Calculate the auto-correlation sequence for the input sequence x(n)[2,3,4,5]. a. The discrete autocorrelation is: n=N-1 x(n)x(n...
ASSIGNMENT 2 (C4,_CO2, PO1) 1. Calculate DFT of the following discrete-time sequence, x(n) using DFT technique x(n) = {72,-56, 159) (C4, CO2,PO1) 2. Calculate the 8-point DFT of the following discrete-time sequence, x(n) using Decimation In Time Fast Fourier transform (DIT-FFT) algorithm. Show the sketch and label all parameters on a signal flow graph/butterfly diagram structure in your answer. (1-3<ns3 x(n) = 0 elsewhere
The output of a discrete-time system is related to the input by Y(n) x(n is 1 1) = - a. Find the transfer function of the system. b. If the input X(n) is stationary with E(X(n)) = 0 Rxx(k) = { 1, for k = 0 for k 0 0 find Sy(f) and EfY'(n) γγ
x[n] = { Consider the discrete sequence S (0.5)" 0<n<N-1 otherwise a) Determine the z-transform X(2)! b) Determine and plot the poles and zeros of X(2) when N = 8!
d) Given a discrete time sequence: x[n] 218(n 2) - (n 1) +358 (n) -(n 1)218 (n - 2) where δ(n) is the unit-impulse sequence and the general Discrete Time Fourier Transform (DTFT) X(ej") is: i) ii) iii) Do the following without explicitly finding X(ejo) Determine χ[0]-4x[1] Evaluate DTFT X(ejw) at ω-0. Using one of the DTFT properties, state the value the phase value of X(eM) (ie. φ(u)) . Explain how you get the answer
1. Auto- and Cross-Correlation. For each of the following, compute the cross correlation T/2 Rry(,) = E[drpd, + n-linx t-Tax(ry(, + rdr . Hint: Use trigonometric identities (see HW 1), 27T such as sin a sin b-2 [cos(a-b)-cos(a + b)] . Also use the fact that j cos(ont-б unless co-0 x(t) = sin(2n/r), y(t)-sin(2nft) (here x and y are the same, so Rry-Rrr is the a. autocorrelation of x). x(t) = sin(2nft), y(t) = sin(2nf(t-to)) c. x(t)-n(), y()2x(t) +n2(t) where...
1. Auto- and Cross-Correlation. For each of the following, compute the cross correlation T/2 Rry(,) = E[drpd, + n-linx t-Tax(ry(, + rdr . Hint: Use trigonometric identities (see HW 1), 27T such as sin a sin b-2 [cos(a-b)-cos(a + b)] . Also use the fact that j cos(ont-б unless co-0 x(t) = sin(2n/r), y(t)-sin(2nft) (here x and y are the same, so Rry-Rrr is the a. autocorrelation of x). x(t) = sin(2nft), y(t) = sin(2nf(t-to)) c. x(t)-n(), y()2x(t) +n2(t) where...
5. A stationary random process X[n] is input to a discrete time LTI system with frequency response j“)-10 zero mean given as A(e nmay be expressed as where Wnlis a zero mea a-HS1 unit variancei.i.d. (independent identically distributed) Gaussian sequence and c, d are constants. Let Yl be the output random a)Determine the mean function for the output random sequence Yn in terms ofa, c and d b) Determine S7 (e), the power spectral density ofthe output random sequence Yn]...
-Σ rinkin + ml. Sequence c[n] is defined as c[n] x(n] = { 1,-1, 1 } as x[k] and 5-point DFT of c[n] as c[k]. (i) Calculate C[1]? 「[I] = 1-e^(-%72%pi/5)+6 alculate the 4-point DFT of sequence Your last answer was interpreted as follows: I-e + e- Incorrect answer. ii) Calculate i [] is the conjugate operator) -96 Your last answer was interpreted as follows:-i Incorrect answer.
-Σ rinkin + ml. Sequence c[n] is defined as c[n] x(n] = {...
7. X(n) is a zero- discrete-time random process. following input-output relationship: zn) -0.95 mean, stationary, identically and independently, Gaussian distributed white The sample functions of this process is filtered according to the n( zn-1)+x(n) (5 points). Write the MATLAB code for the computation of autocorrelation of the processes X(n) and Z(n) by repeating the experiment 100 times. (5 points). b.
7. X(n) is a zero- discrete-time random process. following input-output relationship: zn) -0.95 mean, stationary, identically and independently, Gaussian distributed...
on Bele o Vhich one of the folloving statesents is correct? A. ALI these pictures show valid autocorrelation funetions B, Hone of ths thzse pictures show valid auto correlation functiona c. Ploture C shows valid autocorrelation functios D. Picture A shoes n valid autocorrelation function t. Pleture 8 shows a valid autocorrelation funetlon Ans, I4. Ne repest problia 13 but iastead as sbout pavse spectral dansities SaLe) (PSD) A. BuL 3 ara vala P ts a lo pts. The poues...