Lab 7: Generation of SSB using Hilbert Transform
& Effects of Frequency offset in Demodulation
Conducted on:
Submitted on:
Instructor:
Lab Engineer:
1)
2)
3)
Group Members
Aim
To simulate and understand following using Simulink.
1. Effect of Hilbert Transform in the generation of SSB.
2. Effect of frequency offset in demodulation..
Theory
Chapter 3 “Amplitude Modulation” Fundamentals of Communication System 2nd edition by John
G. Proakis and Masoud Salehi
Equipment
PC with MATLAB Installed
Explanation
We know that a DSB-SC AM signal required a channel bandwidth of B=2W Hz for
transmission. However, the two sidebands are redundant. We demonstrated in the previous labs that the
transmission of either sideband is sufficient to reconstruct the message signal m(t) at the receiver. Thus,
we reduce the bandwidth of the transmitted signal to that of the baseband message signal m(t)
A single-sideband (SSB) AM signal is represented mathematically as
u(t)=Ac m(t) cos2πfct ∓ Ac m^(t) sin2πfct
Where m^(t) is the Hilbert transform of m(t) and the plus or minus sign determines which sideband we
obtain. The plus sign indicates the lower sideband, and the minus sign indicates the upper sideband.
Hilbert transform may be viewed as a linear filter with impulse response
h(t)=1/πt
and frequency response
H(f)={ −j , f>0
j , f<0
0, f=0}
For the generation of SSB using Hilbert Transform, block diagram is as under
Demodulation of SSB-AM Signals
To recover the message signal m(t) in the received SSB-AM signal, we require a phase-coherent or
synchronous demodulator, as was the case for DSB-SC AM signals. Thus, for the upper single-sideband
(USSB) signal, we have
u(t)cos(2πfct+ϕ) = 1/2 Ac m(t) cos ϕ + 1/2 Ac m^(t) sinϕ + double-frequency terms.
.
Tasks
Modulation:
1. Generate a message signal.
2. Add the In phase and Quadrature components.
3. Generate SSB using the Hilbert transform using the provided block diagram.
Demodulation:
4. Mix the received signal with oscillator frequency of 10 kHz.
5. Use Low pass filter to convert spectrum to baseband.
6. Amplify the output using an RF power amplifier.
7. Check the effect of frequency offset.
8. Plot FFT results at each stage and compare with theoretical expectations.
CAUTIONS
1. Display FFT plots before and after each operation.
2. Use MATLAB Simulink, and embed the FFT code within the model properties (not a separate
M-file).
3. Validate the spectral changes at each stage using theoretical principles.
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