For the 1st question euler's formula must be used.
For the 1st question euler's formula must be used. (a) (3 pts) Solve each of the...
Can you do part A through B please? 2 Euler's formula relates the complex exponential to trigonometric functions as e" = cos(9) + j sin(9) This problem considers two alternate forms of Euler's formula. (a) Show that we can represent cos(0) in terms of complex exponentials as eje +e-je cos(e) (b) Derive a similar expression to part (a) for sin(e) (c) Use the results of part (a) to hand com pute cos(2). Verify your result with MATLAB. This result conflicts...
Please show all your works. Thanks. 4.(25 pts) Consider a periodic function X(t) = Sin(3t). Cos . Express x(t) in Exponential Fourier Series form and calculate Fourier Coefficients Co, C1, C-1,C2, C-2 ... etc (as many Fourier Coefficients as needed). What is the fundamental frequency (wo) of the x(t)? (hint: Use Euler's formula to express Sin(.) and Cos(.) in exponential forms)
(50 pts) Determine whether each of the following signal is periodic. If the signal is periodic, find its fundamental period. (a) x(t) = 4, a constant signal. (b) x(t) = 28ej (400#t) (c) x[n] = 28ej(1007n) (d) x(t) = 10 sin(5t) - 4 cos(7t) (e) x[n] = 10 sin(5n) - 4 cos(7n) (f) r(t) = cos(Ft) sin(ft) (g) x(t) = teit (h) x[n] = e(m/v2) (1) x[n] = cos(km2) (Pay attention to the square) (j) x[n] = {X- 8[n -...
hi! I need help with this college level differential equations question. Please show all work and thank you. 3. We will next use matrix exponentials to find a fundamental matrix for the given system of DEs, (t) = P3(t) , P= (a) Letỉ(t) Ty(t), where Ț s a 2 2 constant matrix. Then, the system becomes = Dy, where D-T-1 PT. Find matrices T and D, such that D is a diagonal matrix. (Note that D and T are complex...
[15 total pts] Graphical visualization of a signal's spectrum can help determine the Nyquist rate for sampling. Consider a signal x,(t) = cos(40t) cos(80t). Sketch the 2-sided complex spectrum and [5 pts] determine the minimum sampling rate that can be used to sample the signal without causing aliasing. [5 pts] Repeat Part a for the signal x2 t) cos(4 x 103t) sin(3 x 103Tt) cos(8 x 10Tt). [5 pts] Repeat Part a for the signal x3(t) cos(4 x 103Trt) sin(3...
solve this question early on as possible. 4.28. (a) Let x() have the Fourier transform X(jeo), and lec p) be periodic with fundh l frequency owo and Fourier series representation mental anejnugt Determine an expression for the Fouriet transform of (P4.23-1) (b) Suppose that X(j) is as depicted in Figure P4.28(a). Sketch the spectrum of y(t) in eg. (P4.28-1) for each of the following choices of pt): () p(t) cos t (ili) p(t) cos 2 (lv) p(t) (sin t)(sin 21)...
efficients Wi for the signal w(t) sin(16rt) 14. (8 pts) Determine the FS coefficients W, for the signal w(t) 3 cos(12rt)-5 sin(16rt). (c) (9 pts) Suppose a MATLAB anonymous function X already exists that correctly defines X() Write MATLAB code that uses X to reconstruct and then plot a 10-periodic replication of e(t) over-10sts10. efficients Wi for the signal w(t) sin(16rt) 14. (8 pts) Determine the FS coefficients W, for the signal w(t) 3 cos(12rt)-5 sin(16rt). (c) (9 pts) Suppose...
1.4. Let x[n] be a signal with x[n] = 0 for n < -2 and n > 4. For each signal given below, determine the values of n for which it is guaranteed to be zero. (a) xịn - 3] (b) x[n+ 4] (c) x[-n] (d) x[-n+2] (e) x[-n-2] 1.5. Let x(t) be a signal with x(t) = 0 for t <3. For each signal given below, determine the values of t for which it is guaranteed to be zero....
Sketch the frequency spectrum of he following signal and indicate the complex magnitude of each. All amplitudes must be positive Determine fundamental frequency and period *all phases need to be written in terms of pi between -pi and pi. Sketch the frequency spectrum of the following signal and indicate the complex magnitude of each frequency component Manipulate phase as necessary to plot all components of the spectrum with positive amplitudes: x(t) = 14 cos( 1 60mt-π/4) + 5 cos(280mt-2π/3) -cos(600πt...
Please explain how a) is solved, write what formula is used and explain in detail so I can solve any problem of this type. 2) Find the power and energy of the following signals (20 Points). a) x(t) = sin(t) b) y[n] = (-0.3)”u[n – 2] Solutions: Part (a): The signal r(t) is periodic because 1-cos(2t) (t) = sin(t) = ? Therefore, E = 0. To find the power, we can use the fact that the signal is sinusoid: P:...