= , b= , c= then find 1. d= (a+b)/c 2. e= (a-b)/c 3. f= (a*b)/c 4. g= ((a*b)/c)+( (a+b)/c) P a g e

7 Trigonometric Calculations CHAPTER Trigonometric Calculations In MATLAB we just need to call the name of trigonometric functions and its values will be calculated because of inbuilt toolbox. For example >>sin(0) ans = 0 >>sin(pi/6) ans = >>cos(pi/4) ans = >>tan(pi/4) ans = Practice set 1 Question 1: Find the value of sin(pi/2)+cos(pi/2)+tan(pi/2). Solution : P a g e

8 >>sin(pi/2)+cos(pi/2)+tan(pi/2) ans = e+16 Practice set 2 Question 2: Find the value of sin(pi/2)-cos(pi/4)+tan(pi/2). Solution: >>sin(pi/2)-cos(pi/4)+tan(pi/2) ans = e+16 Practice set 3 Question 3: If a=pi/2, b=pi/4, c=pi/6 find sin(a)+ cos(b)*tan(c). Solution: >> a=pi/2 a = >> b=pi/4 b = >> c=pi/6-8 - P a g e

9 c = >>sin(a)+ cos(b)*tan(c) ans = Assignments If a=pi/6, b=pi/4, c=pi/2 then find 5. d= sin(a+b) 6. e= cos(a-b) 7. f= sin(a+b)+ cos(a-b) 8. g= sin(a)+cos(b)+tan(c) P a g e

10 1.1 Matrix Creation CHAPTER-4 MATRICES In MATLAB it s very easy to create a matrix. Example 1 :We want to create a 2*2 matrix with elements write [2 3; 4 5] then we will >> a=[2 3;4 5] a = Example 2 :We want to create a 3*3 matrix with elements we will write [1 2 3; 4 5 6; 7 8 9] then P a g e >>b=[1 2 3; 4 5 6; 7 8 9] b = Example 3 :We want to create a 3*3 matrix with elements [4 2 5; 4 8 6; 7 8 7] then we will write >>c=[4 2 5; 4 8 6; 7 8 7] c = Matrix Arithmetic We can do addition, subtraction, multiplication operations for the matrices. Example 1 : Create two matrices of 2*2 with elements a=[2 3; 4 5] and b= [3 5; 6 7], add them and find the value of c=a+b. >> a=[2 3; 4 5]

11 a = >> b= [3 5; 6 7] b = >> c=a+b c = P a g e Example 2 : Create two matrices of 3*3 with elements a=[1 2 3; 4 5 6; 7 8 9] and b= [3 5 7; 6 7 7; ], subtract them and find the value of c=a-b. >> a=[1 2 3; 4 5 6; 7 8 9] a = >> b= [3 5 7; 6 7 7; ] b = >> c=a-b

12 c = Example 3 : Create two matrices of 3*3 with elements a=[ ; ; ] and b= [ ; ; ], multiply them and find the value of c=a*b. >> a=[ ; ; ] a = >> b= [ ; ; ] b = >> c=a*b c = P a g e

13 Assignments If a=[ ; ; ], b= [3 5 7; 6 7 7; ], c=[1 2 3; 4 5 6; 7 8 9] then find 1. d= a+b-c 2. e= (a/b)*c 3. f= (a+b)+(a-b)+(a*b)+(a/d) 4. g= a+b-c+(b/a)+(c/b) P a g e

14 CHAPTER 5 FEATURES OF MATRICES 1.1 Transpose: Rows as columns and columns as rows. Example 1 :Find the transpose of matrix A= [4 2 5; 4 8 6; 7 8 7] >> A= [4 2 5; 4 8 6; 7 8 7] A = The symbol of transpose is ( ) >> B=A' B = Example 2 :Find the transpose of matrix B= [1 2 3; 4 5 6; 7 8 9] >> B= [1 2 3; 4 5 6; 7 8 9] B = >> C=B' C = P a g e

15 1.2 Diagonal: Display the principle diagonal elements. Example 3: Find the diagonal of matrix A= [4 2 5; 4 8 6; 7 8 7] >> A= [4 2 5; 4 8 6; 7 8 7] A = >> B=diag(A) B = Inverse: Creates the inverse of the matrix Example 4: Find the inverse of matrix A= [4 5 6; 7 8 9; ] >> A= [4 5 6; 7 8 9; ] A = >> B=inv(A) B = P a g e

16 1.4 Identity Matrix: Matrix with principle diagonal element as unity. Example 5: Create an identity matrix of 3*3 elements >> A= eye(3,3) >> A= eye(3,3) A = Example 6: Create an identity matrix of 4*4 elements >> A= eye(4,4) A = Unit Matrix: Matrix with all elements as unity. Example 6: Create an unit matrix of 3*3 elements >> A= ones(3,3) >> A= ones(3,3) A = P a g e

17 Example 7: Create an unit matrix of 4*4 elements >> A= ones(4,4) A = Magic Matrix: Matrix with all elements sum as same number. Example 8: Create a magic matrix of 3*3 elements >> A= magic(3) A = Example 9: Create a magic matrix of 4*4 elements >> A= magic(4) A = Determinant of a Matrix: Calculates the determinant value of a matrix. Example 10: Calculate the determinant value of a matrix A= [4 5 6; 7 8 9; ]. >> A= [4 5 6; 7 8 9; ] P a g e

18 A = >> B=det(A) B = e-14 Example 11: Calculate the determinant value of a matrix A= [1 2 3; 7 8 9; 1 1 1]. >>A= [1 2 3; 7 8 9; 1 1 1] A = Assignments If a=[ ; ; ], b= [3 5 7; 6 7 7; ], c=[1 2 3; 4 5 6; 7 8 9] then find 1. Determinant of a,b,c 2. Find inverse of a,b,c 3. Create a unity matrix and identity matrix of 3*3 elements P a g e

19 CHAPTER 6 2D-PLOT 1. Two Dimensional Plots 1.1 Steps : First create the range of the signal or plotting points. >> 1.2 Steps : Create the function for the signal. >> b=sin(pi*a); 1.3 Plotting : Plot the function for the signal. >> Program: b=sin(pi*a); Output : P a g e

20 Example 1: Create a sine wave with range 0 to 1 and the phase shift of (2*pi). Program: b=sin(2*pi*a); Output : Assignments Note :Commands for different trigonometric functions 1. SINE: sin 4. COSEC: csc 2. COSINE: cos5. SEC: sec 3. TAN: tan 6. COT: cot P a g e 1. Create a sine wave with range 0 to 1 and the phase shift of (2*pi). 2. Create a cosine wave with range 0 to 1 and the phase shift of (3*pi). 3. Create a tan wave with range 0 to 1 and the phase shift of (5*pi). 4. Create a cosec wave with range 0 to 2 and the phase shift of (2*pi). 5. Create a sec wave with range 0 to 3 and the phase shift of (2*pi). 6. Create a cot wave with range 0 to 2 and the phase shift of (5*pi).

21 7. CHAPTER 7 2D-PLOT-DESIGNING 1. LABEL 1.1 Steps : First create the range of the signal or plotting points. >> 1.2 Steps : Create the function for the signal. >> b=sin(2*pi*a); 1.3 Plotting : Plot the function for the signal. >> 1.4 Steps : Create the label of x axis. >>xlabel( X Axis ) 1.5 Steps : Create the label of y axis. >>ylabel( Y Axis ) Program: b=sin(2*pi*a); Output : P a g e

22 Example 1: Create a cosine wave with range 0 to 1,the phase shift of (2*pi) and label X AXIS and Y AXIS. Program: b=cos(2*pi*a); Output : Assignments 1. Create a sine wave with range 0 to 2, the phase shift of (2*pi) and label X AXIS and Y AXIS. 2. Create a cosine wave with range 0 to 1, the phase shift of (3*pi) and label X Axis of COS and Y AXIS of COS. 3. Create a tan wave with range 0 to 1, the phase shift of (5*pi) and label X Axis of COS and Y AXIS of COS. 4. Create a cosec wave with range 0 to 2,the phase shift of (2*pi) and label X AXIS and Y AXIS. 5. Create a sec wave with range 0 to 3, the phase shift of (2*pi) and label X AXIS and Y AXIS. 6. Create a cot wave with range 0 to 2, the phase shift of (5*pi) and label X Axis of COT and Y AXIS of COT P a g e

23 2. TITLE 1.1 Steps : First create the range of the signal or plotting points. >> 1.2 Steps : Create the function for the signal. >> b=sin(2*pi*a); 1.3 Plotting : Plot the function for the signal. >> 1.4 Steps : Create the label of x axis. >>xlabel( X Axis ) 1.5 Steps : Create the label of y axis. >>ylabel( Y Axis ) 1.6 Steps : Create the TITLE of wave. >>title( SIN Wave ) Program: b=sin(2*pi*a); title( SIN Wave ) Output : P a g e

24 Example 2: Create a cosine wave with range 0 to 1,the phase shift of (2*pi), label X AXIS, Y AXIS and title Cos Wave. Program: b=cos(2*pi*a); title( Cos Wave ) Output : 3. LEGEND 1.1 Steps : First create the range of the signal or plotting points. >> 1.2 Steps : Create the function for the signal. >> b=sin(2*pi*a); 1.3 Plotting : Plot the function for the signal. >> 1.4 Steps : Create the label of x axis P a g e

25 >>xlabel( X Axis ) 1.5 Steps : Create the label of y axis. >>ylabel( Y Axis ) 1.6 Steps : Create the TITLE of wave. >>title( SIN Wave ) 1.7 Steps : Create the LEGEND of wave. >>legend( SIN Wave ) Program: b=sin(2*pi*a); title( SIN Wave ) legend( SIN Wave ) Output: P a g e

26 Example 3: Create a cosine wave with range 0 to 1,the phase shift of (2*pi), label X AXIS, Y AXIS,title Cos Wave and legend ( COS Wave ). Program: b=cos(2*pi*a); title( Cos Wave ) legend( Cos Wave ) Output : Assignments 1. Create a sine wave and cosine wave with range 0 to 1 and the phase shift of (2*pi),add them (sin+cos) give label and titles. Label : X Axis,YAxis Title= Sin+Cos Legend = Sin+Cos P a g e

27 2. Create a sine wave and cosine wave with range 0 to 1 and the phase shift of (2*pi) and subtract them (sin-cos) give label and titles. Label : X Axis,YAxis Title= Sin-Cos Legend = Sin-Cos 3. Create a cosine wave and tan wave with range 0 to 1 and the phase shift of (3*pi) and add them (cos+tan) give label and titles. Label : X Axis,YAxis Title= Cos+Tan Legend = Cos+Tan 4. Create a cosine wave and tan wave with range 0 to 1 and the phase shift of (3*pi) and subtract them (cos-tan) give label and titles. Label : X Axis,YAxis Title= Cos-Tan Legend = Cos-Tan P a g e 5. Create a tan wave and cot wave with range 0 to 1 and the phase shift of (5*pi) and add them (tan+cot) give label and titles. Label : X Axis,YAxis Title= Tan+Cot Legend = Tan+Cot 6. Create a tan wave and cot wave with range 0 to 1 and the phase shift of (5*pi) and subtract them (tan-cot) give label and titles. Label : X Axis,YAxis Title= Tan+Cot Legend = Tan+Cot 7. Create a cot wave and cosec wave with range 0 to 1 and the phase shift of (5*pi) and add them (cot+csc) give label and titles. Label : X Axis,YAxis Title= Cot+Cosec Legend = Cot+Cosec 8. Create a cot wave and cosec wave with range 0 to 1 and the phase shift of (7*pi) and subtract them (cot-csc) give label and titles. Label : X Axis,YAxis Title= Cot-Cosec Legend = Cot-Cosec

28 CHAPTER 8 2D-PLOT-Fig. & Subplot 1. Figure Plot 1.1 Step: First create the program for sine function. b=sin(2*pi*a); 1.2 Step :Write the program for cos wave. b=cos(2*pi*a); P a g e

29 1.4 Step : Combine the codes. b=sin(2*pi*a); c=cos(2*pi*a); figure(1) figure(2) plot(a,c) Output : 1.4 Step : Add the title and legend. b=sin(2*pi*a); c=cos(2*pi*a); figure(1) title( Sin Wave ) legend( Sin Wave ) figure(2) plot(a,c) P a g e

30 title( Cosin Wave ) legend( Cosin Wave ) Output : Assignments [1]. Plot Sin wave and Cosine wave in the two different figures. [2]. Plot Cosine wave and Tan wave in the two different figures. [3]. Plot Tan Wave and Cot wave in the two different figures. [4]. Plot Cot Wave and Sec wave in the two different figures. [5]. Plot Sec Wave and Cosec wave in the two different figures. [6]. Plot Sin wave,cosine wave, Cot wave and Tan wave in the four different figures. [7]. Plot Cosec wave,sec wave and Cot wave in the three different figures P a g e

31 2. Sub Plot 1.1 Step: First create the program for sine function. b=sin(2*pi*a); 1.2 Step :Write the program for cos wave. b=cos(2*pi*a); 1.4 Step : Combine the codes. b=sin(2*pi*a); c=cos(2*pi*a); subplot(1,2,1) subplot(1,2,2) plot(a,c) P a g e

32 1.4 Step : Add the title and legend. b=sin(2*pi*a); c=cos(2*pi*a); subplot(1,2,1) title( Sin Wave ) legend( Sin Wave ) subplot(1,2,2) plot(a,c) title( Cosin Wave ) legend( Cosin Wave ) Assignments 1. Subplot Sin wave and Cosine wave. 2. Subplot Cosine wave and Tan wave. 3. Subplot Tan Wave and Cot wave. 4. Subplot Cot Wave and Sec wave. 5. Subplot Sec Wave and Cosec wave. 6. Subplot Sin wave,cosine wave, Cot wave and Tan wave. 7. Subplot Cosec wave,sec wave and Cot wave P a g e

33 CHAPTER 9 3D PLOT 3D PLOT 1.1 Step: First create the program for sine function. b=sin(2*pi*a); OUTPUT P a g e

34 1.2 Step :Change the program to get 3D plot. b=sin(2*pi*a); c=b *b; surf(c) zlabel('z Axis') legend( Sin 3D Plot ) OUTPUT P a g e

35 Assignments 3-D Figure Plot 1. Plot 3-D Sin wave and Cosine wave in the two different figures. 2. Plot 3-D Cosine wave and Tan wave in the two different figures. 3. Plot 3-D Tan Wave and Cot wave in the two different figures. 4. Plot 3-DCot Wave and Sec wave in the two different figures. 5. Plot 3-DSec Wave and Cosec wave in the two different figures. 6. Plot 3-DSin wave,cosine wave, Cot wave and Tan wave in the four different figures. 7. Plot 3-DCosec wave,sec wave and Cot wave in the three different figures. 8. Subplot Sin wave and Cosine wave. 9. Subplot Cosine wave and Tan wave. 3-D Subplot 1. Subplot 3-D Tan Wave and Cot wave. 2. Subplot 3-D Cot Wave and Sec wave. 3. Subplot 3-D Sec Wave and Cosec wave. 4. Subplot 3-D Sin wave,cosine wave, Cot wave and Tan wave. 5. Subplot 3-DCosec wave,sec wave and Cot wave P a g e

36 CHAPTER 10 INPUT VALUES SINGLE INPUT VALUES (2 D) 1.1 Step: First create the program for sine function. b=sin(2*pi*a); 1.2 Step :Change the program to provide input values. z=input( Please enter the maximum range :- ); a=0:0.01:z; b=sin(2*pi*a); INPUT Please enter the maximum range : P a g e

37 DOUBLE INPUT VALUES (2 D) 1.1 Step: First create the program for sine function. b=sin(2*pi*a); 1.2 Step :Change the program to provide input values. y=input( Please enter the maximum range :- ); z=input( Please enter the minimum range :- ); a=z:0.01:y; b=sin(2*pi*a); INPUT Please enter the maximum range: - 2 Please enter the minimum range: P a g e

38 INPUT VALUES (3 D) 1.1 Step: First create the program for sine function. b=sin(2*pi*a); OUTPUT 1.2 Step :Change the program to provide input values. z=input( Please enter the maximum range :- ); y=input( Please enter the minimum range :- ); a=y:0.01:z; b=sin(2*pi*a); c=b *b; surf(c) zlabel('z Axis') legend( Sin 3D Plot ) INPUT Please enter the maximum range :-2 Please enter the maximum range : P a g e

39 INPUT VALUES (3 D) Assignments 3-D Figure Plot 10. Plot 3-D Sin wave in the two different figures and provide any 1 input. 11. Plot 3-D Cosine wave in the two different figures and provide any 1 input. 12. Plot 3-D Tan Wave in the two different figures and provide any 1 input. 13. Plot 3-DCot Wave and Sec wave in the two different figures and provide any 1 input. 14. Plot 3-DSec Wave and Cosec wave in the two different figures and provide any 1 input. 15. Plot 3-DSin wave,cosine wave, Cot wave and Tan wave in the four different figures and provide any 2 input. 16. Plot 3-DCosec wave,sec wave and Cot wave in the three different figures and provide any 2 input P a g e