What is Discrete Fourier Transform (DFT)? Find DFT of the function:
The discrete Fourier transform (DFT) represents a finite-length discrete signal by a finite set of complex exponentials. For a 2-D M×N array f(x,y) with 0≤x≤M−1 and 0≤y≤N−1, its 2-D DFT is $$ F(k,\ell)=\sum_{x=0}^{M-1}\sum_{y=0}^{N-1} f(x,y)\,e^{-j2\pi\left(\frac{kx}{M}+\frac{\ell y}{N}\right)},\qquad k=0,\dots,M-1,\;\ell=0,\dots,N-1. $$ The inverse is $$ f(x,y)=\frac{1}{MN}\sum_{k=0}^{M-1}\sum_{\ell=0}^{N-1} F(k,\ell)\,e^{+j2\pi\left(\frac{kx}{M}+\frac{\ell y}{N}\right)}. $$ Consider $f(x,y)=\sin(2\pi u_0 x+2\pi v_0 y)$. Using $\sin\theta=\frac{1}{2j}\big(e^{j\theta}-e^{-j\theta}\big)$, write $$ f(x,y)=\frac{1}{2j}\left[e^{j2\pi(u_0 x+v_0 y)}-e^{-j2\pi(u_0 x+v_0 y)}\right]. $$ Then $$ F(k,\ell)=\frac{1}{2j}\sum_{x=0}^{M-1}\sum_{y=0}^{N-1}\left[e^{j2\pi(u_0 x+v_0 y)}-e^{-j2\pi(u_0 _______ _______ ______ ___ _________ ________ ______ _______ ______ _______ _____.
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What do you understand by the term "Entropy" in context of any digital image? Calculate the entropy for the symbols, where probability distribution is given below:
| Symbol | Probability |
| 1 | 0.4 |
| 2 | 0.3 |
| 3 | 0.1 |
| 4 | 0.1 |
| 5 | 0.1 |
The white bars in the test pattern shown are 7 pixels wide and 210 pixels high. The separation between bars is 17 pixels. What would this image look like after application of
i) A 3×3 arithmetic mean filter?
ii) A 7x7 arithmetic mean filter?
iii) A 9×9 arithmetic mean filter?
The arithmetic decoding process is the reverse of the encoding procedure. Decode the message 0.23355 given the coding model.
| Symbol | Probability |
| a | 0.2 |
| e | 0.3 |
| i | 0.1 |
| o | 0.2 |
| u | 0.1 |
| ! | 0.1 |
Apply Prewitt operators and Sobel operators for the image given below:
Consider the two image subsets, S₁ and S2, shown in the following figure. For V = {1}, determine whether these two subsets are (i) 4-adjacent, (ii) 8-adjacent, or
(iii) m-adjacent.
An automobile manufacturer is automating the placement of certain components on the bumpers of a limited-edition line of sports cars. The components are colour coordinated, so the robots need to know the colour of each car in order to select the appropriate bumper component. Models come in only four colours: blue, green, red, and white. Find a solution based on imaging and determine the colour of each car, keeping in mind that cost is the most important consideration.
Consider an 8-pixel line of intensity data, (108,139,135,244,172,173,56,99). If it is uniformly quantized with 4-bit accuracy, compute the rms error and rms signal-to- noise ratios for the quantized data.