Homework2 - Homework Assignment 2 ECE 155A Winter 2009 Due...

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Homework Assignment 2 ECE 155A - Winter 2009 Due Friday, January 23 1. The Nyquist theorem and the Shannon theorem are fundamental results that relate the maxi- mum data rate of a communication channel to its bandwidth, in the case of a noiseless channel and a noisy channel, respectively. a. The bandwidth of a noiseless communication channel is 3500 Hz. The signal has the values 0, 1, 2, ..., 255. What is the maximum data rate of the channel? b. The bandwidth of a noisy communication channel is 3.5 kHz The channel has a signal to noise ratio of 100. What is the maximum data rate of the channel? 2. Consider the ASCII character ’a’, encoded as the 8-bit byte 01100001, which is the bit pattern that is transmitted. Assume that the data rate of the communication channel is 9600 bits/sec, and that the data rate equals the baud rate, i.e. , one bit per signal. a. Graph the square wave for the above bit pattern. b. Find the Fourier approximation for this bit pattern using the first 4 harmonics (terms of the Fourier series).
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