- #1
elyons
- 10
- 1
Problem:
The first six values of the 10-point DFT of a real-valued sequence x(n) are given by
{10, −2 + j3, 3 + j4, 2 − j3, 4 + j5, 12}
Determine the DFT of x[n] = x[n+5] (10 point sequence)
Relevant Equations:
DFT(x[n-m]) = exp(-j*(2pi/N)*k*m) * X(k)
where N = 10 ; m = -5
Attempt:
Using the relevant equation calculating 6 points of the DFT from the shifted input is straight forward as X(k) is given 0<=k<=5 from the six point DFT series given.
I am failing to see how to calculate the 10 point series however. My intuition is that it has something to do with the periodicity of the DFT but I cannot see any patterns emerging from shifting the input. The magnitudes of the coefficients don't seem to change but their angles due, Still I can not spot any patterns...
The first six values of the 10-point DFT of a real-valued sequence x(n) are given by
{10, −2 + j3, 3 + j4, 2 − j3, 4 + j5, 12}
Determine the DFT of x[n] = x[n+5] (10 point sequence)
Relevant Equations:
DFT(x[n-m]) = exp(-j*(2pi/N)*k*m) * X(k)
where N = 10 ; m = -5
Attempt:
Using the relevant equation calculating 6 points of the DFT from the shifted input is straight forward as X(k) is given 0<=k<=5 from the six point DFT series given.
I am failing to see how to calculate the 10 point series however. My intuition is that it has something to do with the periodicity of the DFT but I cannot see any patterns emerging from shifting the input. The magnitudes of the coefficients don't seem to change but their angles due, Still I can not spot any patterns...