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Single Side Band (SSB) Modulation

In DSB-SC it is observed that there is symmetry in the

bandstructure. So, even if one half is transmitted, the other

half can be recovered at the received. By doing so, the

bandwidth and power of transmission is reduced by half.

Depending on which half of DSB-SC signal is transmitted,

there are two types of SSB modulation

1. Lower Side Band (LSB) Modulation2. Upper Side Band (USB) Modulation

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M( )

Baseband signal

DSBSC

USB

LSB

2 B2 B

c c

cc

c c

Figure 1: SSB signals from orignal signal

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Mathematical Analysis of SSB modulation

02 B 2 B

M( )

M ( ) M ( )

+

+

+

00

cc c

cc

c c

ccM ( ) M ( )

M ( )M ( )

+

+

Figure 2: Frequency analysis of SSB signals

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From Figure 2 and the concept of the Hilbert Transform,

USB() = M+( c) + M( + c)

USB(t) = m+(t)ejct

+ m(t)ejct

But, from complex representation of signals,

m+(t) = m(t) + jm(t)

m(t) = m(t)jm(t)

So,

USB(t) = m(t) cos(ct) m(t)sin(ct)

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Similarly,

LSB(t) = m(t) cos(ct) + m(t) sin(ct)

Generation of SSB signals A SSB signal is represented by:

SSB(t) = m(t) cos(ct) m(t) sin(ct)

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m(t)

DSBSC

DSBSC

sin( t)

/2

/2

+

+SSB signal

cos( t)

c

c

Figure 3: Generation of SSB signals

As shown in Figure 3, a DSB-SC modulator is used for SSB

signal generation.

Coherent Demodulation of SSB signals SSB(t) is multiplied

with cos(ct) and passed through low pass filter to get back the

orignal signal.

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SSB(t) cos(ct) =1

2m(t) [1 + cos(2ct)]

1

2m(t) sin(2ct)

=

1

2 m(t) +

1

2 cos(2ct)1

2 m(t) sin(2ct)

M( ) c c

M ( + )

M ( )

+

2 2 c c0

Figure 4: Demodulated SSB signal

The demodulated signal is passed through an LPF to remove

unwanted SSB terms.

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Vestigial Side Band (VSB) Modulation

The following are the drawbacks of SSB signal generation:

1. Generation of an SSB signal is difficult.

2. Selective filtering is to be done to get the original signal

back.

3. Phase shifter should be exactly tuned to 900.

To overcome these drawbacks, VSB modulation is used. It can

viewed as a compromise between SSB and DSB-SC. Figure 5shows all the three modulation schemes.

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ccB

B

0

()VSB

Figure 5: VSB Modulation

In VSB

1. One sideband is not rejected fully.

2. One sideband is transmitted fully and a small part (vestige)

of the other sideband is transmitted.

The transmission BW is BWv = B + v. where, v is the

vestigial frequency band. The generation of VSB signal is

shown in Figure 6

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m(t)

H ( )

( ) ( )t

cos( t)

c

iVSB

Figure 6: Block Diagram - Generation of VSB signal

Here, Hi() is a filter which shapes the other sideband.

V SB() = [M( c) + M( + c)] .Hi()

To recover the original signal from the VSB signal, the VSB

signal is multiplied with cos(ct) and passed through an LPF

such that original signal is recovered.

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cos( t)

LPF

H ( )

m(t) ( )t

0

c

VSB

Figure 7: Block Diagram - Demodulation of VSB signal

From Figure 6 and Figure 7, the criterion to choose LPF is:

M() = [V SB( + c) + V SB( c)] .H0()

= [Hi( + c) + Hi(

c)] .M().H0()

= H0() =1

Hi( + c) + Hi( c)

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Appendix: The Hilbert Transform

The Hilbert Transform on a signal changes its phase by 900. The

Hilbert transform of a signal g(t) is represented as g(t).

g(t) =1

+

g()

t d

g(t) = 1

+

g()

t d

We, say g(t) and g(t) constitute a Hilbert Transform pair. If we

observe the above equations, it is evident that Hilbert transform is

nothing but the convolution of g(t) with 1t

.

The Fourier Transform of g(t) is computed from signum

function sgn(t).

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sgn(t) 2

j

=1

t jsgn()

Where,

sgn() =

1, > 00, = 0

1, < 0

Since, g(t) = g(t) 1t

,

G() = G()jsgn()

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Properties of Hilbert Transform

1. g(t) and g(t) have the same magnitude spectrum.

2. If g(t) is HT of g(t) then HT of g(t) is g(t).

3. g(t) and g(t) are orthogonal over the entire interval to

+.

+

g(t)g(t) dt = 0

Complex representation of signals

If g(t) is a real valued signal, then its complex representation g+(t)

is given by

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g+(t) = g(t) + jg(t)

G+() = G() + sgn()G()

Therefore,

G+() =

2G(), > 0

G(0), = 00, < 0

g+(t) is called pre-evelope and exists only for positive frequencies.

For negative frequencies g(t) is defined as follows:

g(t) = g(t)jg(t)

G() = G() sgn()G()

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Therefore,

G() =

2G(), < 0

G(0), = 0

0, > 0

Essentially the pre-envelope of a signal enables the suppression

of one of the sidebands in signal transmission.

The pre-envelope is used in the generation of the SSB-signal.