stochastic process used in solving the cellular communication.. solution must be without matlab. Continuous Fourier Transform & Discrete Fourier transform are defined below: 21r T "T Zrnm ) F (w) = f...

Answer
1.) Bandwidth given = B
No of Samples = N
Frequency resolution is defined as
= Sample Rate / FFT Points
Frequency resolution = T/N
Observation time window is given by,
Tw = 1/ Frequency resolution
= 1/ T/N
= N/T
Time Resolution is nothing but inverse of Frequency resolution, so
Ts = 1/ frequency resolution
= N/T
Observation frequency Window is,
= Bandwidth of the Same / Sample Size
= B/ N
Answer
From the given equation of Fourier spectrum F(ω) we have,
F(ω) = ∫ ( ) ( )



= ∫ ( ) ( ) ( )



= ∫ ( ) ( ) ( ) ( )


Answer
Speed of train = 120m/s
Frequency = 2GHz
Data rate = 10kbits/s
So, Maximum doppler shift = v*f/c
= 120*2 x 109 / 3 x 108
= 800 Hz
Order of coherent time will be,
= 1/ Doppler shift
= 1/ 800
= 1.25 ms
Approximate Symbol duration,
fs = R / N
800 = 10000 / N
N = 12.5
So, symbol duration will be ,
Ts = 0.1ms
Bandwidth,
B = f*N
= 800*12.5
= 10 kHz
Answer
Then new bandwidth will be,
= 10kHz + 200 kHz = 210kHz
Answer: Slowly varying Narrow band Channel.
Answer
E(x1) , E(x2) , E(x3) = 0 as zero mean gaussian mode.
And ,
STD(σ) = 1
So,
Var(x1) = E(x12) = 1
Var(x2) = E(x22)...