2. i. Consider a binary source alphabet where a symbol 0 isrepresented by 0 volt and a
symbol 1 is represented by 1 volt. Assume these symbols aretransmitted over a
baseband channel having uniformly distributed noise with aprobability density
function:
        px= {18 for-4≤x≤40

Assume that the single decision threshold T is in therange of 0 and l volt. If the
symbols 0 and 1 are sent with probabilities p0 and 1- p0respectively, derive an
expression for the probability of error. (20 pts)

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

    iii. A bandpass noise signal n(t)can be expressed as n(t) = nc(t) cosωct + ns(t) sinωct. Considerbandpass noise n(t) having the power spectral density shown belowin Fig. 1.1. Draw the power spectral density of ns(t) if the centerfrequency 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 ishalved, while other parameters remain unchanged. What is thechannel capacity?