Q.1: Consider the transmission of a sinusoid x(t) = cos(2f0t) through a channel aected
by multipath and Doppler. Let there be two paths, and assume the sinusoid is being sent
from a moving transmitter so that a Doppler frequency shift occurs. Let the received signal
be
r(t) = 0cos(2(f0 ?? v)(t ?? L0=c)) + 1cos(2(f0 ?? v)(t ?? L1=c))
where 0  i  1 are attenuations, Li are the distances from the transmitter to the receiver
that the signal travels in the ith path i = 1,2, c = 3  108 m/sec, and the frequency shift
v is caused by the Doppler eect.
(a) Let f0 = 2 KHz, v = 50 Hz, 0 =1, 1 = 0.9 and L0 = 10,000 meters. What would
be L1 if the two sinusoids have a phase dierence of =2 ?
(b) Is the received signal r(t), with the parameters given above but L1 = 10,000, periodic?
If so, what would be its period and how much does it dier from the period of the
original sinusoid? If x(t) is the input and r(t) the output of the transmission channel,
considered a system, is it linear and time invariant? Explain.
(c) Sample the signals x(t) and r(t) using a sampling frequency Fs = 10 KHz. Plot the
sampled sent x(nTs) and received r(nTs) signals for n = 0 to 2000.
(d) Consider the situation where f0 = 2 KHz, but the parameters of the paths are random,
trying to simulate real situations where these parameters are unpredictable, although
somewhat related. Let
r(t) = 0cos(2(f0 ?? v)(t ?? L0=c)) + 1cos(2(f0 ?? v)(t ?? L1=c))
where v = 50 HZ, L0 = 1,000, L1 = 10,000, 0 = 1 - , 1 = 0/10 and  is a
random number between 0 and 1 with equal probability of being any of these values
1
(this can be realized by using the rand MATLAB function). Generate the received
signal for 10 dierent events, use Fs = 10,000 Hz as the sampling rate, and plot them
together to observe the eects of the multipath and Doppler.

Posted Date: 11/6/2012 8:10:23 AM | Location : USA

Ask an Expert

Related Discussions:- signals,systems and networks, Assignment Help, Ask Question on signals,systems and networks, Get Answer, Expert's Help, signals,systems and networks Discussions

Write discussion on signals,systems and networks
Your posts are moderated

Write your message here..

Related Questions

Example of modular program, Example of modular program: In a modular p... Example of modular program: In a modular program, there would be one main script which calls three separate functions to complete these tasks: A function to prompt an us

Function fieldnames - structure functions, Function fieldnames - structure ... Function fieldnames - structure functions: The function fieldnames will return the names of the fields which are contained in the structure variable. >> pack_fields = fiel

Data structures, Data structures: The Data structures are variables wh... Data structures: The Data structures are variables which store more than one value. In order to made sense to store more than one value in a variable, the values must in some

Function call - modular program, Function call: In the function call, ... Function call: In the function call, not any arguments are passed so there are no input arguments in the function header. The function returns an output argument, therefore th

Examine exponential function - algorithm, Examine exponential function: ... Examine exponential function: The algorithm for the main script program is shown below:  Call a function eoption to show the menu and return the user's choice.  Loop

Symbolic variables and expressions, Symbolic Variables and expressions: ... Symbolic Variables and expressions: The MATLAB has a type known as sym for the symbolic variables and expressions; these work with strings. The illustration, to generate a sym

Square matrices, Square Matrices: If a matrix has similar number of ro... Square Matrices: If a matrix has similar number of rows and columns, for illustration, if m == n, the matrix is square matrix. The definitions which follow in this part apply

Tracing of square matrices, Tracing of Square matrices: The trace of a... Tracing of Square matrices: The trace of a square matrix is the addition of all the elements on the diagonal. For illustration, for the preceding matrix it is 1 + 6 + 11 + 16,

Replacing a string - function strrep, Replacing a string - function strrep:... Replacing a string - function strrep: The function strrep finds all the occurrences of a substring within the string, and substitutes them with a new substring. The order of a

Example of file ploting data, Example of file ploting data: As the oth... Example of file ploting data: As the other example, a data file called 'compsales.dat' stores the sales figures (in millions) for divisions in a company. Each line in the f