Communication systems MATLAB Notes This is in relation to the course material taught at BITS Pilani, Dubai Campus. Refer to the Communication System Notes for more details. For more s…Full description
EE3005: Communication Communication Systems Problem Set 4: Amplitude Modulation
1. Consider Consider a message signal signal m (t) = 2cos 2πt +
π 4
.
(a) Sketch Sketch the spectrum spectrum U p p (f ) of the DSB-SC signal u p (t) = 8m(t)cos400πt . What is the power of u p ? (b) Carefully sketch sketch the output of an ideal envelope envelope detector with input u p . On the same plot, sketch the message signal m (t). (c) Let v p (t) denote the waveform obtained by high-pass filtering the signal u (t) so as to let through only frequencies above 200 Hz. Find v c (t) and v s (t) such that we can write v p (t) = v c (t)cos400πt − vs (t)sin400πt
and sketch the envelope of v p . 2. A message to be transmitted transmitted using AM is given given by 3cos 2πt + 4sin 4sin 6πt m(t) = 3cos where the unit of
time time is millise millisecon conds ds.
It is to be sent using a carrier frequency of 600 KHz.
(a) What is the message message bandwidth? bandwidth? Sketch Sketch its magnitude magnitude spectrum, spectrum, clearly clearly specifying the units used on the frequency axis. (b) Find an expression expression for the normalized normalized message message m n (t). (c) For a modulation modulation index of 50%, write an explicit explicit time domain expression expression for the AM signal. signal. (d) What is the power efficiency of the AM signal? (e) Sketch Sketch the magnitude magnitude spectrum for the AM signal, signal, again clearly clearly specifying the units used on the frequency axis. (f) The AM signal is to be detected detected using an envelope envelope detector detector (as shown in Figure 4.1), with R = 50 ohms. What is a good range of choices for the capacitance C? 3. Consid Consider er a messag messagee signal signal m(t) = cos(2πf mt + φ ), and a corres correspond ponding ing DSB-SC DSB-SC signal u p (t) = Am(t)cos2πf c t, where f c > f m. (a) Sketch Sketch the spectra of the corresponding LSB and USB signals (if the spectrum is complex- valued, sketch the real and imaginary parts separately). (b) Find explicit explicit time domain expressions expressions for the LSB and USB signals.
4-1
4-2
Tutorial 4: Amplitude Modulation
+
Passband vin(t) AM signal −
+
R
C
vout (t)
Envelope detector output
−
Figure 4.1: Envelope detector demodulation of AM, used in problem 2.
