EE448 Midterm review

EE448 Midterm review - (1a.) Definitions for xn sequence:...

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(1a.) Definitions for x n sequence: DTFT - X e j n − x n e j n IDTFT - x n 1 2 X e j e j n d (1b.) The DTFT is uniformly convergent if x n is absolutely summable, i.e., n − | x n | . Mean-square convergent if x n is not absolutely summable (has finite energy), n − | x n | 2 . lim K 1 2 K 1 n K K | A 0 | 2 A 0 2 . (1c.) x n A 0 e j 0 n . Energy − | A 0 e j 0 n | 2 n − | A 0 | 2 . Average power lim K 1 2 K 1 n K K | A 0 e j 0 n | 2 ↑ (1d.) Is x ̃ n 2cos 1 . 1 n 0.5 2sin 0 . 7 n a periodic sequence? If yes, fundamental period? Ans: x ̃ n has 1 1.1 2 0.7 . N 1 2 r 1 1 2 r 1 1.1 20 11 r 1 N 2 2 r 2 2 2 r 2 0.7 20 7 r 2 . To be periodic, N 1 N 2 , implies that 20 11 r 1 20 7 r 2 . Equality holds for r 1 11 r 2 7 N N 1 N 2 20 . (1e.) i A left-sided sequence x n is anti-causal if and only if x n 0 for n 0 . ii A right-sided seq x n is causal only if x n 0 for negative n . iii An absolutely summable sequence is also mean-square summable, and therefore, has finite energy. iv A finite-energy seq is square summable. Ex. seq x n is defined as n | x n | 2 . v An IIR filter h n canbeunstab leeveni f h n is bounded for all n . Ex. accumulator h n u n
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This homework help was uploaded on 04/08/2008 for the course EE 448 taught by Professor - during the Spring '08 term at Stevens.

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EE448 Midterm review - (1a.) Definitions for xn sequence:...

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