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Problem 3. Fun with Convolution 30 points. x[n] h[n] 22 n n -6-5-4-3 2 3 Figure 4: Two signals x[n] and h[n]. Compute the convolution between the signals in Figure 4.

1. In class we used the Blum-Floyd-Rivest-Pratt-Tarjan select algorithm to find the k-th smallest value using n/5 blocks of size 5, each. Assume for this problem, we are using n/3 blocks, each of size 3. (a) Find the number of comparisons for each step of the algorithm. (b) Obtain the overall recurrence equation for the upper bound on the number of comparisons and solve it. (e) What are your observations about the difference in the asymptotic runtime between a block of size 3 vs. 5 (the one we did in class)? Explain the reason for those differences briefly.

m n n 5. (2+3=5 points) Suppose R is a ring such that Z CRCQ. (a) Prove that if me R with m and n relatively prime integers, then the R. (b) Prove that R is a PID. Tip: Let I be an ideal of R and consider A ZnI. In this case, it will be helpful to write aR and aZ for the principal ideals of R and Z respectively, as the notation (a) will be ambiguous.

Figure 2 shows a differential-output amplifier implemented in 18 nm finFET technology. Assume VDD = 1 V, Iref = 40 µA, nfinp = 150 for the pMOS, nfinn = 100 for the nMOS transistors, and C1 = C2 = C3 = C4 = 1 pF.

a) Derive an expression for the small-signal transfer function Vout+(s)/(Vin+(s) – Vin-(s)).

b) Evaluate the low-frequency voltage gain and all poles and zeros.

- = - Problem 2. Figure 2 shows a differential-output amplifier implemented in 18 nm finFET technology. Assume VDD = 1 V, Iref = 40 u?, nfinp = 150 for the PMOS, nfinn = 100 for the nMOS transistors, and C1 = C2 = C3 = C4 = 1 pF. a) Derive an expression for the small-signal transfer function Vout+(s)/(Vin+(s) - Vin-(s)). b) Evaluate the low-frequency voltage gain and all poles and zeros. = 1 VDD M7 M5 M6 M8 Vout- Vout+ 75 c1 C2 C3 C4 1 ref ( Vin+ Vin- M3 M1 M2 M4 M10 M9 Figure 2 Differential-output finFET differential amplifier.

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GENERAL INSTRUCTIONS: Use black text only. • If you have any clarification or question relevant to the items listed in the questionnaire, politely a it to the proctor/instructor concerned. 1. Flow Chart DIRECTION: Create a flow chart for the following scenario. An application for an ATM machine that allows the user to do the following transactions: a. Select Language Option (5 points) b. Pin Security (Verification) (5 points) C. Current and Savings Account (5 points) d. Checking Balance (5 points) e. Deposit Balance (5 points) f. Withdraw Balance (5 points) g. Insufficient Funds (5 points) h. Transfer Money to other Account (5 points) i. Updated Balance after Checking, Deposit and Withdraw Balance (5 points) j. Receipt Dispense (5 points) *Assume the user balance in the account is P10,000.00. Need: *Basic design structure, initialization, indention arrow, and symbol (flow chart) *Input and Output Statements *Appropriate logic applied

Corporate governance is most 2 points likely to occur when: A board of directors holds the top management accountable for organizational performance. The traditional top-down "do as I say form of management prevails. Top managers guide the performance of an organization as a whole. Team leaders report to middle managers about the performance of the non-managerial workers. 2 points A(n) ___ is the ability to translate knowledge into action that results in desired performance. Concept. Agenda Process Skill Who elects the members of the 2 points board of directors? Top managers. Stockholders. Middle managers. First-line managers

Given the training dataset with negative samples x1 = (3, 3)T , x2 = (4, 3)T and positive samples x3 = (1, 1)T , try using primal form of perceptron learning algorithm to get the per- ceptron model: f (x) = sign(w · x + b) , where w = (w(1), w(2))T , x = (x(1), x(2))T . Let the initialvaluesofwandbbew0 = 0andb0 = 0,thelearningrate? = 1,andthesequenceof misclassified samples be x1, x3, x3, x3, x1, x3, x3. Calculate the corresponding w and b of each misclassified sample.

Need in as much details as possible.

 

Calculate the return according to the modified Dietz-method given the following information

Valuation on

31.12.2015 - 72

31.12.2016 - 97

Cash inflow: 15.01.2016 - 35

 

1. How do the rotational variables (e, w, a, T, 1) relate to linear variables? Explain. How are they alike? 2. A 43.6 kg child sits on the edge of a merry-go-round with a radius of 1.3 m at a playground. If the merry-go-round is spinning at a rate of 2 revolutions per minute, what is the centripetal force keeping the child moving in a circle?

Design a contingency plan for a regional cryptocurrency exchange. Focus on operation in the UAE.

200 words only, please