please help solve HW #2 EE 3200 Convolution and Fourier series Problem #1) Evaluate the following...
Problem 6: I7 Points For the following periodic signal, x(t) 4OSesi a) Express the signal exponent +cos(9t) +2cos(15t) al in complex exponential Fourier series form. 13 r series coefficients and sketch the spectral line. [2 Find the fundamental frequency and identilY the harmonics in the signal. 12) Solution
Problem 6: I7 Points For the following periodic signal, x(t) 4OSesi a) Express the signal exponent +cos(9t) +2cos(15t) al in complex exponential Fourier series form. 13 r series coefficients and sketch the...
l, f) is a periodic signal with period f(t)-n(t)-u(t-t/2 ) for 0 2π a.) Find the exponential Fourier series of f() and sketchf). What is the fundamental radian frequency. b.) Evaluate and sketch |Dml, the magnitude of the Fourier series coefficients vs.o in the range of -4s n S4 c.) Evaluate and sketch the phase angle of D, vs. co in the same range (-4S n S4) d.) Find the signal average power e) Find the approximate average power of...
(20 points) 1. (8 points) Suppose that f(t) is a periodic signal with exponential Fourier series coefficients Dn. Show that the power P of f(t) is This is Parseval's theorem for the exponential Fourier series. 2. (12 points) If f(t) is real-valued, Parseval's theorem can be as a) (3 points) Find the power of the PWM signal shown in figure 1. Hint: for this part don't use Parseval's theorem b) (9 points) Use Parseval's theorem for a real-valued signal to...
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Signals and Systems: Discrete time Fourier Series: If: 1. Please find the F.S. representation of x[n] 2. Please plot the amplitude spectrum 3. What is the fundamental frequency of x[n]? 4. How many distinct harmonics can be present in x[n]?--for this fundamental frequency. 5. How many harmonics are actually in x[n]? Trying to prepare for finals, its crunch time, thank you for your help! r[n] = 2sin(n-) + cos(n-) r[n] = 2sin(n-) + cos(n-)
Given the Fourier Series cocfficients and fundamental frequency, find the signal using the Fourier Series synthesis exquation. Assume all Ce not given are vero.) Put into cosine form where possible and state whether the signal is real-valued. (a) Lo - 8, C, EC-2- 3j, C% = e-j/4, C-6 - CT/4 (b) wo = 1/2, Co = 3, G = -2, C-1 = 2, C1 = 1, C-1 = -3
2- In cach of the following, we specify the Fourier series coefficients of a CT signal that i periodic with period To 4. Determine the signal x(t) in each case k 0 a) a sin ,k 0 km -j= ei= (j* = e#. Hint: using Euler's formula: Jkl3 jk b) a fo.0therwise -4 (1,k even c) a 2.k odd Hint: Suppose x(t) 8(t-kT) ke- is an impulse train with impulses spaced every T seconds apart (Figure 2). This is a...
Please solve it step by step
HIM(6) met VC) 2 LPF BW-B Amplifier (x2) 1 ܙܟܠ/ fcos (21fct) -fe - B I fc (A) 544) 23 2B BPE etc BW:B + ylt) A message signal n4) has a spectrum (M(f) | as given above. This sipnal is led to the system given above (rijoht), (a) Draw the spectrum of Vlt). (6) Draw the spectrum of output sipral y (t). (c) Find the total power of the output signal, yct)
Problem 3. Determine the trigonometric Fourier series coefficients an and bn for signal a(t) sin(3t 1)2 cos(7t 2) Determine also the signal's fundamental radian frequency w. No integration is required to solve this problem.
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...