(d) y4 (r) 35in(0.3πι +0.4). 3.9 Determine the average power of the analog signal x (t-Ai sin(Ωǐt) + A2 sin(Q2). Ω&...
Question 1: (Sampling and Aliasing Effeet) (25 Marks) The given analog signal x(t)--sin(16xt)+ sin(11xt)+ sin (5nt), where t is in milliseconds, is sampled at a rate of 12kHz. The resulting samples are immediately reconstructed by an ideal reconstructor. a. Find and sketch the spectrum of x(t) versus Ω. b. Find and sketch the spectrum of the sampled signal versus o. c. Determine the analog signal x (t) at the output of the reconstructor. d. Prove the x(0) and x(t) having...
10 x(t) = { 1-0. 50.4Sts0.4 0 3.6 < t-0.4 A signal x (t) is defined as; (i) Dn (ii) Do (i) To (iv) ω。 (v) Sketch ID, 1 vs nu.。 (vi) Sketch <D (0) vs nw (vi Power of x(t) To implement Fourier Series 4.5 3.5 2.5 1.5 0.5 0 -2 (sec)
Problem 4.(30 pts) Given the analog signal x(t) cos(2 cos(3t)+2 sin(4mt) A.(10 pts) Find the Nyquist frequency (sampling frequency) which guarantees That x() can be recovered from it's sampled version xIn] with no aliasing. B.(10 pts) If the sampling period of Ts 0.4 see is used identify all discrete frequencies Of the signal x(t), also indicate if this sampling period is adequate to recover x(t) from xn] C.(10 pts) Suppose signal x(t) is modulated by signal e(t) = cos(2000mt) what...
Q1) Given an analog signal X(t) = 3 cos (2π . 2000t) + 2 cos (2π . 5500t) sampled at a rate of 10,000 Hz, a. Sketch the spectrum of the sampled signal up to 20 kHz; b. Sketch the recovered analog signal spectrum if an ideal lowpass filter with a cutoff frequency of 4 kHz is used to filter the sampled signal in order to recover the original signal ; c. Determine the frequency/frequencies of aliasing noise . Q2)...
1.35 Determine if each of the following signals is a power signal, an energy signal, or neither (а) х1() — [1 —е 2] u(0) (b) x2(t) 2 sin(4t ) cos(4t) (с) хз(t) — 2 sin(3t) cos(4t) 1.39 Compute the average power of the following signals (a) x eat for real-valued a (3 j4)e7 (b) х2(г) _ * (с) с х3(t) — eјЗejSi
Consider a narrow-band FM signal approximately defined by )A.coset-B,sin)sinff) 21, sm27,t)sin a) Determine the envelope of this modulated signal b) What is the ratio of the maximum to the minimum value of this envelope? Plot this ratio versus B, assuming Osps03. c) Determine the average power of the narrow-band FM signal, expressed as a percentage of the average power of the unmodulated carrier wave. Plot this result versus β, assuming 0 β 03. Consider a narrow-band FM signal approximately defined...
Q2 (a) Given the signal x(t) and system h(t) as presented in Figure Q2(a). Determine the output y(t) using the graphical representation of convolution integral. (7 marks) x(1) h(t) 1 e-'u(t) e-2 (1) 0 Figure Q2(a) Q2 (b) Consider a system as shown in Figure Q2(b). t2 - 1 x(t) y(t) Advance by 1 second Х Figure Q2(b) Find the input-output relation between x(t) and y(t). (i) (1 mark) Examine whether the system is time variant or time invariant. (5...
Show that the average power of the CT periodic signal x(t ) = D e[j(ωt + θ)] is given by |D|2 Please Show all the steps and explain (Do not use Vrms or Irms)
Q2 Consider a communication signal x(t) described by the following mathematical expression: x(t)=2 cos(2000) + 4 sin? (2000) – 2+4rec(t)cos(6000mt) Analyse the communication signal x(t) then consider the following: (i) Determine the Fourier transform of the signal x(t). (ii) Plot the double-sided amplitude spectrum of the signal x(t).
Let x(t) a periodic signal with period To such that x(t)-sin(coot) for。st for To/2 s t s To. To2 and x(t)-0 a) Plot x(t) b) Expand x(t) in trigonometric Fourier series (sine/cosine). c) Calculate the average power of x().