Assignment 1

EE 608 Date: 30.01.15

1. (a) How are the chrominance signals I & Q used in NTSC related to chrominance signals U

and V used in PAL?

(b) The I and Q signals are not required to occupy the 4.2 MHz BW of Y signal. Explain why

this is so.

(c) Describe in detail how Y, I, Q signals are multiplexed into a 4.2 MHz bandwidth, even

though Y itself has frequency components as higher as 4.2 MHz?

(d) Sketch the spectrum of NTSC composite color video signal. Show how frequency

interleaving of luminance and chrominance is done.

(e) For NTSC, the colour sub carrier frequency is fc = 3.58 MHz .The chrominance signals I and Q are QAM onto this carrier via the relation,

C(t) = I(t)cos (2 fct+33) + Q(t)sin(2 fct+33)

(i) What attribute of colour video does the envelope of this QAM signal relative to

luminance signify?

(ii) What attribute does the phase of C(t) signify?

(iii) Which component of C(t) is most affected by additive transmission noise? What effect

does this have on a viewer?

2. (a) Explain the differences between the color modulation of NTSC and PAL.

(b) Why is the NTSC Y signal not the true luminance?

3. The BT.601 recommendation defines a digital color coordinate known as YCbCr. We say

that maximum value of Cr corresponds to red, whereas the minimum value yields cyan.

Similarly maximum and minimum values of Cb correspond to blue and yellow, respectively.

Using the YCbCr to RGB coordinate transformations, verify these statements given above.

4. Consider a NTSC signal that is a 2:1 interlaced video signal with 262.5 lines per field, 60

fields/sec and 4:3 aspect ratio. The horizontal retrace time is 10 s and 20 lines per field are

blanked for vertical back trace. Find the following parameters of the video signal:

(i) Vertical resolution.

(ii) Horizontal resolution.

(iii) Bandwidth of luminance signal. Assume Kell factor is =0.7

5. Consider a horizontal bar pattern on TV screen with 100 cycles/picture-ht. If picture height

is 1m, and the viewer sits at 3 meters from the screen, what is the equivalent angular

frequency in cpd? What if the viewer sits 1 meter or 5 meters distance? In either case, would

the viewer be able to perceive the vertical variation property?

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6. One issue with the YCbCr colour space comes from the constraint of positivity for the

corresponding RGB values.

(a) Using 10-bit values, the range of RGB data is [0, 1023]. What is the resulting range for

each of Y, Cr and Cb?

(b) Does every point in the range you found in part (a) correspond to a valid RGB value, i.e.,

a value in the range [0, 1023]?

7. From the plot of Human Visual System (HVS) response function, how many pixels should

there be vertically on a 100-inch vertical screen, when viewed at a distance of 3H, i.e., 300

inches? at 6H? Assume we want the HVS response to be down to 0.01 at the Nyquist

frequency?

8. Referring to the three-channel theory of colour vision, assume that three partially

overlapping human visual response curves (luminous efficiencies) sR( ), sG( ), and sB( ) are given. Let there be a camera with red, green, and blue sensors with response functions

scR( ), scG( ), and scB( ) , where the subscript c indicates camera. Let the results captured by the camera be displayed with three very narrow wavelength [here

modelled as monochromatic s( ) = ( )] beams, additively superimposed, and centered at the wavelength peak of each of the camera luminous efficiencies. Assuming white incident

light, i.e., uniform intensity at all wavelengths, what conditions are necessary so that we

perceive the same R, G, and B sensation as if we viewed the scene directly?

Neglect any nonlinear effects.

9. In white balancing a camera, we capture the image of a white card in the ambient light,

yielding three R, G, and B values. Now, we might like these three values to be equal;

however, because of the ambient light not being known, they may not be. How should we

modify these R, G, and B values to balance the camera in this light?

If the ambient light source changes, should we white balance the camera again? Why?

10. Consider the sampling that a CCD or CMOS image sensor does on the input Fourier

transform X ( 1, 2). Assume the sensor is of infinite size and that its pixel size is uniform

and square with size T T. Assume that, for each pixel, the incoming light intensity

(monochromatic) is integrated over the square cell and that the sample value becomes this

integral for each pixel (cell).

(a) Express the Fourier transform of the resulting sample values, call it XCCD( 1, 2) in terms

of the continuous Fourier Transform X( 1, 2). (b) Assuming spatial aliasing is not a problem, find the resulting discrete-space transform

X ( 1, 2).

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