Question

2. i. Consider a binary source alphabet where a symbol 0 is represented by 0 volt and a
symbol 1 is represented by 1 volt. Assume these symbols are transmitted over a
baseband channel having uniformly distributed noise with a probability density
function:
        px= {18 for-4≤x≤4 0

Assume that the single decision threshold T is in the range of 0 and l volt. If the
symbols 0 and 1 are sent with probabilities p0 and 1- p0 respectively, derive an
expression for the probability of error. (20 pts)

ii. Consider a telephone line channel. If the signal to noise ratio (SNR) is 40 dB and the bandwidth available is 2 kHz, calculate the corresponing channel capacity. (5 pts)   

    iii. A bandpass noise signal n(t) can be expressed as n(t) = nc(t) cosωct + ns(t) sinωct. Consider bandpass noise n(t) having the power spectral density shown below in Fig. 1.1. Draw the power spectral density of ns(t) if the center frequency ωc/2π is 20 MHz. (20 pts)

S (f)n
).

JJI
  
   (iv) (5 pts) Consider a communication channel where W, S and N0 2 denote the channel bandwidth, the received   signal power and the power spectral density of white noise, respectively. Assume that the power spectral density of noise is halved, while other parameters remain unchanged. What is the channel capacity?

Answer 1