Faculty of engineering sciences
communication and electronics department
communication theory (1)
Sheet (5)
1. For each of the following baseband signals: (𝑖)𝑚(𝑡) = 𝑐𝑜𝑠 1000𝑡; (𝑖𝑖)𝑚(𝑡) =
2𝑐𝑜𝑠1000𝑡 + 𝑐𝑜𝑠2000𝑡; (𝑖𝑖𝑖)𝑚(𝑡) = 𝑐𝑜𝑠1000𝑡 𝑐𝑜𝑠3000𝑡 :
(a)sketch the spectrum of m(t).
(b)sketch the spectrum of the DSB_SC signal m(t)cos 10,000t.
(c) identify the upper sideband(USB) and the lower sideband(LSB) spectra.
(d) identify the frequencies in the baseband, and the corresponding frequencies in
the DSB_SC, USB, and LSB spectra.
2. You are asked to design a DSB_SC modulator to generate a modulated signal
𝐾 𝑚(𝑡)𝑐𝑜𝑠𝑤𝑐 𝑡, where 𝑚(𝑡) is a signal band-limited to B Hz, as shown in Fig 1.b.
Fig1.a shows a DSB_SC modulator. The carrier generator generates 𝑐𝑜𝑠 3 𝑤𝑐 𝑡 (not
𝑐𝑜𝑠 𝑤𝑐 𝑡).
(a) Explain where you would be able to generate the desired signal using only this
equipment. You may use any kind of filter you like.
(b) What kind of filter is required?
(c) Determine the signal spectra at point b and c, and indicate the frequency bands
occupied by these spectra.
(d) what is the minimum usable value of 𝑤𝑐 .
(e) Would this scheme work if the carrier generator output were
𝑐𝑜𝑠 2 𝑤𝑐 𝑡?Explain.
(f) Would this scheme work if the carrier generator output were 𝑐𝑜𝑠 𝑛 𝑤𝑐 𝑡 for any
integer n>=2?
Hint:
𝑐𝑜𝑠 2 𝑤𝑐 𝑡 = 0.5 (1 + cos 2𝑤𝑐 𝑡)
Fig.1
3. Two signals 𝑚1 (𝑡) and 𝑚2 (𝑡), both band limited to 5000 rad/sec, are to be
transmitted simultaneously over a channel by the multiplexing scheme shown in
Faculty of engineering sciences
communication and electronics department
communication theory (1)
the following figure (Fig.2). The signal at point b is the multiplexed signal, which
now modulates a carrier of frequency 20,000 rad/s. the modulated signal at point c
is transmitted over a channel.
(a) Sketch a signal at point a, b and c.
(b) What must be the bandwidth of the channel?
(c) Design a receiver to recover signals 𝑚1 (𝑡) and 𝑚2 (𝑡) from the modulated
signal at point c.
Fig.2
4. System shown in the following figure (Fig.3) is used for scrambled audio signals .
The output 𝑦(𝑡) is the scrambled version of the input 𝑚(𝑡).
(a) Find spectrum of the scrambled signal 𝑦(𝑡).
(b) Suggest a method of descrambling 𝑦(𝑡) to obtain 𝑚(𝑡).
Hint:
Scrambled process used for encryption in audio signal.
Fig.3