Re: fft problem (conjugates)

[Roberto Hernandez]

A necessary condition for the conjugate property you mention (I believe it's 
called Hermitic symmetry) is that the sequence be real:

F(w) = S(-inf,+inf)  f(t) * exp(-jwt) dt
Therefore F(-w) = S(-inf,+inf) f(t) * exp(jwt) dt

F*(w) = S(-inf,+inf) f*(t) * exp(jwt) dt

It follows that F(-w) = F*(w) only if f(t) = f*(t) which means that f(t) must 
be real.

On Saturday 25 August 2001 05:11 pm, Sengupta Sourav wrote:
> Hi all,
>
> Had a qn..when i perform an fft on say an 8 pt
> sequence(radix 2) we get the results as say
>
> X(0), X(1), X(2)...X(7)
>
> now we expect X(1) and X(7) to be conjugates and..
>
> X(3) and X(5) to also be conjugates, also
>
> X(0) = sum of all the elements of the 8 pt input
> sequence etc..
>
> when i gave a real series as the input..this worked
> fine,with the fft results satisfying the abovebut when
> i gave a complex sequence as the i/p to the fft..this
> is what i got
>
>   1 + 0i  2 + 0i  3 - 1i  0 + 0i  1 + 0i  2 + 1i  2 +
> 0i  0 - 1i
>
> octave:15> k
> k =
>
>  Columns 1 through 3:
>
>    11.00000 -  1.00000i   -1.00000 -  2.41421i
> -1.00000 -  3.00000i
>
>  Columns 4 through 6:
>
>     1.00000 +  2.41421i    3.00000 -  1.00000i
> -1.00000 +  0.41421i
>
>  Columns 7 and 8:
>
>    -5.00000 +  5.00000i    1.00000 -  0.41421i
>
> where a is the input and k=fft(a)=fft(a,8), clearly
> the conditions are not satisfied..if anyone knows the
> problem plzz mail me.
>
> Thanks in advance,
>
> Sourav
>
> =====
> Sourav Sengupta
>
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