This is the Last Homework set! And it's an important one, particularly for those who have missed some homeworks. Your homework grade (which is 20% of your final grade) is a straight average of all your homework and the quiz, but with the worst of those grades dropped. If the present, last homework is better than that average (showing an overall improvement during the term), I will drop another low grade from the average, in effect two missed homeworks will be forgiven. So, show me (the TA, actually) how smart you really are!

1. Text, Chapter 7, problem 6

2. Text, Chapter 7, problem 12

3. The frequencies important for voice communication range up to 4000 Hz. (The audiospectrograms of Figure 6-12 extend from 0 to 8 kHz on the vertical - unmarked, tsk tsk - scale; note that the important formants do not extend above 4 kHz, i.e. halfway to the maximum).

1. At what rate should you sample a voice signal for digital reproduction of this frequency range?
2. Next, the sampled signal is quantized. 255 amplitudes turn out to be sufficient (versus the 65536 amplitude steps on a CD, see p. 212 -- voice needs not nearly as much "fidelity" as music!) How many binary bits are needed? This number of binary bits is called a "word".
3. So, what is the number of bits per second (b/s) that need to be transmitted?
4. A "T-1 line" transmits 1.44 Mb/s. How many "voice circuits" can it carry simultaneously (for example, by sequentially transmitting one word at a time from each voice circuit)?
5. What is the name for the process of transmitting several individual signals over a common path?

4. Try your hand at file compression. You will pattern this after the example found in Howstuffworks.

1. Find more redundancies in that example by including parts of words* and word combinations. For example, "what you" can be one dictionary unit, say number 3, and you would write "what your" as 3r. To how small a number of units can you compress the 79-unit sentence? Remember to count spaces and punctuation marks in the sentence, but in the dictionary only if they are part of the definition: you would write the dictionary entry as "3what you" and count that as 9 units.
2. Now you choose a somewhat longer sentence (a saying that rhymes is a good choice) and show how to compress it. Your dictionary may contain parts of words ("the rain in Spain ..." would have an entry "ain"), but you'll find short ones have to occur many times to make a dictionary entry worth while.