35-1 Let x(t) = δ(t). (a) Find i(t) from Eq. (2) and use your result to...
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)...
1. Let x(t)-u(t-1) _ u(t-3) + δ(t-2) and h(t)-u(t) _ u(t-1) + u(t-3)-u(t-5) a. Find and sketch x(t-t) and h(t). (Hint: Break x(t) into two signals) b. Find and sketch y(t) - x(t)*h(t) using the quasi-graphical method. Label and show every step (drawings and calculations)
4.30p Find the Fourier transform of δ(t-t) and use it to find the Fourier transforms of: a) 8(t-2) - 8t 2) b) cos(5t)
1. Use Eq. 1 to derive an expression for the expected output waveform from an ideal differentiator circuit having input waveform Vin=lsin[(21)1000t] V. Let RF1.5 k12 and C=10 nF. 2. Use Eq. 3 to find the peak-peak output amplitude of the ideal differentiator of question 1 for a 2 Vpp sine wave input at 1 kHz and 2 kHz. Put the results in the Calculated Output column of Table 1 in Appendix A. 3. Use the indefinite integral version of...
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).
(a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I α(s) sin(θ(t)) dt Use your result to give another geometric interpretation to the (signed) curva- ture and its sign? to) rindy,R-- parmetrised with unit speed suchhat y -0and kt) - s for all seR. (a) Let θ : R-+ R be a smooth function. Find the (signed) curvature of the curve a:R- R2 given by cos(θ(t)) dt,I...
(a) Let the correlation be defined as r (t) x(T) y (tT) dT T Express R jw= F{r (t)} in terms of X (jw) and Y (jw), the Fourier transform of x (t) and y (t) respectively. (b) Suppose (t) = y (t) = e-H. Find R (jw) using frequency domain properties and the relationship derived in (a) extra Find R (jw) by evaluating the convolution integral in the time domain to get r (t) and then doing the FT.
Signals and systems Problem 2 (20 points) Let -S2t+1, Osts1 x(t) = -t +4, 1sts 3 be a periodic signal with fundamental period T=3 and Fourier coefficients ar a. Determine the value of ao. b. Determine ak, k = 0, by: 1. first finding the Fourier coefficients of ii.then using the appropriate property of the continuous-time Fourier series. c. Use the result of part (b) to express the Fourier transform of x().
9. (a) Use a graph to find a number δ such that 2<x<2+δ if then In(x - 1) (b) What limit does part (a) suggest is true? 10. Given that lim x π CSC-X-o , illustrate Definition 6 by finding values of δ that correspond to (a) M-500 and (b) M 1000 9. (a) Use a graph to find a number δ such that 2
Exercise 7. Let X and Y be A. independent exponential random variables with a common parameter (1) Find the transform associated with aX +Y, where a is a constant. (2) Use the result of part (1) to find the PDF of aX +Y, for the case where a is positive and different than1 (3) Use the result of part (1) to find the PDF of X-Y. Justify your answers. Exercise 7. Let X and Y be A. independent exponential random...