Communications Homework Help

Part C [15Marks] A Telemetry System uses FSK modulation. It has a carrier frequency of 1 MHz, and a frequency deviation of 30KHz. It is modulated by a 10kbps bit stream. Determine: ● ● ● The modulation index. The bandwidth and sketch the signal in the frequency domain. Discuss whether FSK is an appropriate modulation scheme. Support your answer with some technical facts.

An information source can be modeled as a bandlimited process with a bandwidth of 6000 Hz. This process is sampled at a rate higher than the Nyquist rate to provide a guard band of 2000 Hz. We observe that the resulting samples take values in the set A={-4, -3, -1, 2, 4, 7) with probabilities 0.2, 0.1, 0.15, 0.05, 0.3, 0.2. What is the entropy of the discrete time source in bits per output (sample)? What is the information generated by this source in bits per second?

A source has an alphabet (a₁, a2, a3, a4} with corresponding probabilities (0.1, 0.2, 0.3, 0.4). 1. Find the entropy of the source. 2. What is the minimum required average code word length to represent this source for error-free reconstruction? 3. Design a Huffman code for the source and compare the average length of the Huffman code with the entropy of the source. 4. Design a Huffman code for the second extension of the source (take two letters at a time). What is the average code word length? What is the average number of required binary letters per each source output letter? 5. Which is a more efficient coding scheme: the Huffman coding of the original source or the Huffman coding of the second extension of the source?

A discrete memoryless information source is described by the alphabet x = {x1, x2, x3, x4, X5, X6) with probabilities (1/32, 1/8, 1/2, 1/16, 1/32, 1/4), respectively. 1. Design a Huffman code for this source and determine the average code word length of the Huffman code. 2. Can you improve the Huffman code by encoding the second extension of this source (in other words, using two letters at a time and designing the Huffman code for that source)? Why? 3. Is there any way to improve the performance of the Huffman code designed in Part 1? (By improving the performance, we mean designing a code with a lower average code word length.)

In Example 13.2.1, find the minimum distance of the code. Which code word(s) is (are) minimum weight?

By listing all code words of the (7, 4) Hamming code, verify that its minimum dis- tance is equal to 3.

Data at a rate of 6 Kbps is to be transmitted over a channel with a bandwidth of 4 KHz using raised cosine pulses and binary signaling. What is the maximum roll-off factor, a, that can be used?

The message signal m(t) = 10 sinc(400t) frequency modulates the carrier c(t) = 100 cos(2 fet). The modulation index Bf = 6. 1. Write an expression for the modulated signal u(t)? 2. What is the maximum frequency deviation of the modulated signal? 3. Find the bandwidth of the modulated signal.

The signal m(t) is shown below. This signal is used once to frequency modulate a carrier and once to phase modulate the same carrier. Find a relation between kp and kf such that the maximum phase of the modulated signal in both cases are equal.

An angle modulated signal is given by u(t) = 100 cos (2π fet + 4 sin(2000xt)) where fe 1. Determine the average transmitted power. 2. Determine peak-phase deviation. 3. Determine the peak-frequency deviation. 4. Is this an FM or a PM signal? Explain 10 MHz.