Communication Theory and Engineering

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1 Communication Theory and Engineering Master's Degree in Electronic Engineering Sapienza University of Rome A.A

2 Practice work 14 Image signals

3 Example 1 Calculate the aspect ratio for an image with dimensions X max = 70 cm and Y max = 40 cm. Y max X max

4 Example 2 Consider a high definition television screen with a diagonal of 46 inches, aspect ratio R=16/9 and number of lines equal to N=1080 Calculate the screen size (note: 1 inch = 2.54 cm)

5 Example 3 Consider a high definition television screen with a diagonal of 46 inches, aspect ratio R=16/9 and number of lines equal to N=1080. Calculate the optimum viewing distance

6 Example 3 (continued) Calculate the band required to transmit luminance, if the time to transmit the information of a row is T r = 30 μs Assuming that a channel available band B c =8 MHz, calculate the new maximum resolution (N x M ) to which the image can be transmitted, in order to maintain the same aspect ratio and the same time line as above

7 Example 3 (continued) Calculate the new optimal viewing distance and compare it with what obtained with N=1080

8 Example 3 (continued) Calculate how this distance would vary if the user adopted a 15 inch screen

9 Example 4: the G3 fax standard The G3 standard regulates the acquisition of an A4 format page (21 cm x 29.7 cm) in digital format. Each luminance sample is quantized on two levels. The obtained image is then compressed, and finally transmitted on a connection characterized by a bit rate that is typically f b = 28.8 kb/s. The typical time of transmission of a page is T c =10 s (if one only considers the time necessary to transfer bits of information between the source and the destination), and the image file before compression is composed of 1680 x 1145 dots.

10 Example 4: G3 fax standard (continued) Calculate the horizontal and vertical resolution used in the scan, expressing it in number of dots per inch (dpi, or dots per inch)

11 Example 4: G3 fax standard (continued) Determine the compression factor introduced by the source coding algorithm applied to the image before transmission

12 Example 4: G3 fax standard (continued) Determine what the transmission time would be in the absence of compression if you decided to quantize the luminance using a 256- level gray scale, keeping both the resolution and the link speed unchanged

13 Example 5: Fax transmission on telephone channel Consider a fax transmission system on a telephone channel. The transmitted signal consists of an image composed of N = 1200 lines, with an aspect ratio R = 0.7, and presents a 2-level quantization (black and white). The corresponding numerical signal is modulated with two-levels modulator, so as to make it suitable for the channel transfer characteristic, which is supposedly limited in band between and Hz, and represented by a transmission line. The transmitted signal has a rate of f l = 2400 symbols per second. The Transmission filter has roll-off γ=0, and the Receiver filter removes the noise outside the useful bandwidth of the signal. There are no distortions. The attenuation introduced is A=90 db.

14 Example 5 (continued) 1. Calculate the time required to perform the complete image scan 2. Calculate the received power if SNR the noise power is -138 dbm at the receiver is 13 db and 3. Calculate the noise power spectral density in dbm/hz 4. Calculate the transmitted power 5. Calculate the probability of bit error (bit error rate)

15 Example 5 (continued) 1. Calculate the time required to perform the complete image scan

16 Example 5 (continued) 2. Calculate the received power if SNR at the receiver is 13 db and the noise power is -138 dbm 3. Calculate the noise power spectral density in dbm/hz

17 Example 5 (continued) 4. Calculate the transmitted power 5. Calculate the probability of bit error (bit error rate)

18 Example 6: TV standard PAL The PAL (Phase Alternating Line) television standard uses a total of 625 lines per frame of these about M=49 lines per frame are necessary for the vertical return, leaving at most N=576 lines per frame available. To avoid image flicker problems, the actual number of lines used is further reduced by 30%. The signal is transmitted interlaced at a rate of f sf =50 semi-frames/s, and the aspect ratio is R=4/3. Calculate the total time available for each row knowing also that the time required for the horizontal return at the end of each line is equal to T hr = 12 μs, calculate the band necessary to transfer the luminance with same equivalent vertical and horizontal resolutions

19 Example 7: NTSC television standard The television standard NTSC (National Television System Committee) uses a total of 525 lines per frame, and transmits in an interlaced way with a frequency equal to f sf =60 semi-frames/s with an aspect ratio R=4/3. The signal band is B=4.2 MHz, and the horizontal return time is T hr =12 μs. Calculate the number of lines actually used to represent each frame, assuming the same vertical and horizontal resolutions

20 Example 8: Standard DVD Video The DVD Video standard provides several video resolutions; while at maximum resolution a DVD media can contain a video of about two hours, longer movies can be stored using lower resolutions. The highest resolution in the European media (compatible with the TV PAL standard) is 720 x 576. According to the format known as 4: 2: 2, the luminance is evaluated at each pixel, while the chrominance functions are evaluated every other pixel The standard DVD used in Europe is transmitted, like PAL, using 25 frames per second and an aspect ratio R=4/3. Calculate the sampling frequency for the luminance and for each of the chrominance functions

21 Example 9: read an image signal and analyze it (MATLAB) The goal of this exercise is to produce a MATLAB script that computes the luminance signal band associated with the supplied image file, "goldengate3.png", that is characterized by a resolution of 72 dpi [dot (pixel) per inch]. Guidelines: The script should first read the supplied file The first two dimensions of the matrix that MATLAB creates correspond to the resolution of the image The third dimension contains the RGB components The script should then associate luminance values to each line of the image (use MATLAB function rgb2hsv and keep only the third dimension of the resulting matrix: this is the luminance) The script should finally compute the band of this signal (reporting the results on a graph), as the reading time of the row changes: consider line # 200 of the image, and β equal to 0.25, 0.5 and 1. Try to figure out how MATLAB computes luminance from the RGB values Note: To find the luminance value: help rgb2hsv For frequency representation: help fft / help fftshift

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