ECE 5256 Test 2 Spring 2021

1(4) What is the geometric mean of the following values: 4, 7, 20?

(4*7*20)^1/3 = 8.24

2(4) What is the harmonic mean of the following values: 100, 100, 50?

3/(1/100 + 1/100 + 1/50) = 75

3(2) An image undergoes uniform linear motion in at angle of 45 degrees with respect to the horizontal for a time T√2. Would you get the same result if the motion was in the horizontal direction for time T, then in the vertical direction for time T?

No – turns out to be someone difficult to get a definitive answer. Gave full credit to both responses

4(4) Given an image with a power spectrum equal to sin(f) corrupted with additive noise with a constant power spectrum of 0.25, what is the value of the Wiener filter at f = pi/2?

1/(1+0.25) = 0.8

5(3) Given a 256 x 256 pixel image, if a projection is taken every 1 degree in a complete circle, how many rows will there be in the sinogram where the sinogram is x l (vertical x horizontal).

360

6 (4) Given a 256 x 256 pixel image, if a projection is taken every 1 degree in a complete circle, how many columns will there be in the sinogram where the sinogram is x l (vertical x horizontal).

256sqrt(2) = 362.03 (362 to 363 acceptable)

7(4) Given a 256 x 256 image that consists of a vertical line, what will be its Radon transform (,l)? Could get different answers depending on coordinate system. Gave full credit except for last two answers.

A point at 90,0

A point at 90,128

A point at 0,128

A sinusoid

A horizontal line

8(3) When creating a backprojection image from the Radon transform, the image should be:

High-pass filtered

Low-pass filtered

Doesn’t have to be filtered

9(4) For length 256 length signal, how many wavelet coefficients are generated at the level of a wavelet transform?

128

10(4) For length 256 length signal, how many wavelet coefficients are generated at the 2nd level of a wavelet transform?

64

11(4) For a 256 x 256 pixel image, how many basis functions are there for a wavelet transform?

256 x 256 = 65,536