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In
pulseshape2.m , examine the effect of using
different oversampling rates
M .
Try
M= 1, 5, 100.
Change
pulseshape2.m so that the data sequence
is drawn from the alphabet
.
Can you visually identify the correct values in thepulse shaped signal?
In
pulseshape2.m , examine the effect of using
sinc approximations of different lengths
L .
Try
L= 1, 5, 100, 1000.
In
pulseshape2.m , examine the effect of adding noise
to the received signal
x . Try M
atlab commands
randn and
rand . How large can the noise be and still
allow the data to be recognizable?
The goal is to design a frequency-division multiplexed (FDM) system with a square root raised cosine as thetransmitter pulse shape. The symbol period is = 137 msec. The design uses sampling, pulse lengths of , and a rolloff factor of 0.9, but it does not work, since only three modulated carrier signalsfit into the alloted bandwidth without multiuser interference. Five are needed. What parameters in the design would you change and why?
Using the code from
[link] ,
examine the effects of adding noise in
pulseshape2.m .
Does the same amount of noise in the 6-level datahave more or less effect than in the 2-level data?
Modify
pulseshape2.m to include the effect of a
nonunity channel. Try both a highpass channel and abandpass channel. Which appears worse? What are reasonable criteria
for “better” and “worse” in this context?
A M
atlab question: In
pulseshape2.m , examine the effect of using
the
filtfilt command for the convolution instead
of the
filter command. Can you figure out
why the results are different?
Another M
atlab question: In
pulseshape2.m , examine
the effect of usingthe
conv command for the convolution instead
of the
filter command. Can you figure out
how to make this work?
Consider a multilevel signal drawn from a finite alphabet with values , where is the sampling interval. Let be the impulse response of the linear filter representing the pulse shape. The signal just afterpulse shaping is
where is the pulse train signal [link] .
The corresponding output of the received filter is
as depicted in [link] , where is the impulse response of the channel and is the impulse response of the receive filter. Let be the overall equivalent impulse response. Thenthe equivalent overall frequency response (i.e., ) is
One approach would be to attempt to choose so that attained a desired value (such as a pure delay) forall . This would be a specification of the impulseresponse at all , since the Fourier transform is invertible.But such a distortionless response is unnecessary, since it does not reallymatter what happens between samples, but only what happens at the sample instants.In other words, as long as the eye is open, the transmitted symbols are recoverableby sampling at the correct times. In general, if the pulse shape is zeroat all integer multiples of but one, then it can have any shape in between without causing intersymbol interference.
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