# How to scale fundamental frequency to [0,1]?

[Sorry for the noobish question...]

I have a signal which is known to be generated by a process operating at some known rate $f$ Hz and the sampling rate is also know to be $K$ Hz. Now I do a periodogram of the signal and its first peak (aka fundamental frequency, right?) closely corresponds to $f$ - so I'm quite happy.

But now I want to estimate the amplitude and phase using a standard algorithm which I am taking from this good book (Algorithm 9.2). The snag is that there the frequency $f_{0}$ is supposed to satisfy $0 < f_{0} <\frac{1}{2}$ and I am at a loss as to how to convert my $f$ to Kay's $f_{0}$. I tried to take $f_{0}=\frac{f}{K}$ but got gibberish results.

• I'm pretty sure that $f_0$ is the frequency normalized by the sampling frequency. Maybe you can add some details to your question so we can try to figure out what's going on. – Matt L. Mar 11 '15 at 11:19
• @MattL. But why then $f_{0}$ is limited to one half? – Felix Goldberg Mar 11 '15 at 12:58
• Because that's the maximum frequency of a discrete-time signal (i.e. $f_s/2$), all other frequencies are not unique ("aliasing"). – Matt L. Mar 11 '15 at 13:56