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| − | # Let <math>A=\begin{pmatrix}1&2&3\\4&5&6\\7&8&10\end{pmatrix}</math>. Find a matrix X such that <math>X\cdot A=\begin{pmatrix}7&8&10\\4&5&6\\1&2&3\end{pmatrix}</math>. What do you get if you compute <math>A\cdot X</math>? | + | # <math>\checkmark</math> Let <math>A=\begin{pmatrix}1&2&3\\4&5&6\\7&8&10\end{pmatrix}</math>. Find a matrix X such that <math>X\cdot A=\begin{pmatrix}7&8&10\\4&5&6\\1&2&3\end{pmatrix}</math>. What do you get if you compute <math>A\cdot X</math>? |
# Find a 4x4 orthogonal matrix with at least 5 non-zero entries. | # Find a 4x4 orthogonal matrix with at least 5 non-zero entries. | ||
# Can you find a 3x3 orthogonal matrix with no zeroes? [http://helmut.knaust.info/class/201310_5311/Notebooks/Assignment03.nb Notebook] | # Can you find a 3x3 orthogonal matrix with no zeroes? [http://helmut.knaust.info/class/201310_5311/Notebooks/Assignment03.nb Notebook] | ||
| − | # Find the vertical edges of a grayscale image (of your choice). Hint: For horizontal edges this is done in Notebook 031. | + | # <math>\checkmark</math> Find the vertical edges of a grayscale image (of your choice). Hint: For horizontal edges this is done in Notebook 031. |
| − | # Pick a small grayscale image (your choice) and use matrix transposition and multiplication with suitable matrices to produce the following six images: [[image:FN.jpg|500px]] | + | # <math>\checkmark</math> Pick a small grayscale image (your choice) and use matrix transposition and multiplication with suitable matrices to produce the following six images: [[image:FN.jpg|500px]] |
# In Notebook 032 you have seen how to convert a color image to its YCbCr components. Recreate the original color image from its Y-, Cb- and Cr- components. (Check your result by computing the Peak Signal to Noise Ratio to the original image. Note that when computing the luminance/chrominance components, we round to the nearest integer. ) | # In Notebook 032 you have seen how to convert a color image to its YCbCr components. Recreate the original color image from its Y-, Cb- and Cr- components. (Check your result by computing the Peak Signal to Noise Ratio to the original image. Note that when computing the luminance/chrominance components, we round to the nearest integer. ) | ||
# Problem 3.8 | # Problem 3.8 | ||
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# Problem 3.50 | # Problem 3.50 | ||
# Problem 3.42 | # Problem 3.42 | ||
| + | # Compute the real and/or complex Fourier series for the functions <math>f(t)=t</math> or <math>f(t)=|t|</math>. | ||
Revision as of 06:06, 13 June 2013
- \(\checkmark\) Let \(A=\begin{pmatrix}1&2&3\\4&5&6\\7&8&10\end{pmatrix}\). Find a matrix X such that \(X\cdot A=\begin{pmatrix}7&8&10\\4&5&6\\1&2&3\end{pmatrix}\). What do you get if you compute \(A\cdot X\)?
- Find a 4x4 orthogonal matrix with at least 5 non-zero entries.
- Can you find a 3x3 orthogonal matrix with no zeroes? Notebook
- \(\checkmark\) Find the vertical edges of a grayscale image (of your choice). Hint: For horizontal edges this is done in Notebook 031.
- \(\checkmark\) Pick a small grayscale image (your choice) and use matrix transposition and multiplication with suitable matrices to produce the following six images:
- In Notebook 032 you have seen how to convert a color image to its YCbCr components. Recreate the original color image from its Y-, Cb- and Cr- components. (Check your result by computing the Peak Signal to Noise Ratio to the original image. Note that when computing the luminance/chrominance components, we round to the nearest integer. )
- Problem 3.8
- Problem 3.16
- Problem 3.23
- Problem 3.26
- Problem 3.35
- Problem 3.37
- Problem 3.50
- Problem 3.42
- Compute the real and/or complex Fourier series for the functions \(f(t)=t\) or \(f(t)=|t|\).
