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WHAT'S YOUR ENGINEERING QUOTIENT?

Problem 1—Anyone who has worked with spectral analysis knows that a squarewave contains all of the odd harmonics, where the amplitude is one over the frequency ratio. In other words, if the fundamental frequency has an amplitude of one, the third harmonic has an amplitude of one third, and so on.

What is special about the following waveform, which can be constructed by taking two squarewaves and adding them together after shifting one by one-sixth of a period relative to the other?

ANSWER

Problem 2—Draw a hybrid circuit using flip-flops and opamps that can produce the above waveform.

ANSWER

Problem 3—If you have four flip-flops and three resistors, how would you calculate the resistor values to get the best approximation to a sinewave? What is the advantage of synthesizing sinewaves this way?

ANSWER

Problem 4—Assuming 1% resistors, what is the largest reasonable number of stages to use?

ANSWER

Problem 5—You are given the task of designing a foward-error-correcting (FEC) scheme that will tolerate a bit error rate (BER) of 10^-3 with no significant degradation. Furthermore, you must use a minimum of additional bandwidth to accomplish this, preferably less than 4%.

"Fine," you say. "I'll use Reed-Solomon coding with a relatively large block size, say 200 bytes. A BER of 10^-3 is about one bad bit in 1000. In a block of 200 bytes (1600 bits), I'll typically see one or two errors. R-S coding requires two check bytes per byte corrected, so I only need 4 out of the 200 bytes to be check bytes, for an overhead of just 2%."

What is the flaw in this reasoning?

ANSWER

Problem 6—For a given bit error rate, how do you calculate the probability of an error in an 8-bit byte?

ANSWER

Problem 7—What is the probability of finding more than two byte errors in a block of 200, given a BER of 10^-3?

ANSWER

Problem 8—How many check bytes would be required in a block of 200 in order to reduce the probability of an uncorrectable block to approximately 0.001, given a BER of 10^-3?

ANSWER

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