# EE263 HOMEWORK SOLUTIONS

To find the predictive ability of an AR model with coefficients a0 , b1 ,. The vehicle starts at the origin, at rest, i. In the first, you simply generalize all the results to work for complex matrices, vectors, and scalars. You might find the matlab functions dct and idct useful; dct eye N and idct eye N will return matrices whose columns are the DCT, and inverse DCT transforms, respectively, of the unit vectors. In this example, nodes 1 and 3 are connected by communication link 4, and the associated arc points from node 1 to node 3. Do not hesitate to use matlab. You are encouraged to try adjusting the powers by hand, as Bob does, to achieve small e.

Posted on Aug Read: If there are some assumptions you need to make say, on rank of some matrix, independence of some vectors, etc. You may not assume anything about the dimensions of A, its rank, nullspace, etc. This M-file will also define a second data set, Xtest and ytest, of the same size i. Plot the responses when verifying. Then, predict what y ,. You can assume that the data contains an integral number of days, i.

In this problem we consider the unit sphere in Rnwhich is defined as the set of vectors with norm one: Miki proposes the estimate and cancel method. A digital circuit consists of a set of n logic gates, interconnected by wires.

In this part, we ignore the issue of noise or sensor errors; we assume the spot measurements are exactly as described above. A communication system is based on 3 symbols: For this communication system, a valid sequence of symbols x1x2. Compute and report the Ew263 prediction error.

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In a color matching problem, an observer is shown a test light and is asked to change the intensities of three primary lights until the sum of the primary lights looks like the test light. In that case you obtained the quadratic extrapolator by interpolating the last three samples; now you are obtaining it as the least squares fit to the last ten samples.

The prices change according to the following equations: Plot the vehicle trajectory, using plot p 1,: As an example, consider node 3 in the network of part 2. The problem is to find a rational function of homewokr degree that is consistent with this data. For i odd, yi depends only on xj for j even. We measure the total pollutant level at m spots, located at t1. Not needed to solve the problem. In each experiment we measure and note the temperatures at the two critical locations.

## ee263 homework 3 solutions

If the matrix is onto, then so are the matrices A and B. What is your method? Each of these models is specified by its parameters, i. This is what we needed to show.

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Plot the optimal force fand the resulting p and p. The MA model, on the other hand, has a finite solutioms Verify that the matrix R is orthogonal. In this problem we explore a simple version.

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Your answer can involve any of the concepts used in the course so far, e. This will produce three different smoothed estimates.

Running this M-file will define ydes and the matrices A i given as a 3 dimensional array; for example, A: Note that there is no requirement on the vehicle velocity at the way-points. Identify any pairs of the methods soutions coincide i.

# ee homework 3 solutions

Such a function is called a rational function of degree m. You can assume that the matrices A and B are skinny and full rank i.

You can assume that the data contains an integral number of days, i. We want just your answer, which will consist of lists of mutually equivalent statements; we do not need any justification. The scalar signal u is the input, and soluitons scalar signal z is the output. Explain how to find the smallest such estimator matrix, i.

Please try to give simple examples, hmework make it easy for you to justify that the ranks of A, B, and AB are what you claim they are.