Date post: | 23-Dec-2015 |
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The spreading and smearing of the signal such that the energy from one symbol effects the next ones in such a way that the received signal has higher probability of being interpreted incorrectly is called Inter symbol interference.
Pulse generator
Decision device
Receiving Filter
Channel 1Transmitted filter +
White gaussian
noise
x(t)
y(t)yi(t)
Clock pulses
Sample at time t= nTb
Causes of ISI
• Imperfections in the overall frequency response of the system.
• When short pulse is transmitted, frequency components are differentially attenuated and differentially delayed by the system.
• Pulse appears to be dispersed.
What can be done to solve it?
• Simplest thing can be to slow down the signal.
• If delay spread is less than or equal to symbol time, there will be no ISI.
• But slowing down the data rate is very unacceptable in today’s time.
What else can be done?
• Pulse shaping.
How it helps?
• When timing pulse slices the signal to determine the value of signal at that instant, digital demodulator does not care about shape of the pulse.
Bandwidth
• Bandwidth of the signal is equal to symbol rate for low pass signals twice of the symbol rate for band pass
signals
Disadvantages of Square pulse
• Square pulse is difficult to crate in time domain because of the rise time and decay time.
• Its frequency response goes on forever and decays slowly.
• Very sensitive to ISI.
• If the square pulse gives sinc function in frequency domain, then couldn’t we use sinc function in time domain to get brick wall square pulse in frequency domain?
• Yes we can use sinc function shaped pulse and have nothing spilling out of the bandwidth.
One more wonderful part about using sinc function !
• Bandwidth required is half of the symbol rate.• Nyquist bandwidth.
Problem faced with sinc function
• In time domain, sinc function have infinite length with tails extending to infinity, so theoretically energy continues to add up even after signal has ended.
• The pulse that falls in adjacent symbols decay at the rate of 1/x so if there is error in timing, its not forgiving.
Solution ?
• Nyquist offered ways to build realizable pulses that had a good quality as sinc pulse and has less disadvantages.
• One class of pulse offered was raised cosine pulses.
• Sinc pulse has bandwidth, W= 1/2Ts, while raised cosine pulses have adjustable Bandwidth between W to 2W.
• Purpose is to achieve bandwidth as near to ideal Nyquist bandwidth as possible.
• The factor α called roll off factor relates ideal bandwidth to achieved bandwidth as
• Another way to indicate utilized bandwidth is