image processing

Question 1

Name some basic signals.

Answer 1

unit impulse and a unit step function.

Question 2

describe complex exponential signals?

Answer 2

any signals can be written as a sum of complex exponential signals. And they are eigenvalues of convolution that is its frequency is unchanged only its amplitude and phase shifts.

Question 3

what is the period of e^(jwn1)?

Answer 3

k * 2 * pi / w

Question 4

what is the highest possible frequency a signal can reach

Answer 4

pi.

Question 5

define a linear and spatial invariant system

Answer 5

a system is linear if it

the sum of the output of two different signal and the output of the superposition of the two signals are same. zero input will definitely give zero output but also a non-zero output.

spatial invariant if the system does not care where the origin is.

Question 6

what is the significance of impulse signal?

Answer 6

a continuous signal can be represented as a discrete signal (sum of the product of signal and delayed impulses).

by knowing a response of a system to an impulse signal ie the impulse response of an LTI system we can tell its response to any other signal.

Question 7

define the use of high and low pass filters in image processing?

Answer 7

low pass filter eliminates the gaussian noise in the image but the image gets blurry.

High pass filter can be used for edge detection.

Question 8

what does flat 3*3 filter mean?

Answer 8

it is a filter with 9 pixels each of value 1/9.

Question 9

what is boundary effects? explain some of the types.

Answer 9

when using filter lets say 3*3, the left corner of the image does not have pixels on its left for applying the filter so we need some pixels on the left.

symmetry, zero padding, circular are some eg.

Question 10

what are the type of noises in an image and how you eliminate it?

Answer 10

gaussian noise eliminated by usage of low pass filter.

salt and pepper noise eliminated by usage of median filter.

Question 11

what is fourier transfrom?

Answer 11

fourier transform converts any signal to linear sum of sinusoidal signal of different frequencies. thus time domain signal is converted into frequency domain

Question 12

name some important properties of fourier transform?

Answer 12

• it is continuous with period 2 pi
• any spatial shift in time domain will result in phase shift in frequency domain
• modulation property: multiplication with e^jw in spatial domain will result in frequency shift in frequency domain.
• convolution

Question 13

what is sampling and why it is required?

Answer 13

almost all signals are continuous in nature but the system that process are discrete in nature so for changing the signal from continuous to discrete the signal is multiplied with impulse train this is called sampling

Question 14

what is critical sampling?

Answer 14

the minimum frequency at which sampling to be done for recreating the signal is called critical sampling it is given by Nyguist theorem, which says the sampling freq should be at least twice the max frequency present in the system.

Question 15

what is aliasing?

Answer 15

wkt fourier transform is periodic so the frequency spectrum repeat itself with the period 2*pi/Ti. if the sampling is below ciritical sampling the high frequency content merges with the low frequency content thus original signal cannot be recreated this is called aliasing.

Question 16

Advantages of discrete Fourier transform

Answer 16

in continuous Fourier transform we need the amplitude at all frequencies to construct the signal (ie frequencies are continuous in nature) which is impossible

in discrete Fourier transform we only need the amplitude of the signal at particular frequencies thus it is discrete in nature.

Question 17

define sampling of a 2d image and what are the control parameters?

Answer 17

in a 2d rectangular periodic sampling image is multiplied with a grid of rectangular array in which the intensities in the node points have unit value and rest 0 thus image of continuous nature is converted to discrete nature.

the control parameters are distance between grid points in x and y direction.

Question 18

Define what is happening when you take Fourier transform of an image?

Answer 18

Image has pixel values in x and y values if u take along the x direction the variation of intensities can be written as a mathematical function (x distances)

and this fn can be written as a linear combination of sinusoidal signal which is done by Fourier transform.

thus Fourier transform of image gives linear sum of sin signals in x and y directions.