(ELEC121)[2010](s)quiz~1748^_10276.pdf

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ELEC121

Quiz #2 Review Question

Problem 1. Suppose management has decided to use 20-bit data blocks in the company's new (n,20,3) error correcting code. What's the minimum value of n that will permit the code to be used for single bit error correction, i.e., that will achieve a minimum Hamming distance of 3 between code words?

Problem 2. Consider the following (n,k,d) block code:

D0 D1 D2 D3 D4 |P0

D5 D6 D7 D8 D9 |P1

D10 D11 D12 D13 D14 | P2

P3 P4 P5 P6 P7 |

where D0-D14 are data bits, P0-P2 are row parity bits and P3-P7 are column parity bits. The transmitted code word will be:

D0 D1 D2 ... D13 D14 P0 P1 ... P6 P7

A.

Please give the values for n,k,d for the code above

B.

If D0 D1 D2 ... D13 D14 = 0 1 0 1 0, 0 1 0 0 1, 1 0 0 0 1, please compute P0

through P7.

C.

Now we receive the four following code words:

M1: 0 1 0 1 0, 0 1 0 0 1, 1 0 0 0 1, 0 0 0 1 1 0 1 0

M2: 0 1 0 1 0, 0 1 0 0 1, 1 0 0 0 1, 0 0 1 1 1 0 1 0

M3: 0 1 0 1 0, 0 1 0 0 1, 1 0 0 0 1, 1 1 0 1 1 0 1 0

M4: 0 1 0 1 0, 0 1 0 0 1, 1 0 0 0 1, 1 0 0 1 1 0 1 0

For each of received code words, indicate the number of errors. If there are errors, indicate if they are correctable, and if they are, what the correction should be.

Problem 3. In answering the following questions, please refer to the following three plots of the magnitude of three frequency responses, |HI(ej.)|, |HII(ej.)|, and |HIII(ej.)|, given below.

A. Suppose the input to a linear time invariant system is the sequence

2 n

x[n] = 2 + cos n + cos n + 3(.1)

66

What is the maximum value of the sequence x, and what is the smallest positive value of n for which x achieves its maximum?

B. Suppose the sequence X from part A is the input to a linear time invariant

system described by one of the three frequency response plots above (I, II or III).

If y is the resulting output and is given by

y[n] = 8 + 12(.1)n,

Which frequency response plot describes the system, and what is the value of M

in the plot you selected? Be sure to justify your selection.

Problem 4

Single-sideband (SSB) modulation is a modulation technique designed to minimize the amount of footprint used to transmit an amplitude modulated signal. Here's one way to implement an SSB transmitter.

(A)

Starting with a band-limited signal s[n], modulate it with two carriers, one phase shifted by /2 from the other. The modulation frequency is chosen to be B/2, i.e., in the middle of the frequency range of the signal to be transmitted. Sketch the real and imaginary parts of the Fourier coefficients for the signals at points A and B. The figure below shows the Fourier coefficients for the signal s[n].

(B)

The modulated signal is now passed through a low-pass filter with a cutoff frequency of B/2. Sketch the real and imaginary parts of the Fourier coefficients for the signals at points C and D.

(C)

The signal is modulated once again to shift it up to the desired transmission frequency. Sketc