CS6515 - ALGORITHMS- EXAM
1 2026/2027 ACTUAL QUESTIONS
WITH VERIFIED ANSWERS.
What is the difference between FFT of one item vs FFT
multiplication of two functions? - correct answer -- ω is not
squared
- there is no odd even separation
- coefficients produced are n = 0 to 2_n -1, same for the only j
loop
- lastly, you multiply the coefficients together
- then have to do the inverse FFT
How can you express the inner product of ω_n matrix and
coefficients of "a"?
How can it be represented for the inverse? - correct answer -A =
M_n(ω_n) * a == FFT(a,ω_n)
How do you construct a matrix for an FFT - correct answer --
Take A(1), A(W_n)... A((ω_n)^(n-1))
==
,- 1 for the top row and column
- for each row, take that ω and square it
- so (ω^2) == (ω^2, ω^4 ...ω^(2(n-1)) )
What are the different ways the following ω can be represented?
a.) (ω_16)^4 - correct answer -a.) (ω_8)^2
or
(ω_8)^2
What is important to remember about the inverse of "ω"? - correct
answer -You are trying to figure out, what is required that.. if
multiplied, would make your (ω) == 1.
- In the case of (ω_8)^2, the inverse would be ω_8)^6
- In the case of (ω_8) (which exponent == 1), the inverse would
be ω_8)^7
What does the following represent?
1.) A = M_n(ω_n)a = FFT(a,ω_n)
2.) how would you calculate the inverse?
, 3.) What would the function call be for the inverse? - correct
answer -1.) THis represents the result of a regular FFT function.
You are trying to get the function A or values by using the FFT
function with inputs the coefficients and ω_n
2.) a.) M_n(ω_n)^-1 *A = a
b.) (1/2) * M_n((ω_n)^-1)
3.) a = (1/2)FFT(A, (ω_n)^n-1)
What is the direction of roots of unity calculation with FFT vs
inverse FFT? - correct answer -inverse FFT == counterclockwise
FFT == clockwise
For (ω_n)^2, what is its multiplicative inverse?
More precisely, for what power k is (ω_n)^k × (ω_n)^2 = 1? -
correct answer -k = (n-2)
It is whatever it takes to get to 0, which becomes one
so if applied: For (ω_16)^2 *(ω_16)^(16-2) == (ω_16)^16 ==
(ω_16)^0 == 1
1 2026/2027 ACTUAL QUESTIONS
WITH VERIFIED ANSWERS.
What is the difference between FFT of one item vs FFT
multiplication of two functions? - correct answer -- ω is not
squared
- there is no odd even separation
- coefficients produced are n = 0 to 2_n -1, same for the only j
loop
- lastly, you multiply the coefficients together
- then have to do the inverse FFT
How can you express the inner product of ω_n matrix and
coefficients of "a"?
How can it be represented for the inverse? - correct answer -A =
M_n(ω_n) * a == FFT(a,ω_n)
How do you construct a matrix for an FFT - correct answer --
Take A(1), A(W_n)... A((ω_n)^(n-1))
==
,- 1 for the top row and column
- for each row, take that ω and square it
- so (ω^2) == (ω^2, ω^4 ...ω^(2(n-1)) )
What are the different ways the following ω can be represented?
a.) (ω_16)^4 - correct answer -a.) (ω_8)^2
or
(ω_8)^2
What is important to remember about the inverse of "ω"? - correct
answer -You are trying to figure out, what is required that.. if
multiplied, would make your (ω) == 1.
- In the case of (ω_8)^2, the inverse would be ω_8)^6
- In the case of (ω_8) (which exponent == 1), the inverse would
be ω_8)^7
What does the following represent?
1.) A = M_n(ω_n)a = FFT(a,ω_n)
2.) how would you calculate the inverse?
, 3.) What would the function call be for the inverse? - correct
answer -1.) THis represents the result of a regular FFT function.
You are trying to get the function A or values by using the FFT
function with inputs the coefficients and ω_n
2.) a.) M_n(ω_n)^-1 *A = a
b.) (1/2) * M_n((ω_n)^-1)
3.) a = (1/2)FFT(A, (ω_n)^n-1)
What is the direction of roots of unity calculation with FFT vs
inverse FFT? - correct answer -inverse FFT == counterclockwise
FFT == clockwise
For (ω_n)^2, what is its multiplicative inverse?
More precisely, for what power k is (ω_n)^k × (ω_n)^2 = 1? -
correct answer -k = (n-2)
It is whatever it takes to get to 0, which becomes one
so if applied: For (ω_16)^2 *(ω_16)^(16-2) == (ω_16)^16 ==
(ω_16)^0 == 1
