HW10%20Solutions[1] - EECS 314 Winter 2007 HW 10 Problem 1...

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Unformatted text preview: EECS 314 Winter 2007 HW 10 Problem 1 Student's name ___________________________ Discussion section # __________ (Last name, first name, IN INK) 2007 Alexander Ganago The big picture As you know from lecture notes, music on CD is recorded with 16- or 20-bit resolution, at the sampling rate of ~ 44 kHz. As you know from reading the labels, a blank CD has the capacity of 700 MB (megabytes; 1 Byte = 8 bits; 1 MB ~ 10 6 Bytes) and is rated for 80 minutes of music recording. In this Problem, you will put 2 and 2 together in order to see whether all of the above numbers make sense. Problem Part 1 (15 points) Assume that the music is recorded in two channels (stereo = left and right) that have the same resolution of 16 bits and the same sampling rate of 44 kHz. Calculate the amount of memory in MB required to record 1 minute of music. Your answer: _______________________ MB per minute of music Assume that a blank CD has the capacity of 700 MB. Calculate how many minutes of music can be stored on the CD. Your answer: T = _______________________ minutes on CD If your answer above is less than 80 minutes, it means that a data compression algorithm is used to record the data on music CDs. The compression can be easily quantified: for example, if you estimate the needed memory as 1 MB and the actual record requires only 0.8 MB, then the compression ratio equals 1/.8 = 1.25, which is very modest compared to that used in MP3 technology. Discuss your answer: if you found T > 80 minutes, no compression is needed. If, however, you found T < 80 minutes, compression is needed, and you are asked to calculate the compression ratio. Your answer on compression: _______________________________________________ Part 2 (10 points) Repeat Part 1 for 20-bit music recording. Your answer: _______________________ MB per minute of music Your answer: T = _______________________ minutes on CD Your answer on compression: _______________________________________________ Show your work for both parts on a separate page. Problem #1 Solution Each sample is recorded as a 16 bit binary number. Since both channels share the same parameters, we can solve for one channel and double the result. Starting with the sampling rate and the resolution, we can find the number of MB required for 1 minute of recording min 56 . 10 2 min 1 60 10 1 8 1 1 16 sec 44000 6 MB s byte MB bits byte sample bits ond sample = Now divide the capacity of the blank CD by the storage rate. . min 29 . 66 . min 56 . 10 700 = MB MB The answer is less than the 80 minutes which means that a data compression algorithm was used to record the data. Next, find the compression ratio....
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HW10%20Solutions[1] - EECS 314 Winter 2007 HW 10 Problem 1...

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