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2007년 Communication Signal Processing이라는 강의를 맡았었는데, 실제 내용은 Array Signal Processing에 관한 것이었습니다. 이 강의에서 사용했던 중간고사 문제입니다.

Communication Signal Processing : MidExam

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1.

(a) [5 pts] Explain a (temporal) sampling theorem.

(b) [10 pts] Consider a linear array with sensor distance . Source signal has a wavelength . Show that should be

.

2. Consider a linear array as following figure.

(a) [5 pts] When , (assume that the sensor noise is )

(b) [5 pts] When , find a conventional (delay-and-sum) beamformer's output .

(c) [10 pts] Input SNR can be defined by

.

Find output SNR of conventional beamformer.

(d) [15 pts] When , normalized directional gain pattern for direction finding can be defined as

,

where . Find .

3. Consider a linear array signal model

where and has zero mean.

(a) [5 pts] A weight vector of conventional beamformer is given by , and the beamformer's output . Find the output power

.

(b) [10 pts] Solve the following optimization problem.

and find the output power .

(c) [15 pts] Since , is also equal to 1. By using Cauchy-Schwarz inequality (), prove that .

4. Let narrowband coherent signals arrive at the array from direction .

(a) [10 pts] Describe the reason why MUSIC algorithm can't find the DOA.

(b) [10 pts] Describe how to solve the coherent problem.