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Basic of Digital Designs

Quick practice

Question 1 of 3

The DFT of the vector \left[\begin{array}{llll} a & b & c & d \end{array}\right]  is the vector \left[\begin{array}{llll} \alpha & \beta & \gamma & \delta \end{array}\right] . Consider the product \left[\begin{array}{llll} p & q & r & s \end{array}\right]=\left[\begin{array}{llll} a & b & c & d \end{array}\right]\left[\begin{array}{ccccc} a & b & c & d \\ d & a & b & c \\ c & d & a & d \\ b & c & d & a \end{array}\right]. The DFT of the vector \left[\begin{array}{llll} p & q & r & s \end{array}\right]  is a scaled version of [2013]

A

[\alpha+\beta \quad \beta+\delta \quad \delta+\gamma \quad \gamma+\alpha]

B

\left[\begin{array}{llll} \alpha & \beta & \gamma & \delta \end{array}\right]

C

\left[\begin{array}{llll} \alpha^{2} & \beta^{2} & \gamma^{2} & \delta^{2} \end{array}\right]

D

\left[\begin{array}{llll} \sqrt{\alpha} & \sqrt{\beta} & \sqrt{\gamma} & \sqrt{\delta} \end{array}\right]

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