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AWR1642: The

Part Number: AWR1642

Hi,

In the index.html,in the section Scaling says"1D processing: If the input to the FFT were a pure tone at one of the bins, then the output magnitude of the FFT at that bin will be (N/(2^(log4(N)-1)) )( N is the FFT order) times the input tone amplitude (because tone is complex, this implies that the individual real and imaginary components will also be amplified by a maximum of this scale)".According to the description,the magnitude ratio between the original  signal and the FFT data at the bins is N/(2^(log4(N)-1))= 2*sqrt (N ) . How  is this ratio obtained?In my derivation,the ratio is N as belows:

 if x(n)=A*exp(j2*pi*f0/fs*n),0 <=n<N-1,

  X(k)=sum(A*exp(j2*pi*f0/fs*n)*exp(-j2*pi*k/N*n))

        =sum(A*exp(j2*pi*n*(f0/fs-k/N )))

 In the bin f0, 2*pi*n*(f0/fs-k/N)=0,

 => X(k)=sum(A) =>X(k)=N*A=>X(k)/A=N.

In the Dss demo, why is the ratio N/(2^(log4(N)-1)) ?Is there any literature to be referred?

Thanks in advanced,

Regards,

Rata

  • Hi,

    We are researching litterature and will get back to you

    Thank you
    Cesar
  • Hi Rata,

    Scaling within an FFT is essentially a function of the implementation of the algorithm.

    Your derivation assumes that there is no  scaling within the algorithm. In such a case the  gain is N.

    However, the 16 bit FFT function is radix-4 FFT, and therefore there are log4(N) stages. In all but the last stage there is a divide by 2 after the butterfly computation.

    Therefore, the scaling factor becomes N/(log4(N)-1).

    Regards

    Anil