The signal xi has a duration nx = 16. If the DFT is evaluated using the 20th harmonic f20, the resulting value is the same as for harmonic fk, where the value of k =________.

Question

Fill in the blank(s) with the appropriate word(s).

Answer 1

f20 = 20/16 = 16/16 + 4/16. cos(2?f20k) = cos(2?(1 +4/16)k) = cos(2?k + 2?(4/16)k) = cos(2?(4/16)k) = cos(2?f4k). Hence, k=4.