Analysis Linear Systems
Problem 17. Consider the standard amplitude-modulation system shown in Figure 3 Figure 3 x) Channel Filter he(r) cos wor cos ωοι M(w) H(u) (a) Sketch the spectrum of r(t). (b) Sketch the spectrum of y(t) for the following cases: (i) 0S WcWo-m (iii) wc >wowm (c) Sketch the spectrum of z(t) for the following cases: (i) 0 S WcWo-m (iii) wc >wowmProblem 17. Consider the standard amplitude-modulation system shown in Figure 3 Figure 3 x) Chann...
2. (14 points) This problem shows an example of using the Fourier transform to analyze communication systems. The system in Figure 4, where (t)-f(t)+sin(wt) and has been proposed for amplitude modulation. f(t) + sin(o) Figure 4: System proposed for amplitude modulation. (a) (7 points) The spectrum of the input f(t) is shown in Figure 1, where 2mB o/100. Sketch and label the spectrum Y(w) of the signal y(t). Hint: You will need to use the frequency convolution property of the...
A cascaded system that consists of an LTI system and a delay system is shown in Figure Q4(b). The input signal X(t) and impulse response of the LTI system, h(t) are given as the following: x(t) = 6-2&u(t) h(t) = e-fu(t) Determine: The Fourier transform of y(t). (3 marks) The Fourier transform of z(t). (3 marks) A basic modulator circuit is shown in Figure Q4(c). Modulation is a multiplication between input signal, m(t), and a carrier signal, c(t). The process...
Consider the following Amplitude Modulation (AM) signal given by Xc(t)=Ac[1 + μx(t)]cos(wct) where x(t) is the message signal, and μ the modulation index. Also consider the following message signal x(t) for parts (a) and (b)' shown in Fig 1. a) Provide a sketch of the AM signal when the modulation index μ < 1. b) Provide a sketch of the AM signal when the modulation index μ = 1. c) Provide a sketch of the AM signal when the modulation index μ > 1. d) If the bandwidth...
please answer all parts . Assume the following amplitude modulation and demodulation systems. Answer the following questions using tables of Fourier transform uploaded to e-Learning. a(t m (t) Xm(t) r(t) m(t) m(t) x(t) = sin(m) sin(2nt) hLPF(t) = m(t) = cos( 10πt) a) Sketch magnitude and phase spectra of X(). b) Sketch magnitude and phase spectra of M(). c) Sketch magnitude and phase spectra ofXm(w). d) Sketch magnitude and phase spectra of Xa(a). e) Sketch magnitude and phase spectra of...
4: An AM signal has the form s(t) = A (1 + il cos(mt) cos wet with wm <we and u <1. The signal is to be demodulated using the simple envelope detector shown in the following plot. AM sinal (a) Sketch v.(t) when wm <1/RC <we (b) Comment on suitability of such an envelope detector for demodulating an amplitude modu- lated signal: (i) With both sideband and full carrier as in the AM radio system. (ii) With full carrier...
Consider the following AM system x(t) z(t) y(t) H(a) 10ω -10 othwise 2cos (100t) Ifthe input signal x(t), the has a spectrum function, X(w), shown above, a) Write the expressions of r(w) and Z(w) in terms of X(w). b) Sketch the spectrums, x(ω), and r(a)Jdentify the LSE and USB components on the graphs? 14] 131 lain the type of AM modulation is the output z(03 Consider the following AM system x(t) z(t) y(t) H(a) 10ω -10 othwise 2cos (100t) Ifthe...
1. Given a baseband signal m(t) sin(1000mt) cos(3000nt) + cos(3700nt a. Sketch the spectrum of m(t) (Hint. sin(a) cos(b) 0.5 sin(a +b) +0.5sin a-b)) b. Sketch the spectrum of DSB-CS signal m(t)cos(10000mt) C ldentify the upper sideband {USB) and lower sideband (LSB) spectra d. Give the black diagram of the receiver to receive DSB-CS signal in (b). 2. baseband signal m(r)--0.5 + Σ..小(t-n)-u(t-0.5-n)] where ult) is the Given unit step function, an amplitude modulated signal is as SAM 107+ m(0cos...
Question 4 (35 points). Two message signals, ?1 (?) = 200??(100??) cos(103πt) volts and ?2 (?) = 900??2 (450??) cos(103πt) volts, are required to be combined and then transmitted over a channel around 2 MHz using amplitude double-side modulation. We assume that the channel is ideal with no delay and no attenuation. Design a system consisting of mixers, filters, etc. to transmit and restore perfectly these two signals (i.e. ?1 (?) and ?2 (?)) at the receiving side after the...
Prob. 5 (a) Consider the FM signal with modulation index B 2 is passed through an ideal band-pass filter (BPF) with mid-band frequency f and bandwidth 5f. where f is the carrier frequency and fmis the frequency of the baseband modulating signal (i) Sketch the spectrum of the BPF output. (ii) Determine the fraction of the power of the FM signal that is present at the output of the filter (b) Consider the FM signal given by фFM (t)-100 cos...
This is taken from Section 4.6, "Amplitude Modulation and the Continuous-Time Fourier Transform," in the course text Computer Explorations in signals and systems by Buck, Daniel, Singer, 2nd Edition. I need the answers for the basic and intermediate questions. 4.6 Amplitude Modulation and the Continuous-Time Fouriei Transform This exercise will explore amplitude modulation of Morse code messages. A simple ampli tude modulation system can be described by x(t) = m(t) cos(Crfot), (4.13) where m(t) is called the message waveform and...