MATLAB: Writing a problem for a sine wave

for loop

For the attached document, can someone look at my code. Im confused as if I got the equation right or not.

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Nick:

You only need Est, not Est(1) because Est is not an array - it's a scalar. Also, don't assign Est to x as the first line because there is no x yet. And you need to initialize Est to x, not 1, AFTER you get x.

N=input('Please enter how many terms you would like to go out:')
x=input('Please enter the angle in radians:')
Est=x;
for k= 2:N
  termK = (-1)^(k-1)*x^(2*k-1)/factorial(2*k-1);
  Est = Est + termK;
  fprintf('Term %d = %.6f, so now Est = %.6f\n', k, termK, Est);
end
fprintf('The final Estimated Value = %.6f\n', Est)
fprintf('Actual Value of sin(%.6f) = %0.6f\n', x, sin(x))
fprintf('Difference is %0.6f\n', Est-sin(x))

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MATLAB: What is the difference between “dwt2()” and “wavedec2()”

Basically dwt2() applies 2-D discreet wavelet transformation on the image and provides the approximation and detail coefficients matrices directly. Whereas, wavedec2() only provides the wavelet decomposition vector and the bookkeeping matrix, which contains the number of coefficients by level and orientation. And you can to get approximation and detail coefficients matrices from the wavelet decomposition vector and the bookkeeping matrix using the detcoef2() and appcoef2() function.

Exact same approximation and detail coefficients matrices can be generated using any of those (dwt2 or wavedec2) functions. See the example below

close all; clc;
% Decomposition using wavedec2 and appcoef2
load woman;
[c, s] = wavedec2(X, 1, 'db1');
A1 = appcoef2(c, s, 'db1', 1);
figure; imshow(A1, []); title('Using wavedec2 and appcoef2');
% Decomposition using dwt2
load woman;
[A2, ~, ~, ~] = dwt2(X, 'db1');
figure; imshow(A2, []); title('Using dwt2');
% Difference image between A1 and A2
diffImage = imabsdiff(A1, A2);
figure; imshow(diffImage, []); title('Difference Image');

Now, here is an example how you can display different sub-bands at different wavelet decomposition levels.

clc; close all;
load woman;
[c, s] = wavedec2(X, 3, 'haar');
% Extract the level 1 approximation and detail coefficients.
[H1, V1, D1] = detcoef2('all', c, s, 1);
A1 = appcoef2(c, s, 'haar', 1);
% Display images


figure; subplot(2, 2, 1); imshow(A1, []); title('Approximation Coef. of Level 1');
subplot(2, 2, 2); imshow(H1, []); title('Horizontal Detail Coef. of Level 1');
subplot(2, 2, 3); imshow(V1, []); title('Vertical Detail Coef. of Level 1');
subplot(2, 2, 4); imshow(D1, []); title('Diagonal Detail Coef. of Level 1');
% Extract the level 2 approximation and detail coefficients.
[H2, V2, D2] = detcoef2('all', c, s, 2);
A2 = appcoef2(c, s, 'haar', 2);
% Display images
figure; subplot(2, 2, 1); imshow(A2, []); title('Approximation Coef. of Level 2');
subplot(2, 2, 2); imshow(H2, []); title('Horizontal Detail Coef. of Level 2');
subplot(2, 2, 3); imshow(V2, []); title('Vertical Detail Coef. of Level 2');
subplot(2, 2, 4); imshow(D2, []); title('Diagonal Detail Coef. of Level 2');
% Extract the level 3 approximation and detail coefficients.
[H3, V3, D3] = detcoef2('all', c, s, 3);
A3 = appcoef2(c, s, 'haar', 3);
% Display images
figure; subplot(2, 2, 1); imshow(A3, []); title('Approximation Coef. of Level 3');
subplot(2, 2, 2); imshow(H3, []); title('Horizontal Detail Coef. of Level 3');
subplot(2, 2, 3); imshow(V3, []); title('Vertical Detail Coef. of Level 3');
subplot(2, 2, 4); imshow(D3, []); title('Diagonal Detail Coef. of Level 3');

Hope this helps!

MATLAB: Indexing through an array

num = input('Enter a number you would like to find the cubed root of: ');
est = input('Enter your initial estimate: ');
err = abs(num - est^3);
k = 2;
while err > 1e-9    
    est(k) = (1/3)*(2*est(k-1)+num./(est(k-1)^2));
    err = abs(num - est(k)^3);
    k = k + 1;
end
plot(1:length(est),est);
fprintf('The cubed root of %g is approximately %.3f',num,est(end));

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MATLAB: What is the difference between “dwt2()” and “wavedec2()”

MATLAB: Indexing through an array

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