(a) If I pick a number n that can be any integer from 1 to whose…

Question Answered step-by-step (a) If I pick a number n that can be any integer from 1 to whose… (a) If I pick a number n that can be any integer from 1 to ∞ whose probability distribution of being selected is ( 1 2 ) n , and you ask a series of ‘yes/no’ questions which I will answer truthfully, how many such ‘yes/no’ questions should you expect to ask before discovering which number I have picked? Justify your answer by invoking a known series limit. What sequence of questions would be the most efficient to ask, and why? [4 marks] (b) An inner product space containing complex functions f(x) and g(x) is spanned by a set of orthonormal basis functions {ei}. Complex coefficients {αi} and {βi} therefore exist such that f(x) = X i αiei(x) and g(x) = X i βiei(x). Show that the inner product hf, gi = X i αiβi . [4 marks] (c) Consider a data sequence f[n] (n = 0, 1, . . . , 15) having Fourier coefficients F[k] (k = 0, 1, . . . , 15). Using the 16th roots of unity labelled around the unit circle as powers of w1 , the primitive 16th root of unity, construct a sequence of the wi that could be used to compute F[3] when an inner product is computed between your sequence of wi and the data sequence f[n]. Im Re w 0 =1 w 1 w 2 w w 3 4 w 5 w 6 w 7 w 8 w 9 w 10 w 11 w 12 w 13 w 14 w 15 [4 marks] (d) Explain how vector quantisation exploits sparseness to construct very efficient codes. Use the example of encoding a natural language lexicon with a 15 bit coding budget. Contrast the strategy of using codewords for single letters versus using codewords as pointers to a sparse index of combinations of letters. [4 marks] (e) A continuous signal f(t) has Fourier transform F(ω). Explain why computing derivatives of f(t) such as f 0 (t) or f 00(t) amounts simply to high-pass filtering. For the n th derivative f (n) (t), what exactly is this filtering operation when expressed in terms of F(ω)? Show how this operation could be used to define derivatives of non-integer order (for example the 1.5 th derivative). [4 marks] 10 CST2.2019.9.11 10 Mobile and Sensor Systems A mobile phone software developer is programming her own behaviour tracking app and she wants to make it suitable for use in areas with intermittent and low bandwidth cellular connectivity. (a) Explain the precautions the developer can take to make the app work well in this environment. Describe examples of mechanisms which can help with this. [5 marks] (b) The app uses various sensors to monitor user activity and its surrounding environment. In particular, it uses the microphone to monitor location ambience (surrounding sounds). Describe a suitable machine learning approach and discuss system considerations. [6 marks] (c) Describe how the developer can use location data to provide mobility prediction and how mutual information can improve the mobility prediction algorithm. [4 marks] (d) A very able user wants to test the app for privacy leaks before using it on their own phone. What techniques can be used? Illustrate each technique’s specific purpose and the assumptions it is predicated on. [5 marks] 11 (TURN OVER) CST2.2019.9.12 11 Optimising Compilers (a) Describe the phase-order problem in a compiler and illustrate your answer with some example code. [4 marks] (b) You are advising a semiconductor design company on building a compiler for their latest processor. The processor has the following features: • Sixteen 64-bit registers (r0-r15) and sixteen 32-bit registers (s0-s15), the latter corresponding to the lower 32 bits of each of the 64-bit registers. • A one-cycle branch delay slot after each control-transfer instruction (i.e. the instruction after a branch is executed before the branch takes effect). • Complex arithmetic instructions that implicitly use r15 as their first source operand. What are the challenges of code generation for this processor, given these features and how can they be addressed within the compiler? [8 marks] (c) To ease compilation, the chief designer suggests that the processor’s instructions could be executed directly in SSA form (i.e. all destination registers unique). This would use a small cache to provide fast access to the most recently used virtual registers. Discuss the advantages and disadvantages of such an approach from the compiler writer’s viewpoint. [8 marks] 12 CST2.2019.9.13 12 Principles of Communications (a) Describe max-min fair share allocation of resources, explaining what it can be used for. [10 marks] (b) The Transmission Control Protocol (TCP) can be seen as a distributed optimisation of the dynamic resource allocation problem. Describe how capacity at bottlenecks (congested points in the network) is effectively allocated in proportion to demands, and how this is equivalent to the joint optimisation of user and network utilities. [10 marks] Image transcription textQuestion 16 4 pts What following statementsare correct for data mining? [j extraction ofactionable information and insi… Show more… Show moreImage transcription textQuestion 4 (1 point) Attributegrammars have been used in all of thefollowing types of applicat… Show more… Show more  Computer Science Engineering & Technology Python Programming CUS 1126 Share QuestionEmailCopy link Comments (0)