User:Inconspicuum/Physics (A Level)/Communication Questions

Digital Storage

1. An image transmitted down a SVGA video cable is 800 pixels wide, and 600 pixels high. How many pixels are there in the image?
2. A grayscale image is encoded using 3 bits. How many possible values can each pixel have?
3. The characters in a text document are numbered from 0 - 255. How many bits should each character be encoded with?
4. A page contains 30 lines of text, with an average of 15 characters on each line. Each character is represented by 4 bits. How many megabytes of uncompressed storage will a book consisting of 650 pages like this fill on a computer's hard disk?
5. A 10cm wide square image is scanned into a computer. Each pixel is encoded using 3 channels (red, green and blue), and each channel can take on 256 possible values. One pixel is 0.01 mm wide. How much information does the scanned image contain? Express your answer using an appropriate unit.

Digital Processing

1. How could the above methods be applied to a digital sound sample?
2. Which of the above methods would be suitable for smoothing sharp edges? Why?
3. Use median smoothing to remove noise from the following image of a white cat in a snowstorm (the black pixels have a value of 255):

000	255	000	000
000	000	000	255
255	000	000	000
000	000	255	000

1. Why would mean sampling not be appropriate for smoothing the image given in question 3?
2. Use mean smoothing to remove noise from the following image of a black cat in a coal cellar:

255	255	255	255
255	255	000	255
255	255	255	255

Digitisation

1. Take samples for the signal below every 0.1ms, and then produce a reconstructed signal. How does it differ from the original?
   
2. A signal is sampled for 5 seconds at a sampling rate of 20 kHz. How many samples were taken?
3. Most sounds created by human speech except for 'ss' and 'ff' have a maximum frequency of 4 kHz. What is a suitable sampling rate for a low-quality telephone?
4. Using a sampling rate of 20 kHz and 3 bits, sample the following signal, and then produce a reconstructed signal. What is the maximum frequency that can be perfectly reconstructed using this sampling rate?

Signal Frequencies

1. What is the frequency of an X-ray (wavelength 0.5nm)?
2. A sound wave, with a frequency of 44 kHz, has a wavelength of 7.7mm. What is the speed of sound?
3. What is the fundamental frequency of the following signal?
   
4. Approximately how many harmonics does it contain?
5. The three sine waves sin x°, 4sin(2x-50)° and 0.5sin(3x+120)° are added together to form a signal. What are the frequencies of each of the waves? What is the signal's fundamental frequency? Assume that the waves are travelling at the speed of light, and that 60° = 1mm.

Bandwidth

1. A broadband internet connection has a bit rate of 8Mbit s^-1 when downloading information. What is the minimum bandwidth required to carry this bit rate?
2. The same connection has a bandwidth of 100 kHz reserved for uploading information. What is the maximum bit rate that can be attained when uploading information using this connection?
3. A lighthouse uses a flashing light and Morse Code to communicate with a nearby shore. A 'dash' consists of the light being on for 2s. The light is left off for 1s between dots and dashes. What is the bandwidth of the connection?
4. The broadband connection in question two is used to upload a 1Mbyte image to a website. How long does it take to do this?