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