1. The available bandwidth for FM radio is 88 - 108 MHz. When each channel is allocated a bandwidth of 200 kHz, what is the maximum number of channels that are available assuming the bands are adjacent with no guard bands?

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.

Problem 1. (12 points) A random variable X takes on the value +1 exactly 3/8 time, -1, exactly 1/8 of the time and can take on any values in the interval [-3 to 3] uniformly the rest of the time. a) Sketch the probability density function (PDF) of X. f(x) d) Calculate the probability X> +1.

10. Find the number of voice channels for a TDMA link with the total transmission rate of 50Mbps, if the TDMA frame efficiency of 74%, calculate the total useful bit rate. If the voice channel rate of 64 Kbps.

1. What is the resulting bit rate in bits per second? 2. What is the resulting SQNR (in dB)? 3. What is the required transmission bandwidth? 4. If the available transmission bandwidth is 70 kHz, what is the maximum achiev- able SQNR (in dB)?

Part A [20 Marks] Consider an ASK (Amplitude Shift Keying) modulation system. The modulating signal is digital bit stream with a bitrate of 2kbps. The modulating signal amplitude is 0 to 5 Volts. The carrier signal is 12 Vpp signal and has a frequency of 800kHz. ● ● ● Sketch the ASK signal indicating signal levels. Calculate the modulation index. Sketch the frequency spectrum. Determine the bandwidth of the ASK signal.