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Basic of Digital Designs

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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]

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

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

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

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

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Basic of Digital Designs

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Question 1 of 3

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