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Question1) a) State and prove the convolution theorem. b) The process of sampling a function 𝑓 may be represented by multiplication of the function by a Dirac comb (an infinite set of regularly spaced Dirac distributions). Prove that in the Fourier domain the sampling in the object (time / space) domain is equivalent to replication in the Fourier domain of 𝐹 = ℱ(𝑓), the Fourier transform of 𝑓 (i.e. replication of the spectrum). c) What is the equivalent operation in the object space of sampling in the Fourier domain? d) Show the relationship between the sequences of samples transformed by the Discrete Fourier Transform (DFT) and the continuous Fourier transform with appropriate sampling in both object and Fourier domain.

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Describe the situation in words that is modeled by the linear function. Represent the situation using a function. Represent the situation using a table of values by inserting your table of values as an image. Graph the function using Desmos.com (opens in new window). For support on using Desmos, ple ...

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Discrete Mathematics Assignment. Topics include: Functions, Injections and Bijections, Algorithms, Complexity, Integers, Primes, Modular Arithmetic, Change of Base, Euclidean, Algorithm, Integers, RSA Encryption and Decryption, Maxtrix Algebra, Mathematical Induction, Counting; Basic Counting, Floor ...

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Question 1. Consider the double integral [5 marks] I = − √ Z 3 −2 dx √ 4−x2 Z 0 f(x, y) dy + Z 0 − √ 3 dx 2− √ 4−x2 Z 0 f(x, y) dy. (a) Sketch the region of integration (by hand or using computer); (b) Re-write the ...

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ask 1The first thing to do is look at the presentation (PowerPoint). Next, look at the two examples of Progress Maps, and think about how they describe student development along a described continuum. Try to see if you can pin-point the key features of a Progress Map, and record your ideas in a seri ...

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