U 1.1. Express each of the following complex numbers in Cartesian form (x + jy): bej, ke-ja, eja/2, e-ju/2, 359/2, 2ej#14, 2e396/4, 2e-39714, 2e-ja14 Express each of the following complex numbers in polar form (reje, with - 1 < 0 = T):5.-2-3;, ; - ; 3.1+j, (1 - i)?, j(1 - 1)(1+j)/(1-j), (/2 + ;/2) (1 + 1/3). Determine the values of P. and E. for each of the following signals: (a) xi(t) = e-2u(t) (b) x2(t) = el(21+ 7/4)...
Problem 1 (10): Let x[n] be a signal with x[n] = 0 for n < -2 and n > 4. For each signal below, determine the value of n for which it is guaranteed to be zero. a. x[n + 2] b. x[n - 1] c. x[-n] d. x[-n - 2] e. x[n/2] f. x[n + 1]
au. Let x(t) be a signal with x(t) =0 for t > 1 . For each signal given below, determine the values of t for which it is guaranteed to be zero (if any). (a) x(1-t) (d) x(3t) (b) x(1 -t) +x(2-t) (e) x(u3) (c) x(1-t)x(2-1) Solution:
P-3.8 Consider the signal ob d x (t) = 10 + 20 cos(21 (100)t + ) + 10 cos(21 (250)t) L (a) Using Euler's relation, the signal x(t) defined above can be expressed as a sum of complex exponential signals using the finite Fourier synthesis summation (3.37) Determine values for fo, N, and all the complex amplitudes, az. It is not necessary to evaluate any integrals to obtain ak. (b) Is the signal x(t) periodic? If so, what is the...
Question 3 (30 points) Consider the signals defined below: *:(t) = cos(2) xz(t) = cos(4+) a) Determine the fundamental period for each signal. b) Determine the fundamental period and fundamental frequency of the signal: y(t) = x;(C)x(0) (t) and x2(c) when the fundamental frequency is c) Determine the Fourier Series coefficients of defined as determined in part (b). d) Using Parseval's relation, determine the power of xy(t) and xy(t) e) Determine and plot the Fourier Series Coefficients of y(t). Show...
Problem 3: Let x(n) be an arbitrary signal, not necessarily real valued, with Fourier transform X (w). Express the Fourier transforms of the following signals in terms of X() (C) y(n) = x(n)-x(n-1) (d) v(n) -00x(k) (e) y(n)=x(2n) (f) y n even n odd , x(n/2), (n) 0 Problem 4: etermine the signal x(n) if its Fourier transform is as given in Fig. P4.12. X(a) 0 10 10 10 X(o) 0 X(a) Figure P4.12 Problem 3: Let x(n) be an...
8. Find the Fourier transform of the following signal. (5 points) x(0) 2 1 9. Determine whether or not the following signals are periodic, and if periodic, give their periods in seconds and frequency in hertz. a. X(t) = 12.8 Cos (320xt - . (3 points). b. x(n) = 11.6 Cos (3n). (3 points). 6. x(n) = 1.45 sinn). (3 points). 10. Determine whether or not the LTI systems with the following impulse responses are causal and stable. Note that...
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.
Let x(t) denote a signal and X(f) denote the corresponding Fourier transform which is given in the graph below. Given this graph, sketch the Fourier transforms of the following signals: -2 2 a, x b.x) Cos(8m) c. x(t) sinc (t) 2/ Let x(t) denote a signal and X(f) denote the corresponding Fourier transform which is given in the graph below. Given this graph, sketch the Fourier transforms of the following signals: -2 2 a, x b.x) Cos(8m) c. x(t) sinc...
for the plot, provide the matlab code. 3. Let the input signal x[n] (defined for -<n < oo) to the system be x[n] = 3 cos( 0.05πn) + 4 cos( 0.45πn) + cos( 0.95 n) and the transfer function be 1-re-je a) Plot this signal as a function of n. b) Determine and plot the output y[n] produced by the system due to the input analyzed in part a) of this problem. Do this first with r 0.05 and then...