1. Let u and v be orthogonal vectors. If u tv and u-u are orthogonal, show that ||1|| = ||2||.(5%) 2. Let the inner prod

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1 Let U And V Be Orthogonal Vectors If U Tv And U U Are Orthogonal Show That 1 2 5 2 Let The Inner Prod 1 (61.05 KiB) Viewed 27 times

1. Let u and v be orthogonal vectors. If u tv and u-u are orthogonal, show that ||1|| = ||2||.(5%) 2. Let the inner product on vector space V be (u, v)= S'uvdr. Use the Gram- Schmidt process to transform {1, 2x, z?} into an orthogonal basis for V (10%) 3. Consider the following signal y=3sin (507t)+sin(807t)+sin(1107t)+7sin (180t) +9 sin (380st) (a) If an 80Hz sampler is applied, determine all the output signal frequencies after sampling. (10%) (b) At least what sampling rate is required to observe the whole signal without any alias? (5%) 4. Consider a signal frequency recovery. Suppose there are two samplers with sampling rates 200Hz and 180Hz. The corresponding aliasing frequencies are 70Hz and 10Hz respectively. What may be the possible true frequency of the signal? (10%)