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(50 pts) Determine whether each of the following signal is periodic. If the signal is periodic,...
Chapter 1: Problem 1. Determine whether or not each of the following signals is periodic. In case a signal is periodic, specify its fundamental period. a.X (n) = 3 cos (5n + 4) b. x(n) = 2 exple-t) C. x(n) = cos () cos (4) d. "(m) = cos (3)- sin (a) + 3 cost 8 cos )
Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and the fundamental frequency (in rad/s). Otherwise prove that the signal is not periodic. [1 + 1 - 2 marks) a) X(t) = cos(5t) + sin(25t) b)x() = sin 91 + + sin(61 - 7) + cos(391)
3. Determine whether or not each of the following signals is periodic. If a signal is periodic fundamental period x(t)=cos(2t+4 Determine whether the following signals are Energy signals or Power signals a. 4.
1. Determine whether or not each of the following signals is periodic. In case a signal is periodic, specify its period. sin(411t n+2) • cos? (in) . Can we use the formula, f = min ( - 14|1 - 4 + l{\), to find the period of sin(fnt n) or cos(2ft n)?
Determine whether the following discrete-time signals are periodic or not? For the periodic ones, find their fundamental period. 2. (5 points each) a. x1 [n] =sin(0.5n +z/4) c. x1n] = cos (tn/3) + sin(nn/5)-2cos(tn/10) d. x4[n]- sin(tn/12) cos(tn/3) (Hint: use trigonometric identities to write the signal as a sum of sinusoids)
Instruction: Determine whether or not each of the following signals is periodic. If a signal is periodic, determine its fundamental period.1. x[n] = ej(π/4)n 2. x[n] = cos1/4n 3. x[n] = cosπ/3 n + sinπ/4 n 4. x[n] = cos2π/8 n
Problem 1: A signal f(t) is said to be periodic if for some positive constant To f(t) = f(t+%), for all t. Determine whether or not each of the following continuous-time signals is periodic. If the signal is period eriodic, determine the fundamental a) f(t) = cos2(20t + π35/180) + sin(40t-725/180) + cos( 10t + π/4) cos(20t-n/4) b) f(t) = 10 cos(t + π/4) + c) f(t) = Σ+0000(-1)"u(t-1-4m) 25 sin(V3t - T/2)
The Signal x(t)= e^(j*(3pi/2)*t)*cos((5pi/2)*t)+j*sin(pi*t) i) show that x(t) is periodic and what is the fundamental period? ii) What is the average value and power of x(t)?
For the continuous-tine periodic signal 4nt (-), 2mt x(t) = 2 + cos (-) + sin determine the fundamental frequency wo and the Fourier series coefficients ak such that kwot k=-oo
Consider the following DT periodic signal: in X(t) = sin 2πη) 10 + cos 30) a) What is the fundamental period? b) What are the exponential Fourier series coefficients? c) Sketch magnitude and phase spectral plots.