Difference between revisions of "ECE438 Week14 Quiz" - Rhea

Latest revision as of 09:43, 11 November 2011

Quiz Questions Pool for Week 14

Q1. Assume we know (or can measure) a function

$ \begin{align} p(x) &= \int_{-\infty}^{\infty}f(x,y)dy \end{align} $

Using the definition of the CSFT, derive an expression for F(u,0) in terms of the function p(x).

• Solution.

Q2. Consider the following 2D system with input x(m,n) and output y(m,n)

$ y(m,n) = x(m,n) + \lambda \left( x(m,n) - \frac{1}{9} \sum_{k=-1}^{1}\sum_{l=-1}^{1}x(m-k,n-l) \right) $

a. Is this a linear system? Is it space invariant?
b. What is the 2D impulse response of this system?
c. Calculate its frequency response H(u,v).
d. Describe how the filter behaves when $ \lambda $ is positive and large.
e. Describe how the filter behaves when $ \lambda $ is negative and bigger than -1.

• Solution.

Q3. Consider a 3 * 3 FIR filter with coefficients h[m, n]

a. Find a difference equation that can be used to implement this filter.

b. Given an input image, find the center pixel value of output image.

c. Find a simple expression for the frequency response (DSFT) H(u,v) of this filter.

• Solution.

Q4. Consider the following discrete space system with input x[m,n] and output y[m,n]given by

$ y[m,n]=x[m,n]+\frac{1}{2}y[m+1,n-1] $

Compute the transfer function

$ H(z_1 ,z_2)=\frac{Y(z_1 ,z_2)}{X(z_1 ,z_2)} $

• Solution.

Q5. Consider the following discrete space system

where $ b(i,j) $ is the quantized binary image, $ f(i,j) $ is the input and $ \tilde{f}(i,j) $ is the modified image by means of the past quantization errors.

Furthermore we have that

$ \begin{align}e(i,j)&=\tilde{f}(i,j)-b(i,j) \\ \tilde{f}(i,j)&=f(i,j)+H(i,j)\ast e(i,j) \\ \end{align} $

Now, we have $ H(i,j)=\delta(i-1,j)\,\! $ is a strictly causal filter and the quantizer $ Q(\tilde{f}) $ given as

$ Q(\tilde{f})=\left\{ \begin{array}{ll}1,& \tilde{f}(i,j)>0.5 \\ 0, & \tilde{f}(i,j)\leq 0.5 \end{array} \right. $

Assuming that $ e(i,j)=0 $ for $ i<0 $ and $ j<0 $ and the input $ f(i,j) $ to be defined as

a. compute the modified input $ \tilde{f}(i,j) $.

b. compute the output $ b(i,j) $.

• Solution.

Back to ECE 438 Fall 2010 Lab Wiki Page

Back to ECE 438 Fall 2010