dsp mulation and translation

1. PRESENTATION ON
1.FREQUENCY TRANSLATION
2.MODULATION TECHNIQUES
3.SINAL DETECTION
4.OVER RANGING ISSUE
Motilal Nehru National Institute of Technology Allahabad (MNNIT Allahabad)
Department Of Electrical Engineering
PRESENTED BY:-
Abhishek Kumar (2022PE22)
Prity Kumari (2022PE16)

2. Frequency Translation
One of the basic problems of communication engineering
in the design and analysis of systems which allow many
individual messages to be transmitted simultaneously over
a single communication channel.
A method by which such multiple transmissions are done
is known as multiplexing
It may be achieved by translating each message to a
different position in the frequency spectrum.

3. ► Such multiplexing is called frequency multiplexing.
► Frequency multiplexing involves the use of an auxiliary
waveform, usually sinusoidal,called a carrier.
► The operation performed on
frequency multiplexing result
the signal to achieve
in the generation of
waveform which may be described as the carrier modified
in that its amplitude, frequency or phase varies with time
► Such a modified carrier is called a modulated carrier

4. Frequency Translation
It is often advantageous and convenient to translate a signal
from one region in the frequency domain to another region
Theprocess of frequency translation is one in which the
original signal is replaced with a new signal whose spectral
range extends from f1’ to f2’ and which new signal bears,in
recoverable form, the same information as was borne by the
original signal.

5. Frequency Multiplexing
Suppose that we have several different signals, all of which
encompass the same spectral range.
Let it be required that all these signals be transmitted along a
single communications channel in such a manner that, at the
receiving end, the signals be separately recoverable and
distinguishable from each other.
The single channel may be a single pair of wires or the free
space that separates one radio antenna from another.
Such multiple transmissions, i.e., multiplexing, may be
achieved by translating each one of the original signals to a
different frequency range.

6. Suppose, say, that one signal is translated to the frequency range f1’ to f2’,the
second to the range f1" to f2”, and so on.
If these new frequency ranges do not overlap, then the signal may be separated
at the receiving end by appropriate bandpass filters.
The outputs of the filters are processed to recover the original signals.
Practicability ofAntennas:
When free space is the communications channel, antennas radiate and receive
the signal

7. It turns out that antennas operate effectively only when
their dimensions are of the order of magnitude of the
wavelength of the signal being transmitted.
A signal of frequency 1 kHz (an audio tone) corresponds
to a wavelength of 300,000 m, an entirely impractical
length.
The required length may be reduced to the point of
practicability by translating the audio tone to a higher
frequency.

8. Narrowbanding:
Returning to the matter of the antenna, just discussed,
suppose that we wanted to transmit an audio signal directly
from the antenna, and that the inordinate length of the
antenna were no problem
We would still be left with a problem of another type
Let us assume that the audio range extends from, say, 50 to
104 Hz.
The ratio of the highest audio frequency to the lowest is
200.

9. Therefore, an antenna suitable for use at one end of the range
would be entirely too short or too long for the other end
Suppose, however, that the audio spectrum were translated so
that it occupied the range, say, from (106 + 50) to (106 + 104)
Hz.
Then the ratio of highest to lowest frequency would be only
1.01.
Thus the processes of fre¬quency translation may be used to
change a “wideband” signal into a “ narrowband ” signal which
may well be more conveniently processed.

10. The terms “ wideband ” and “ narrowband ” are being used here to refer not to
an absolute range of frequencies but rather to the fractional change in
frequency from one band edge to the other.
Common Processing:
It may happen that we have to process a number of signals similar in general
character but occupying different spectral ranges
It will then be necessary, as we go from signal to signal, to adjust the
frequency range of our processing apparatus to correspond to the frequency
range of the signal to be processed
If the processing apparatus is rather elaborate ,it may well be wiser to leave
the processing apparatus to operate in some fixed frequency range and instead
to translate the frequency range of each signal in turn to correspond to this
fixed frequency.

11. A method of Frequency Translation
A signal may be translated to a new spectral range bymultiplying
the signal with an auxiliary sinusoidal signal.
To illustrate the process, let us consider initially that the signalis
sinusoidal in waveform and given by:
vm(t)=Am cosωmt=Amcos2πfmt
𝑒𝑗𝜔𝑚𝑡+ 𝑒−𝑗𝜔𝑚𝑡
= 𝐴𝑚
= 𝐴𝑚
2 2
(1a)
𝑒𝑗2𝜋𝑓𝑚
𝑡+ 𝑒−𝑗2𝜋𝑓𝑚𝑡
(1b)
in which Am is the constant amplitude and fm=wm/2π is thefrequency.

12. The two sided spectral amplitude pattern of this signal is shown
in fig.(a).
(a)Spectral pattern of the waveformAmcosωmt
(b)Spectral pattern of the product waveform AmAc cosωmt cosωct

13. The pattern consists of two lines,each of amplitude Am/2 locatedat
f = fm and at f = -fm.
Consider next the result of multiplication of vm(t) with an auxiliary
sinusoidal signal
vc (t)=Ac cos ωct=Ac cos 2πfct
𝑒𝑗
𝜔
𝑐
𝑡+ 𝑒−𝑗𝜔𝑐𝑡
= 𝐴𝑐
= 𝐴𝑐
2 2
(2a)
𝑒𝑗
𝜋
𝑓
𝑐
𝑡+ 𝑒−𝑗2𝜋𝑓𝑐
𝑡 (2b)
In which Ac is the constant amplitude and fc is the frequency.

14. Using the trigonometric identity
cosα.cosβ= 1
cos(α + β)+ 1
cos(α - β),we have for the product
2 2
vm(t). vc(t)= 𝐴𝑚𝐴𝑐
2
cos 𝜔𝑐 + 𝜔𝑚 𝑡+ cos 𝜔𝑐 − 𝜔𝑚 𝑡 (3a)
= 𝐴𝑚𝐴𝑐
4
𝑒
𝑗𝜔𝑐+𝜔𝑚 𝑡+ 𝑒−j 𝜔𝑐+𝜔𝑚 𝑡+ 𝑒
𝑗𝜔𝑐−𝜔𝑚 𝑡+ 𝑒−j 𝜔𝑐−𝜔𝑚 𝑡
(3b)
The new spectral pattern is shown in fig.(b)
Observe that the two original spectral lines have been translated,
both in the positive frequency direction by amount fc and also in the
negative frequency direction by the same amount.

15. There are now four spectral components resulting in two
sinusoidal waveforms, one of frequency fc+fm and the
other of frequency fc-fm.
Note that the product signal has four spectral components
each of amplitude AmAc/4,there are only two frequencies,
and the amplitude of each sinusoidal component isAmAc/2

16. RECOVERY OF THE BASEBAND
SIGNAL
Suppose a signal m(t) has been translated out of its
baseband through multiplication with cos ωct
How is the signal to berecovered?
The recovery may be achieved by a reverse translation,
which is accomplished simply by multiplying the
translated signal with cos ωct
The difference-frequency signal obtained by multiplying
m(t).cos ωct by cos ωct, t is a signal whose spectral range
is back at baseband

17. ► Alternatively, we may simply note that
[m(t).cos ωct ] cos ωct = m(t).𝑐𝑜𝑠2ωct
2 2
= m(t)(1
+1
cos 2ωct ) (1a)
(1b)
= 𝑚(𝑡)
+𝑚(𝑡)
cos2ωct
2 2
Thus, the baseband signal m(t) reappears.

18. Conclusion
This feature of the process of translation by multiplication
may, depending on the application, a matter of
indifference, or even an adavantage.
Hence this feature of the process is, of itself, neitheran
advantage nor a disadvantage.
It is, however, to be noted that there is no otheroperation
so simple which will accomplish frequency translation.
18

19. • In a digital communication system, the source to be
transmitted is discrete both in time and amplitude
• The source information is normally represented as
a baseband (low-pass) signal
• In digital modulation a high frequency analog carrier
signal is modulated by digital bit stream
Modulation Technique

20. • Modulation = Adding information to a carrier
signal
• The sine wave on which the characteristics of
the information signal are modulated is
called a carrier signal
What is modulation ?

21. Modulationssystems

22. Types of digital modulation technique
• Coherent
• Non coherent
Coherent; In coherent modulation technique process
received signal with a local carrier of same
frequency and phase.
Non coherent ; In Non coherent digital modulation
technique there is no requirement of reference wave.

23. Digital modulation technique
• ASK (Amplitude shift keying)
• PSK (Phase shift keying)
• FSK (Frequency shift keying

24. Amplitude shift keying
In ASK, the amplitude of the signal is changed in response
to information. Bit 1 is transmitted by a signal of one
particular amplitude to transmit 0, we change the amplitude
keeping the frequency constant.it is shown below

25. In PSK,we change the phase of the sinusoidal carrier to
indicate information . Totransmit 0,we shift the phase of
the sinusoidal by 180 phase shift represents the change
in the state of the information.
Phase shift keying

26. Frequency shift keying
In FSK,we change the frequency in response
to information one particular frequency for 1
and another frequency for a 0.

27. Advantages
• Digital modulation can easily detect and
correct the noise.
• Security is more in digital modulation.
• Digital modulation signal can travels a long
distance.