Develop a matlab program to design algorithm, MATLAB Programming

Write a pseudo-code showing the list of steps to take for solving the given problem. In this process, you should identify the functions that are to be used in the program. Develop a Matlab program based on the designed algorithm. Correct the program for any syntax errors.

Test the program for any logic errors.

1.1 Derivative of a Function

The derivative of a continuous function f (x) is defined by the equation

2284_limit equation.png

In a sampled function, becomes

f'(x(¡)) =  [f(x(i)   + 1) - f(x(i)]  /  ?x

where ?x =( x(i)  + 1) - x(i)

Assume that a vector vector vect contains n samples of a function taken at a spacing of dx per sample. Write a function that will calculate the derivative of this vector from above discrete equation. The function should check to make sure that dx is greater than zero to prevent divide-by-zero errors in the function.

To check your function, you should generate a data set whose derivative is known and compare the result of the function with the known correct answer. A  good  choice for a test function is sinx, whose derivative is cosx. Generate an input vector containing 100 values of the function sinx starting at x = 0 and using a step size ?x of 0.05. Take the derivative of the vector with your function, and then compare the resulting answers to the known correct answer. Calculate how close your function came to the correct value by computing error as sum of squared distance of all the 100 points.

1.2 Derivative in the Presence of Noise

Explore the effects of input noise on quality of the numerical derivative. First, generate an input vector containing 100 values of the function sinx starting at x = 0 and using a step size ?x of 0.05, just as you did in the above problem. Next, use function 'rand' to generate a small amount of random noise with a maximum amplitude of  ±0.02, and add that random noise to the samples in your input vector. Note that the peak amplitude of the noise is only 2% of the peak amplitude of your signal, since the maximum value of sinx is 1. Now take the derivative of the function using the derivative function that you developed in the above problem. Calculate how close your function came to the correct value by computing error as sum of squared distance of all the 100 points.

YOU MUST USE THIS PROGRAM SKELETON FOR THIS LAB BUILD UPON THIS SKELETON

%SKELETON Program for Program3

%data.m returns the 100 sample values

x=data();

%Generate 3 function values (y1,y2,y3)

% and their derivatives (yd1,yd2,yd3)

[y1 yd1]=fn1(x);

[y2 yd2]=fn2(x);

[y3 yd3]=fn3(x);

%Add noise to the y-values

[y1_ns]=add_noise(y1,0.02);

[y2_ns]=add_noise(y2,0.02);

[y3_ns]=add_noise(y3,0.02);

%Compute derivative for each of the three functions with/without noise

my_yd1=my_derivative(x,y1);

my_yd1_ns=my_derivative(x,y1_ns);

my_yd2=my_derivative(x,y2);

my_yd2_ns=my_derivative(x,y2_ns);

my_yd3=my_derivative(x,y3);

my_yd3_ns=my_derivative(x,y3_ns);

%Compute Sum Square error of the derivative for each of the three functions

error1=sumsqerror(yd1,my_yd1);

error1_ns=sumsqerror(yd1,my_yd1_ns);

error2=sumsqerror(yd2,my_yd2);

error2_ns=sumsqerror(yd2,my_yd2_ns);

error3=sumsqerror(yd3,my_yd3);

error3_ns=sumsqerror(yd3,my_yd3_ns);

error1

error1_ns

error2

error2_ns

error3

error3_ns

 1.3

What to Hand In

Run your program for THREE functions, where you know the derivatives. You need to generate data for these functions; one of this function is sinx, as described above. Print the error for each function, with and without noise, and make a script file for grading.

1.4 Write a new functions: factorial_loop(n) as described below, and run your own tests. Note: you must use the type of loop specified.

1.  factorial_loop will use 'for' loop to compute factorial of n

Use the diary command to save your work into a file: lab09.txt you need to submit for grading. In the command window, type:

 factorial_loop.m

factorial_loop(5)

factorial_loop(9)

Posted Date: 3/13/2013 3:45:57 AM | Location : United States







Related Discussions:- Develop a matlab program to design algorithm, Assignment Help, Ask Question on Develop a matlab program to design algorithm, Get Answer, Expert's Help, Develop a matlab program to design algorithm Discussions

Write discussion on Develop a matlab program to design algorithm
Your posts are moderated
Related Questions
In this lab, we study the three concepts. Vector is used to store more than one value into single variable. It is similar to array (other programming language). Script is a collect

Example of Variables and assignment statements: The expression is computed and then that value is stored in the variable. For illustration, this is the way it would appear in

Operators: There are in general two types of operators: unary operators that operate on a single value or operand; and binary operators, that operate on two values or operands

Output Statements: disp and fprintf: The Output statements display strings and the answers of expressions and can permit for formatting or customizing how they are exhibited.

1;write the matlab of LU decomposion that can do any n*n matrix by considering scaling and pivoting?

how to design a digital fir filter using anfis in matlab.get the code for that.

How to Start Working withSimpower: 1. In the Simulink screen, open a new "Model" (File àNewà Model), name it and save it. 2. Expand the SimPowerSystems library, select and

Need help with creating functions in matlab.

Q.1: Consider the transmission of a sinusoid x(t) = cos(2f0t) through a channel a ected by multipath and Doppler. Let there be two paths, and assume the sinusoid is being sent fro

We wish to numerically perform the following integration: (a) Use Matlab's quad function to perform the above integral. (b) Analytically evaluate the integral (e.g. do t