Hw3_supplement - -1 1 1-0.125 0.5-0.125-0.25 1.0-0.25-1-0.125 0.5-0.125 a Find a difference equation that can be used to implement this filter b

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Due Friday 29 April 2005 at 5:00 PM ECE 438 Assignment No. 10 Spring 2005 1. For each function given below, do the following: i. Sketch f ( x , y ) ii. Express f ( x , y ) in terms of the special functions given in class. iii. Find its CSFT F ( u , v ) using transform pairs and properties. iv. Sketch F ( u , v ) in enough detail to show that you know what it looks like. a. f ( x , y ) = cos 2 π ( x y ) ( ) , x 2 + y 2 < 4 0, else b. 2. The 2-D signal f ( x , y ) =1+cos 2 (3 x + y ) ( ) is sampled with an ideal sampler at 4 samples/inch to generate the signal f s ( x , y ) = f (0.25 m n m ,0.25 n ) δ ( x 0.25 m , y 0.25 n ) This signal is then convolved with sinc(4x,4y) to yield the reconstructed signal f r ( x , y ) . a. Sketch f( x , y ) showing a top view of the x-y plane in which the points where f( x , y ) = 1 are clearly labeled. b. Find a simple expression for f r ( x , y ) . c. Sketch f r ( x , y ) showing a top view of the x-y plane in which the points where f r ( x , y ) = 1 are clearly labeled.
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Due Friday 29 April 2005 at 5:00 PM 3. Consider a 3 × 3 FIR filter with coefficients h [ m , n ] m n
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Unformatted text preview: -1 1 1-0.125 0.5-0.125-0.25 1.0-0.25-1-0.125 0.5-0.125 a. Find a difference equation that can be used to implement this filter. b. Find the output image that results when this filter is applied to the input image shown below: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 c. Find a simple expression for the frequency response (DSFT) H ( μ , ν ) of this filter. d. Plot H ( , ) along the axis ( = 0) , along the axis ( = 0) , along the line = , and along the line = − . e. Discuss the relation between your answer to part b. and the filter frequency response....
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This note was uploaded on 02/19/2012 for the course ECE 638 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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Hw3_supplement - -1 1 1-0.125 0.5-0.125-0.25 1.0-0.25-1-0.125 0.5-0.125 a Find a difference equation that can be used to implement this filter b

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