All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Ask a Question
AI Study Help New

Search
Sign In
Register

study help
business
linear state space systems

Questions and Answers of Linear State Space Systems

Sometimes nonlinear regression models can be converted to ordinary GLMs by employing a link function for the mean response and/or transforming the explanatory variables. Explain how this could be
Refer to the form of iterations for the Gauss–Newton algorithm described in Section 11.3.7. Show that an analogous formula????̂ − ???? = (XTX)−1XT????holds for the ordinary linear model, where
Randomly generate nine observations satisfying a normal linear model by taking xi ∼ N(50, 20) and yi = 45.0 + 0.1xi + ????i with ????i ∼ N(0, 1). Now add to the dataset a contaminated outlying
For the data analyzed in Section 11.1.8 on risk factors for endometrial cancer, compare the results shown there with those you obtain using the lasso.
For the horseshoe crab data introduced in Section 1.5.1 and modeled in Section 7.5, suppose you use graphics to investigate how a female crab’s number of male satellites depends on the width (in
For the horseshoe crab dataset, Exercise 5.32 used logistic regression to model the probability that a female crab has at least one male satellite. Plot these binary response data against the
For the Housing.dat file analyzed in Sections 3.4 and 4.7, use methods of this chapter to describe how the house selling price depends on its size.
Continue the previous exercise, now using all the explanatory variables.
2.4. Given the following FIR filter impulse responses what are their H(z) and H(z-1)? What are the zeros of the filters? Express the transfer functions in terms of zeros and poles? Prove that these
2.3. Which of the FIR filters defined by the following impulse responses are linear phase filters?a. h[n] = {0.2, 0.3, 0.3, 0.2}b. h[n] = {0.1, 0.2, 0.2, 0.1, 0.2, 0.2}c. h[n] = {0.2, 0.2, 0.1, 0.1,
2.2. Show how the z-Transform can become the DFT.
2.5. Which of the following vector pairs are orthogonal or orthonormal?a. [1, -3, 5]T and [-1, -2, -1]Tb. [0.6, 0.8]T and [4, -3]Tc. [0.8, 0.6]T and [0.6, -0.8]Td. [1, 2, 3]T and [4, 5, 6]T
2.6. Which of the following matrices are Toeplitz?What is special about matricesc, d,e, and f? 3 2 1 2 3 3 2 1 [1 2 3] a. 4 3 2, b. 12 3, c. 111, d. 2 12,e. 2 12 543 1 2 3 (1+j) (1-j) f. (1-j) 1
2.7. Which of the following matrices are orthogonal? Compute the matrix inverses of those that are orthogonal. 0 10] 1 1 0 0 [12 3 a. 0 0 1 , b. 0 1 0 00 . C. , d. 0 20 , e. 21 2 0 0 0 0 3 3 2
2.8. Why are ergodic processes important?
2.9. Find the eigenvalues of the following 2 x 2 Toeplitz matrix,Find the eigenvectors for a = 4 and b = 1. A a b b a
7.8. Compute the MV spectral estimate of a random phase complex exponential process in white noise, defined by,[ ][ ] has a variance of .is a random variable uniformly distributed over , .where :[ ]
2.10. Compute the rounding quantization error variance for an Analogue to Digital Converter (ADC) with a quantization interval equal to Δ. Assume that the signal distribution is uniform and that the
2.12. Given the autocorrelation function for the random phase sinusoid in the previous Problem 2.11 compute the 2 x 2 autocorrelation matrix.
2.1. Does the equation of a straight line y = α x + β, where α and β are constants, represent a linear system? Show the proof.
10.2. What is the main disadvantage of the adaptive Volterra filter?
6.4. Can the exponentially weighted RLS algorithm (refer to Chapter 8) be considered to be a special case of the Kalman filter?
5.2. In Problem 5.1 the optimum first-order FIR Wiener filter for σ v2 =1 andα = 0.8 is, W(z) = 0.4048 + 0.2381z−1 . What is the signal to noise ratio(S/N) improvement, computed in dB, achieved
12.6 The three-layer Perceptron network shown in Figure 12.11, when properly trained, should respond with a desired output d = 0.9 at y1 to the augmented input vector x = [1,x1,x2]T = [1,1,3]T. The
12.5. Specify some possible applications for ANNs.
12.4. Can ANNs be seen as magic boxes which can be applied to virtually any problem?
12.3. What are the main types of ANN?
12.2. Name some general characteristics of ANNs.
12.1. What are two most important aspects of artificial neural network technology?
10.4. What would the LMS weight update equations be for Problem 10.3?
10.3. Compute the gradients of the mean square error function, E{e2[n]} , with respect to h0, a and B, for the second-order Volterra filter in the case when the data are complex.
2.13. The autocorrelation sequence of a zero mean white noise process is rv (k) =σ v2δ (k) and the power spectrum is ( ) v2 jPv e σ θ = , where 2σ v is the variance of the process. For the
9.5. What is the main purpose of the so called overlap-save and the overlapadd methods in frequency domain filtering?
7.5. For a total data length N what can you say about the relationship between the resolution and variance as function of K, the number of nonoverlapping data sections, for Bartlett’s spectral
7.4. Does the variance of the periodogram spectral estimate of white noise reduce as the data length N increases?
7.3. Assume that a random process can be described by two equal amplitude sinusoids in unit random variance white noise as defined by the following equation, x[n] = Asin(nθ1 +φ1) + Asin(nθ 2 +φ 2
7.2. What is the power spectrum of white noise having a variance of σ x 2 ?
7.1. What are the two main approaches to spectral estimation and in what way do they differ?
9.6 What is the disadvantage of the circular convolution method?
6.3. Use a Kalman filter to estimate the first-order AR process defined by, x[n] = 0.5x[n −1]+ w[n] , where w[n] is zero mean white noise with a varianceσ w2 = 0.64 .The noisy measurements of x[n]
6.2. Develop a Kalman filter to estimate the value of an unknown scalar constant x given measurements that are corrupted by an uncorrelated, zero mean white noise v[n] that has a variance of σ v 2 .
6.1. Is the Kalman filter useful for filtering nonstationary and nonlinear processes?
5.8. Find the optimum causal and noncausal IIR Wiener filters for estimating a zero-mean signal s[n] from a noisy real zero-mean signal x[n] = s[n]+ v[n] , where v[n] is a unit variance white noise
7.6. By looking at the performance comparisons of the various nonparametric spectral estimation methods what general conclusions can be drawn?
7.7. Compute the optimum filter for estimating the Minimum Variance (MV)power spectrum of white noise having a variance of 2σ x .
7.9. Compute the qth order Maximum Entropy (ME) spectral estimate for Problem 7.8.
9.4. For frequency domain filtering define the inverse of the p x p DFT matrix F.
9.3. What computational savings can be had by using a radix-2 decimation-intime FFT to perform the DFTs required in Problem 9.2?
9.2. Show how linear convolutions on sequences can be done by using frequency domain operations.
9.1. Compute how many multiplication operations are saved in the coefficient update equation for a time domain BLMS algorithm per block of L input points. Is it worth the trouble?
8.6. For the exponentially weighted RLS algorithm prove thatΦ(n)w[n] =θ (n) by setting the derivative of the weighted error ξ(n) with respect to w*[n] to zero, given that,????=Φ = −n kn n k k T
8.5. Compute and sketch a graph of the expectation of the squared error as a function of the single real-valued filter coefficient for a simple zero-order MA(0) process .
8.4. If the process and the FIR filter coefficients are complex valued show that the adaptive LMS update equation is w[k+1] = w[k] +μ e[k] x*[k].
8.3. Use the normalised LMS algorithm to derive the FIR filter coefficient update equations for the second-order AR(2) linear prediction equation of Problem 8.1.
8.2. In Problem 8.1 if the autocorrelation sequence rx (k) is given as rx (0) = 5.7523 and rx (1) = 4.0450 find the maximum bound for the step size in the LMS algorithm.
8.1. Assume x[n] is a second-order autoregressive process defined by the difference equation, x[n] = 1.2728x[n −1] − 0.81x[n − 2]+ v[n] , where v[n] is unit variance white noise the optimum
5.7. Compute the minimum mean square error for Problem 5.6 for 1 to 5 step predictors. What do you find odd about the sequence of errors from step 1 through to step 5?
5.6. Consider a random process whose autocorrelation sequence is defined by,r (k) (k) (0.9) cos( k / 4) k x =δ + π . The first six autocorrelation values are, rx [ ]T = 2.0 0.6364 0 −0.5155
4.5. Explain the main idea behind the Padé approximation method and why it is likely to be problematic in practice.
4.4. Explain why the Padé “approximation” method is badly named.
4.3. Show that Partial differentiation of Equation 4.5 with respect to variables*ak results in Equation 4.6.
4.2. Which models, MA, AR or ARMA, are the easiest to solve for their unknown parameters?
4.1. Under what conditions are Equations 4.1 and 4.2 referred to as a Moving-Average (MA), Autoregressive (AR) and Autoregressive Moving-Average(ARMA) model?
3.4. In the Acoustic Positioning System example why were the modified set of model equations, G0 H0 Tused instead of the original model equations, Tcc Tc1 Tc3 Tc2 Tc0 to solve the LSE problem?
3.3. Assume that you have three independent measurements, y1, y2 and y3 with a measurement error variance of σ 2, of the volume of water in the tray of optimum volume (tray of Problem 3.1). Show how
3.2. Show how you could use the LSE equations to solve Problem 3.1.
3.1. Assume that you have a square piece of sheet steel which you wish to bend up into a square open tray. The sheet is 6 by 6 units in area and the bend lines are x units in from the edge as shown
2.15. If x[n] is a zero mean wide-sense stationary white noise process and y[n] is formed by filtering x[n] with a stable LSI filter h[n] then is it true that, and are the variances of [ ] and [ ]
4.6. Given the signal, x = [1 1.5 0.75]T , find the Padé approximation model for,a. p = 2 and q = 0b. p = 0 and q = 2c. p = q = 1
4.7. Given the signal,???? ???? ????==0, otherwise 1, 0,1,..,20[ ]n x n , use Prony’s method to model x[n] with an ARMA, pole-zero, model with p = q = 1.
4.8. Find,a. the first-order, and,b. the second-order all-pole models for the signal, x[n] =δ [n] −δ [n −1] .
5.3 as σ v2 →0 .
5.5. Show that the solution to Problem 5.4 approaches the solution to Problem
5.4. Reconsider Problem 5.3 when the measurement of x[n] is contaminated with zero-mean white noise having a variance of 2σ v , i.e., y[n] = x[n]+ v[n] . Find the optimum first-order linear
5.3. Find the optimum first-order linear predictor having the form xˆ[n +1] = w[0]x[n]+ w[1]x[n −1] , for a first-order AR process x[n] that has an autocorrelation sequence defined by rs k( ) =α
10.1. What is a key feature of the Volterra filter that allows for the use of optimum filter theory?
5.1. Find the optimum first-order FIR Wiener filter for estimating a signal s[n]from a noisy real signal x[n] = s[n]+ v[n] , where v[n] is a white noise process with a variance 2σ v that is
4.12. For Problem 4.11 compute the next two values in the autocorrelation sequence, i.e., rx (4) and rx (5) .
4.11. Solve the autocorrelation normal equations using the Levinson-Durbin recursion to find a third-order all-pole model for a signal having the following autocorrelation values, rx (0) = 1, rx (1)
4.10. Use the modified Yule-Walker equations to find the first order ARMA model (p = q = 1) of a real valued stochastic process having the following autocorrelation values, 2 7rx (0) = 26, rx (1) =
4.9. Find the second-order all-pole model of a signal x[n] whose first N = 20 values are x = [1,−1,1,−1,...,1,−1]T by using,a. the autocorrelation method, and,b. the covariance method.
2.14. Let x[n] be a random process that is generated by filtering white noise w[n] with a first-order LSI filter having a system transfer function of, 1 0.25 1 1( ) − −=z H z If the variance of

Showing 400 - 500 of 482

1
2
3
4
5

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved