Thread: About FFT scaling factor in SAC

Hi, ALL

We suppose that x[n] and y[k] are a DFT pairs, i.e.
y[k]=1/N*sum_n(x[n]*exp(-2*pi*j*k*n/N)) n=0,1,...,N-1
where sum_n means the sum for n=0,1,N-1(similar for sum_k),
and dt is the sampling interval, df is the sampling frequency,
N is the sampling number.
To obey Parseval's theorem, we get
sum_n(x[n]*x[n])*dt=sum_k(y[k]*y[k])*df
since sum_n(x[n]*x[n])=N*sum_k(y[k]*y[k])
and df=1/(N*dt), also consider the amplitude symmetry of the real series,
we should multiply a coefficent to y[k]:
sqrt(2)*N*dt
but in SAC software, this value is N*dt/2,
so do you have any idea?

Thanks.