Problem 4 Sketch the sinusoid x(t) 2 cos(2 10)t T/2) over the range -0.1 s ts0.2.
Problem 4 Sketch the sinusoid x(t)-2 cos(2n(10)t + π/2) over the range-0.1 0.2.
Problem 1. x(t) = 2 cos(210.8t) + 3cos(270.2t) 1) Sketch x(t) for 0<t<2 2) Find the Fourier Series coefficients for x(t)
Problem 4.(30 pts) Given the analog signal x(t) cos(2 cos(3t)+2 sin(4mt) A.(10 pts) Find the Nyquist frequency (sampling frequency) which guarantees That x() can be recovered from it's sampled version xIn] with no aliasing. B.(10 pts) If the sampling period of Ts 0.4 see is used identify all discrete frequencies Of the signal x(t), also indicate if this sampling period is adequate to recover x(t) from xn] C.(10 pts) Suppose signal x(t) is modulated by signal e(t) = cos(2000mt) what...
and is X(t) a WSS process? 6.11 Sinusoid with random phase. Consider a random process x(t)-A cos(wot + ?), where wo are nonrandom positive constants and o is a RV uniformly distributed over A and (0, ?), i.e., ? ~11(0, ?). (a) Find the mean function 2(t) of X(t).
volem 2. SINUSOIDAL MULTIPLICATION PROBLEM Consider the multiplication of a 10 kHz sinusoid W and 2kHz. The respective amplitudes are given in the figure below. Picauon of a 10 kHz sinusoid with a signal consisting of the sum of two sinusoid V1(t)=5cos[21*10kHz*t] wo sinusoids having frequencies of: 3kHz - > Vor=V1(t)xV2(t) V2(t)=cos[21*3kHz"t]+4cos[2*2kHz*t) a. Accurately draw the entire input amplitude-frequency spectrum ACCURATELY and CLEARLY. b. Accurately draw the entire output amplitude-frequency spectrum ACCURATELY and CLEARLYTT. Note: You may use the front...
this course is signals and systems Problem 2. (A05) For arbitrary w, express e(t) 4 cos(wt) + sin(wt) as a single sinusoid.
4. Shown in the figure below is a sinusoid. r(t) sec -10 -2 This sinuosoid may be expressed as (a) From this plot, determine the values of A, ao, fo, td, and φ. Choose the value of the angle (phase) φ such that-π 〈 φ π. (b) Suppose that x(t) is sampled using a sample period of T, seconds to produce x[n] What is the sample rate fs? Indicate the units. If linear interpolation is used (this is what MATLAB...
2. Consider the random process x(t) defined by x(t) a cos(wt 6), where w and 0 are constants, and a is a random variable uniformly distributed in the range (-A, A). a. Sketch the ensemble (sample functions) representing x(t). (2.5 points). b. Find the mean and variance of the random variable a. (5 points). c. Find the mean of x(t), m(t) E((t)). (5 points). d. Find the autocorrelation of x(t), Ra (t1, t2) E(x (t)x2 )). (5 points). Is the...
Consider x(t) 1 + cos(50t) + cos( 150t) a. (5) Is x(t) periodic? If so, what is the fundamental period of x(t)? Which harmonics are contained in the signal? b. (5) Sketch the spectrum of x(t) c. (10) Determine x [n] if fs is the Nyquist rate and sketch its spectrum over the Nyquist interval. (5) Sketch the spectrum of x[n] over the Nyquist interval if fs is half of the Nyquist rate. What observations can you make about the...