Experiment 4 As usual, you are encouraged to send e-mail to
firstname.lastname@example.org for help. All office hours will be
held as per schedule.
Please note the correction in III.4, you are supposed to use a time scale of 0.05 ms, and not 0.05 s as mentioned earlier.
Objective: Generating bandpass WGN and studying the effect of AWGN on DSB-SC AM.
Description: In this experiment you will generate
bandpass white Gaussian noise using two different methods. Then, you
will see the effect of this noise on a DSB-SC system.
Copy the initialization files for the
experiment into your Matlab working directory.
Note that the initialization files have changed
The following constants should be set by the startup
file. Use who in the matlab workspace to check if the
constants are all there. Some additional constants may also be set,
but you may ignore them. Set the simulation time to T_SIM
and the sample time to T_SAMPLE in the simulink models you
- F_CARR = 2*pi*5e05 ----------Carrier Frequency, rad/sec
- T_PERIOD = 2*pi/F_CARR ------Time period of carrier
- T_SAMPLE = T_PERIOD/4.01 ----Sampling period used in Simulink
- T_SIM = 0.002 s ---------- --Total simulation time
- BW_MESSAGE = 2*pi*2e04 ------Message Bandwidth.
- F_CUTOFF = BW_MESSAGE -------Cutoff frequency of lowpass Butterworth filter
- N_0 = 0.01 ---------------------Power of noise
- II. Generating bandpass white noise
- Use the ece359lib/White Noise block to generate zero mean
white gaussian noise. The noise power spectral density is already set
to N_0/2. Pass this noise through the ece359lib/Band
Pass filter block (bandwidth=2F_CUTOFF, and center
frequency F_CARR). The resulting signal is the bandpass
noise n1 (t).
- Use the HF scope and 359 PSD blocks from
ece359lib to observe the time and frequency domain
characteristics of n1 (t). The HF scope
works in the same way as in the previous experiments (help available here).
- Print the PSD of n1 (t).
- III. Componentwise generation of bandpass noise
(This part will use many blocks, so try and space blocks close together)
- Generate two lowpass noise processes n_s, n_c(t) using the ece359lib/White Noise and
ece359lib/low pass filter blocks. To make the two processes
independent, change the random number generator seed in one of the
- Produce the signal
n2(t) = n_s(t) sin(w0 t) + n_c(t) cos(w0 t).
Here w0 refers to the carrier frequency
F_CARR. (You are free to use multipliers and sine
and cosine generators )
- Use the HF scope to see the lowpass signals n_c(t), n_s(t) and also the bandpass signals
n2(t), n_c(t) cos(w0 t), n_s(t) sin(w0
t). Save all these signals in the workspace using the save to
workspace option of scope.
- Use the subplot function of matlab to plot the three
bandpass signals above on the same figure (use subplot(3,1,row_number)). On this scale, it is
difficult to observe the difference between the sine and cosine
On a separate figure with an enlarged time scale, plot on
the same axis (overlap the plots using hold on, and make
one of the plots to be a dotted line) the two
signals n_c(t) cos(w0 t), n_s(t) sin(w0
t). Your entire time scale should be no more than 0.05 ms.
This plot shows how the two components of noise differ.
- Use the ece359lib/359 PSD block to plot the PSD of n2(t).
IV. DSB-SC performance in bandpass noise
(We will use DSB-SC system as in simulink #2.)
- Construct a DSB-SC transmitter/receiver. Let the message signal
m(t) be a sinusoid of frequency
BW_MESSAGE/2 and amplitude 100. The modulating waveform is a
cosine wave with zero phase shift, frequency F_CARR and
amplitude 1. For the low pass filter at the receiver, use
ece359lib/DSB-Low Pass block.
- We will add noise to the modulated signal s(t) of DSB-SC and observe the result at the
demodulator. Suppose you used variable name n2 to save the
bandpass noise in part III. Now use the ece359lib/From Workspace
block to input this signal into simulink.
- To measure the noise level of the demodulated signal, we will need
to resort to some indirect methods. Pass the source signal m(t) through the same lowpass filter that you
used in the demodulator. This gives us a version of the source signal
delayed by the same amount as the demodulated signal. Call this signal
- Multiply the demodulated signal by 2 and call the
resulting signal v(t). Subtract the
signal m1(t) from it. Call the resulting
n_r(t) = v(t) - m1(t)
Save n_r(t) to the workspace using the scope.
- Use subplot to plot both n_c(t) and
n_r(t) on the same figure. Compare the
shape of the two signals.
- Submit a block diagram for part II
- Submit a block diagram for part III.
- Submit both the required plots from III.4. Explain the difference
between the two (sine and cosine) noise components as seen in the plots.
- Submit the PSD plots from II.3 and III.5. Compare the magnitude of
the PSD peak in both. The filters are known to be near perfect. Give
equations or step-by-step PSD drawings to support your observation.
- Submit a block diagram for part IV.
- Comment on the similarity between the waveforms in IV.5.
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