Calculate the energy and the energy-spectral-density for the signal x(t) 100 sine(200 π t)cos (1400mt)
1.x(t) =Aexp((-t^2)/T^2) (T>0) (a) Energy Spectral Density (b)Autocorrelation Function y(t)=x(t)cos(2m/t) (1) Energy spectral Density 1.x(t) =Aexp((-t^2)/T^2) (T>0) (a) Energy Spectral Density (b)Autocorrelation Function y(t)=x(t)cos(2m/t) (1) Energy spectral Density
2. (30 points) Let X(t) be a wide-sense stationary (WSS) random signal with power spectral density S(f) = 1011(f/200), and let y(t) be a random process defined by Y(t) = 10 cos(2000nt + 1) where is a uniformly distributed random variable in the interval [ 027]. Assume that X(t) and Y(t) are independent. (a) Derive the mean and autocorrelation function of Y(t). Is Y(t) a WSS process? Why? (b) Define a random signal Z(t) = X(t)Y(t). Determine and sketch the...
Consider the sinusoidal signal X(t) = sin(t + Θ), where Θ ∼ Uniform([−π, π]).Let Y (t) = d/dtX(t). (a) Find the first-order PDF of the process Y (t). (b) Find E[Y (t)]. (c) Find the autocorrelation function of Y . (d) Find the power spectral density of Y . (e) Is Y ergodic with respect to the mean?
Say, X1(t)-A( 2 . t/9) × e-15-t/1x cos (2 π . t-π/4) ; l Using the format of time frequency pairs: 1. t S5, and zero elsewhere. a. b. c. d. Produce an educated guess (by hand) for the spectral decomposition of the signal x,(t) Carry on the spectral decomposition computation of x, (t) Compare the results in parts a and b above. Consider this time contamination with additive white Gaussian noise.
(a) The signal x(t) 3 cos (2n404 t + π/4) + cos(2n660t-n/5) is sampled at 20kHz. How many samples would be stored after 60 ms? (b) If x(t) = 4 cos(2π250t + 2n/7), what is the period of this signal? (c) For CDs, the sampling rate is 44,100 samples per second. How often (in seconds) must the ADC sample the signal? (a) The signal x(t) 3 cos (2n404 t + π/4) + cos(2n660t-n/5) is sampled at 20kHz. How many samples...
x(t)=exp(-at) u(t), u(t) is unit step function what is x(t) autocorrelation function? energy spectral density? energy? bandwidth?
Find the spectral density of the output signal ex(): Um u(0) uex(t) Reccomendation: Use the known spectral density of the rectangular pulse and apply properties of the Fourier transforms Find the spectral density of the output signal ex(): Um u(0) uex(t) Reccomendation: Use the known spectral density of the rectangular pulse and apply properties of the Fourier transforms
Find the spectral density of the output signal uex(): u(t) uex(0) 0 At 24t Reccomendation: Use the known spectral density of the rectangular pulse and apply properties of the Fourier transforms Find the spectral density of the output signal uex(): u(t) uex(0) 0 At 24t Reccomendation: Use the known spectral density of the rectangular pulse and apply properties of the Fourier transforms
Digital Signal Processing DFT Consider a speech signal x() that has the following frequency spectrum: xga) 1 + cos( -/100 a) Select appropriate values of N and T that will help us carry out DFT-based spectral analysis of this signal x401@) 800 such that the continuous-time frequencies are sampled no farther than 10 Hz apart. b) Ignore the issue of spectral leakage; under this assumption, provide a closed-form expression for the DFT of the signal using the values selected in...
Expand the given function in an appropriate cosine or sine series f(x) = 1x1, -π <x<π F(x) = sin nx cos nx + n=1L Suhmit Answor Savo Drogroso