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 MULTIPLE CHOICE TEST INFORMAL DEVELOPMENT OF FAST FOURIER TRANSFORM FAST FOURIER TRANSFORMS Pick the most appropriate answer.

Q1.  Using the definition W=e-i(2π/N) , and the Euler identity e± = cos(θ) ± i sin(θ), the value of W(N/6)  can be computed as

0.866 - 0.5i

-0.866 + 0.5i

-0.5 - 0.866i

0.5 - 0.866i

Q2.  Using the definition W=e-i(2π/N), and the Euler identity e± = cos(θ) ± i sin(θ), the value of W(6N)  can be computed as

1 + i

1 - i

1

-1

Q3. Given N=2, and

.

The first part of  can be expressed as

The values for can be computed as

Q4.  For N =24 =16, level L=2 and referring to the figure 1 shown at this link, the only terms of vector ƒ2(-)which only need to compute are

ƒ2(4-7,12-15)

ƒ2(0-3,8-11)

ƒ2(0-7)

ƒ2(8-15)

Q5For N =24 =16, level L=3 and referring to referring to the figure 1 shown at this link, the only companion nodes associated with ƒ3(0) and ƒ3(1) are

ƒ3(4) and ƒ3(5)

ƒ3(6) and ƒ3(7)

ƒ3(14) and ƒ3(15)

ƒ3(2) and ƒ3(3)

Q6.  Given N = 4, and

.

Corresponding to level L = 1, one can compute  ƒ3(2) as

-2 - 2i

4 - 6i

4 - 6i

-4 - 4i

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