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
Command Window: To the left of the Command Window, there are 2 tabs for the Current Directory Window and Workspace Window. If the Current Directory tab is selected, the files

Write a function called threshold2 (in a file called 'threshold2.m'). The function takes an arbitrary number of input variables. The first input variable, t, is required and is the

1.      Write a MATLAB program to generate and plot the signal                                     x1(n) = [3 2 -2 0 7],  n = 0,1,2,3,4. 2.      Write a MATLAB program to gen

I want to write a function in matlab which gives me a population pyramid bar chart. could you please help me do this.

The average speed of vehicles on a freeway is being studied. Assume that the standard deviation of vehicle speed is known to be 8 km/h. (a) Suppose observations on 120 vehicles

Build a single phase model for the simple 3-phase system shown in the single line diagram shown below using SimPowerSystems in MATLAB Simulink. Data: Source Voltage

This assignment is designed to compare performance between Matlab and Excel for performing nonlinear regression analysis of a set of data. There are two data sets in the accompa

how do you make a program for a parachute man falling to determine his terminal velocity, having in consideration the drag force (cv^2). I have the formula to be v(i+1)=v(i)*delta(


design a rc phase shift oscillator for a particular frequency of oscillation and generate a sinusoidal signal