ISI,PULSE SHAPING,RAISED COSINE FILTERS

1. One gains ¼ of the knowledge from the Acharya (the teacher), ¼ from
his own self-study and intellect, ¼ from his classmates and the
remaining ¼ is gained as a person becomes matured as time passes.

2. COMMUNICATION ENGINEERING
Mr.R.VIJAY ANANDH

3. • INTER SYMBOL INTERFERENCE (ISI)
• PULSE SHAPING
• DUOBINARY SIGNALLING
SESSION TOPICS

4. ➢ The input pulse get broaden beyond its Tbor
ꞇ when it travels long distance in channel
and causes errors in the correct detection of
pulses at the receiver.

5. ➢ The input pulse get broaden and interfere with each
other in the channel causing ISI.
➢ It occurs in time domain.
➢ Receiver misinterpt the data as all ones.
Note: Aliasing occurs in frequency domain due to
improper sampling
1 1 0 1 0 0 1
1 1 1 1 1 1 1

6. ➢ During the modulation process of the signal, if the
modulation rate increases, the signal's bandwidth increases.
➢ The signals are time-limited and not band-limited but
channel is band limited one.
➢ When the signal's bandwidth becomes larger than the
channel bandwidth, the channel starts to introduce distortion
(spreading out) to the signal.
➢ This distortion usually manifests itself as intersymbol
interference.
➢ Question : What is the reason for the Channel to distort the
signal ?
Basic cause of ISI

7. Bandlimited channels
• The cause of intersymbol interference is the
transmission of a signal through a bandlimited channel,
• i.e., Bandlimited means the frequency response is zero
above a certain frequency (the cutoff frequency).
• Passing a signal through such a channel results in the
removal of frequency components above this cutoff
frequency.
• In addition, components of the frequency below the
cutoff frequency may also be attenuated by the channel.

8. How to eliminate ISI
To eliminate ISI,
• Pulse shaping
• Cosine filters
• Duo binary encoding

9. ➢ Data is transmitted as ones and zeros which can be represented using
rectangular pulses of finite duration ꞇ.
➢ The frequency domain representation of rectangular pulse is a sync
pulse of infinite duration whose most of the energy is concentrated
within - ꞇ/2 and + ꞇ/2.
➢ This implies a pulse of duration ꞇ requires twice its bandwidth for
reliable transmission for a band-limited system

10. This implies a pulse of duration ꞇ requires
twice its bandwidth for reliable transmission
for a band-limited system

11. For a band-limited system, if we want to
increase the data rate, then we have to increase
the number of pulses transmitted every second.
What happens when u increase the pulses ?
No. of Pulses increased

12. What happens when u increase the pulses ?
This implies that the pulse duration Tb or ꞇ will have to be decreased.
A decrease in the
time period ꞇ
indicates an increase
in the bandwidth
If the channel is band limited this increase in the bandwidth may
overlap with the neighbouring channels leading to ISI.

13. ➢ If the channel is band limited this increase in the
bandwidth may overlap with the neighbouring channels
leading to inter-symbol interference (ISI).

14. ➢ To mitigate ISI Nyquist suggested theoretically, that the
minimum bandwidth needed for transmission of Rb symbols
per second is Rb/2 Hertz and when a pulse is transmitted
through a channel with sufficient bandwidth. Here , Rb is
called bit rate of transmission.
BW >= Rb /2
BW < Rb /2
Rb Symbols per second

15. To maintain zero ISI, the following conditions must satisfy :
i.e., the pulse should be 1 at sampling instant zero and should
be equal to 0 for all other integral multiples of bit period Tb
How do practically implement the conditions…?

16. The answer is pulse shaping .
• Pulse shaping is the process of changing the
waveform of transmitted pulses suited to
the communication channel.
• It is done by limiting the effective bandwidth of the
transmission.
• By filtering the transmitted pulses this way,
the intersymbol interference caused by the channel
can be kept in control.

17. Pulse Shaping
• In many base band communication systems the
pulse shaping filter is implicitly a boxcar filter.
• Its Fourier transform is of the form
𝑆𝑖𝑛 𝑥
𝑥
, which
is known as Sinc function.
(ie.., Sinc ∅=
𝑆𝑖𝑛 ø
ø
)

18. Pulse shaping filters
➢Not every filter can be used as a pulse shaping
filter. The filter itself must not introduce
intersymbol interference — it needs to
satisfy Nyquist ISI criterion.
➢Examples of pulse shaping filters that are
commonly found in communication systems are:
• Sinc shaped filter
• Raised-cosine filter
• Gaussian filter

19. • There are two criteria for non interference systems where
pulse shaping is employed.
(1) The pulse shape exhibits a zero crossing at the sampling
point of all pulse intervals except its own. (i.e..,it is zero at
all points outside of the present pulse interval. )
(2) The pulse shape must be such that the amplitude decays
rapidly outside the pulse interval. (i.e., Thus, the quicker a
pulse decays outside of its pulse interval, the less likely it is to
allow errors when sampling adjacent pulses.)
TIME DOMAIN FREQUENCY DOMAIN
Nyquist criterion

20. 1st Nyquist Criterion for Zero ISI
• In the first method, Nyquist achieves zero IS1 by choosing a
pulse shape that has a non zero amplitude at its center (say t
= 0) and zero amplitudes at t = ±nTb
(n = 1, 2, 3, . . .),
• We can write such a pulse as:
• There exists one (and only one) pulse that meets Nyquist's 1st
criterion and has a bandwidth Rb/2 Hz. This pulse is
p(t) = sinc (nRbt)
• The Fourier transform of this i
• Using this pulse, we can transmit at a rate of Rb pulses per
second without ISI, over a bandwidth of Rb/2.
s

21. 1st Nyquist Criterion Pulse shape
10

22. Limitation of 1st criterion pulse
• Unfortunately, this pulse is impractical because it
starts at ‐∞.
• But even if this pulse were realizable, it has the
undesirable feature that it decays too slowly at a rate
1/t.
• This causes some serious practical problems.
11

23. What is the solution…
• Practically, energy does not decay rapidly outside the
pulse , in fact it extends to infinity bandwidth.
• Hence, we have to use a raised cosine pulse, which
satisfies both the criteria and thus provide an ISI free
system .

24. Raised Cosine pulse
• A raised cosine pulse takes the shape of a sinc pulse
in time domain and hence it’s frequency domain
representation is similar to a gating function does
(ie., mask unwanted signals) .

25. Raised Cosine pulse
• we can limit the signal bandwidth in the frequency
domain avoiding ISI using rasied cosine pulses.

26. Raised Cosine spectrum
• The solution is to find a pulse p(t) that
satisfies the condition specified but decays
faster than l / t .
• Nyquist had shown that such a pulse requires
a bandwidth of kRb/2, with 1 ≤ k ≤ 2.

27. Bandwidth =
Freq. spectrum

28. Bandwidth =
Freq. spectrum

29. Raised cosine Spectrum

30. Hence, ensure an optimum balance between the role of factor
and the bandwidth it occupies in order for the pulse to travel
undistorted in a band-limited channel.
Raised cosine Spectrum

31. Roll Off factor
• Let r (roll off factor) be the ratio of the excess bandwidth w,
to the theoretical minimum bandwidth then
r =
Excess BW
=2W / R
Wx
Theoretical Minimum BW
=
Rb / 2 x b

32. Observe that because wx is at most equal to wb/2 and
0 < r < l
The theoretical minimum bandwidth is Rb/2 Hz, and
the excess bandwidth is thus fx = r Rb/2 Hz.
Therefore, the bandwidth of P(w) is

33. Pulses satisfying the Nyquist criterion.

35. SUMMARY