# [R] R-help Digest, Vol 35, Issue 24

Gabor Grothendieck ggrothendieck at gmail.com
Wed Jan 25 05:36:32 CET 2006

```Its not really you.  Its a fact of life that this list is inhabited by
some rather rude participants but everyone puts up with
them in the hope that they do have some useful remarks.
This has been discussed repeatedly on the list and there
is even a group of thought that feels it is a justifiable way
to keep the list volume under control.

> Dear Prof Ripley,
>
> First of all, unless you are an english professor, then I do not think you have
> any business policing language. I'm still very much a student, both in R, and
> regarding signal analysis. My competence on the subject as compared too your
> own level of expertise, or my spelling for that matter, may be a contension for
> you, but it would have been better had you kept that opinion too yourself. There
> are plenty of other reasons besides laziness or carelessness that people will
> consistently error in language use, such as learning disorders, head injuries,
> and/or vertigo.
>
> On the contrary, I am aware of the definition of a periodogram, and I know what
> the unnormalized periodogram in the data I presented looks like. Spec.pgram()
> is actually normalized too something, because it's discrete integral is not
> well above the SS amplitude of the signal it computed the periodogram for. In
> other words, the powers are not in units of around 4,000, which the peak would
> be if the units were merely the modulus squared of the Fourier coeficients of
> the data I presented. Alas, the modulus squared of the Fourier coeficients IS
> the TWO SIDED unnormalized periodogram, ranging from [-fc, fc] | fc=nyquist
> critical frequency. The definition of the ONE SIDED periodogram IS the modulus
> squared of the Fourier coeficients ranging over [0, fc], but since the function
> is even, data points in (0, fc) non-inclusive, need to be multiplied by 2. Thus
> is according too the "definition" given by Press, et al (1988, 1992, 2002, c.f.
> cp 12 & 13). I'm assuming that R returns an FFT in the same layout as Press, et
> al describe.
>
> Press, et al. are also very clear about the existence of far too many ways of
> normalizing the periodogram too document, which they stated before delving into
> particularly how they normalized to the mean squared amplitude of the signal
> that the periodogram was computed from. In the page before, and perhaps this is
> where some of the confusion arises from, they document the calculations for MS
> and SS amplitudes and "time integral squared amplitude" of the signal in the
> "time" domain, not the frequency domain. The page after that, their example
> only shows how to normalize a periodogram so its sum is equal too the MS
> amplitude. In short, but starting from SS amplitude:
>
> a). sum(a[index=(1:N) or t=(0:N-1)]^2) = SS amplitude calculated in time domain
>
> b). 1/N * sum(Mod(fft[-fc:fc])^2) = two sided periodogram that sums too the SS
> amplitude
>
> c). Same as b but over the range [0, fc], and (0, fc) multiplied by 2 is the one
> sided periodogram, also sums too the SS amplitude
>
> For MS amplitude, the procedures are identical, only the time domain is divided
> by N, and the frequency domain figures are divided by N^2 instead of N.
>
> When the periodogram is in power per unit time, as in the above, so that the
> power is interpretable at N/2+1 independent frequencies, it is a normalized
> periodogram. spec.pgram() IS normalized, I just do not know what it's
> normalized too because I can not seem to get spec.pgram to stop tapering (at
> which point the normalization should be dead on, not just "close").
>
> By the way, "normalized" does not automatically mean anything unless "to what"
> is stated. I could normalize something arbitrarily to the number of tics on my
> dogs back side, and still call it normed, or erroneously refer too it as
> unnormed. If "normalized" is suposed to mean something specific, then I am
> confident that more than 90% of undergraduates are not familiar with what the
> term "should" mean. Stats and coding and using programs are a human endeavor.
> This human seems to have made meaning out of terms differently than what those
> who wrote the documentation seem to have intended. Only, I do not know where
> the documentation or my understanding may have been missled (R docs, Numerical
> Recipes, or any other source I looked at since I started).
>
> Cheers,
> KeithC.
>
>
> Second, please study the references on the help page, which give the
> details.  That is what references are for!  The references will also
>
> The help page does not say it is `normalized' at all: it says it computes
> the peridogram, and you seem unaware of the definitions of the latter (and
> beware, there are more than one).
>
> On Tue, 24 Jan 2006, Keith Chamberlain wrote:
>
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