1. What is the definition of "Nyquist rate"? What is the "Nyquist sampling theorem"? Plot the signal ??(??) = sin(4????).
a. Assuming a sampling period ???? = 0.3 s, plot its samples. What has happened? Have you sampled above the Nyquist rate?
b. Assuming a bit depth of 4 bits and a sampling rate ???? = 24 Hz, plot its samples and convert the analog waveform defined by ??(??) into digital.
c. Convert the digital waveform back to analog using your results in (c). The reconstructed waveform should look like a staircase.
2. ASCII encodes English text by using 1 byte (including parity bit) per symbol. Takeany book that you have read recently and pick a page at random. Take any full line on that pageand count the number of symbols in the line of text. Do not forget to count spaces and punctuation marks. Next, count the number of lines on the page. Now multiply the number of symbols per line by the number of pages in the book. Make sure to justify your work, indicate the total number of pages in the book you picked and include a hard copy of the page in your report.
a. About how many bytes would it take to store all of the characters and punctuation in this book, using ASCII code as a formatting method?
b. A CD-ROM holds around 700 MB of information. How many similar books could be stored on a CD-ROM using ASCII?
c. Using the same full line on that page, find the Huffman codebook and the number of bytes needed to store one line of text. About how many bytes would it take to store all of the characters and punctuation in this book, using Huffman as a formatting method? Compute the compression ratio using your results in (a).
3. (30 points) An 8 × 8 pixel image is defined as follows. The four corner pixels all have a value of 15. The two central columns and the two central rows have a value of 15. All other pixels have a value of 0.
a. Write this image as a grid of numbers and draw it. What is the total number of pixels in the image? How many bits are needed to represent the gray values of the pixels? What is the total number of bits needed to represent the image?
b. If we reduce the sampling rate for the image by a factor of two along rows and columns, what will be the size of the new image? Write this image as a grid of numbers rounded to the nearest integer. Draw the new image.
c. Many different 8 × 8 images will look the same as the result you found in (b) when the sampling rate is reduced by a factor of two. Specify one of these 8 × 8 images that is as different from the image specified in (a) as you can make it. Write your image as a gridof numbers and draw it.