2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
2. Determine the following: T/2 (3 sin2 t cost İ + 3 (a) j + 2 sin t cos t k) dt sin t cos" t tan2 t t3-8 (b) lim sin t sin 2t t +2
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
2. A dragon is flying around in a pattern given by the parametric curve r(t) (cos(t) cos((sin(t) sin(t) cos(t)j. cos(t) - cos sin(t)-sin(t) cos(t))j (a) Find a formula for the velocity of the dragon at time t (b) Find all the times at which the dragon's speed is zero. Explain your reasoning. c) Does the path of the dragon contain any cusps? Explain your reasoning
2. A dragon is flying around in a pattern given by the parametric curve r(t)...
TT 1) Consider the following signal x(t) = -5 + 9 sin (61t + 3 cos(12nt) + V V7ej24nt a) (5 points) Write the complex exponential Fourier series for x(t). b) (5 points) Sketch the amplitude and phase spectra of x(t). c) (5 points) Find the total average power of the signal.
If u(t) = (sin(2t), cos(3), t) and v(t) = (t cos(3), sin(2t)), use Formula 4 of this theorem to find lu(e) • vce). dt
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...
Find the Fourier Transform of the following signals: (a) x(t) = Sin (t). Cos (5 t) (b) x(t) = Sin (t + /3). Cos(5t-5) (c) a periodic delta function (comb signal) is given x(t) = (-OS (t-n · T). Express x(t) in Fourier Series. (d) Find X(w) by taking Fourier Transform of the Fourier Series you found in (a). No credit will be given for nlugging into the formula in the formula sheet.
3(20%) Assume a message signal is given by m(t) = 4 cos(2π//) + cos(4π.t). Let x (t)-5m(t) cos(2t f t) + 5m(t) sin( 2 fct), where m(t) İs the Hilbert Transform of m(t). (10%) (a) Derive x(t) (10%) (b) Prove, by sketching the spectra, that x(t) is a lower-sideband SSB signal of m(t).
3(20%) Assume a message signal is given by m(t) = 4 cos(2π//) + cos(4π.t). Let x (t)-5m(t) cos(2t f t) + 5m(t) sin( 2 fct), where m(t)...
got 50 min
sgn(t) and unmodulated carrier cos(wct), draw the output of unmodulate 3. a. For the message signal m(t)-2sgn(t) phase modulator with m(t) (k/4) cos(o t b. For the message signal m(t)--2sgn(t) and unmodulated carrier cos(wet ) shown above where ue-207, draw the output of frequency modulator with m(t) (k-10n)
sgn(t) and unmodulated carrier cos(wct), draw the output of unmodulate 3. a. For the message signal m(t)-2sgn(t) phase modulator with m(t) (k/4) cos(o t b. For the message signal...
let two vectors be a(t) = e^t i + (sin 2t) j + t^3 k and b(t) = (e^-t , cos 3t, - 2 t^3) in euclidean three space R^3. Find d/dt [a(t) * b(t)].