The selection algorithm (to find the kth smallest value in a list), described in the class (and in the book), uses columns of size 5. Assume you implement the same selection algorithm using columns of size 9, rather than 5. (a) Exactly how far from either end of the array is the median of medians guaranteed to be. Just give the high order term. (Recall that with columns of size 5 we got 3n 10 .) (b) It turns out that there is an algorithm that finds the median of 9 elements with 14 comparisons. Using this algorithm, briefly list each step of Selection with columns of size 9 and how many comparisons the step takes. Note that partition can now be done with only (4/9)n comparisons; use this value in your analysis. (c) Write a recurrence for the number of comparisons the algorithm uses. (d) Solve the recurrence using constructive induction. Just get the high order term exactly. (e) With more careful analysis, in class we could have obtained 16n comparisons using columns of size 5. How does this new value, using columns of size 9, compare?

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Now you’re on your own. include a short summary of this section with plots in your lab report. write a matlab script file to do steps (a) through (d) below. include a listing of the script file with your report. 1 the soundsc(xx,fs) function requires two arguments: the first one (xx) contains the vector of data to be played, the second argument (fs) is the sampling rate for playing the samples. in addition, soundsc(xx,fs) does automatic scaling and then calls sound(xx,fs) to actually play the signal. mcclellan, schafer, and yoder, dsp first, 2e, isbn 0-13-065562-7. prentice hall, upper saddle river, nj 07458. c 2015 pearson education, inc. 4 mcclellan, schafer and yoder, signal processing first. prentice hall, upper saddle river, new jersey, 2003. c 2003 prentice hall. (a) generate a time vector (tt) to cover a range of t that will exhibit approximately two cycles of the 4000 hz sinusoids defined in the next part, part (b). use a definition for tt similar to part 2.2(d). if we use t to denote the period of the sinusoids, define the starting time of the vector tt to be equal to t , and the ending time as ct . then the two cycles will include t d 0. finally, make sure that you have at least 25 samples per period of the sinusoidal wave. in other words, when you use the colon operator to define the time vector, make the increment small enough to generate 25 samples per period. (b) generate two 4000 hz sinusoids with arbitrary amplitude and time-shift. x1.t / d a1 cos.2

Mastercard managers are motivated to increase (1) the number of individuals who have and use a mastercard credit card, (2) the number of banks and other clents who issue mastercards to customers and/or employees, and (3) the number of locations that accept mastercard payments. discuss how mastercard could use its data warehouse to it expand each of these customer bases.