# [R] Odp: Help with 'spectrum'

stephen sefick ssefick at gmail.com
Fri Sep 12 17:02:31 CEST 2008

```1/(x-axis value) = frequency in time
(the x-axis is in cycles per time)

2008/9/12 Petr PIKAL <petr.pikal at precheza.cz>:
> Hi
>
> r-help-bounces at r-project.org napsal dne 09.09.2008 18:44:34:
>
>> For the command 'spectrum' I read:
>>
>> The spectrum here is defined with scaling 1/frequency(x), following
> S-PLUS.
>> This makes the spectral density a density over the range
> (-frequency(x)/2,
>> +frequency(x)/2], whereas a more common scaling is 2π and range (-0.5,
> 0.5]
>> (e.g., Bloomfield) or 1 and range (-π, π].
>>
>>
>> Forgive my ignorance but I am having a hard time interpreting this. Does
> this
>> mean that in the spectrum output every element of the \$spec array is
> scaled by
>> 1/frequency(x)? I am having a hard time determing what is meant by
>> 'frequency'.Say I define a time series for a year with samples for every
> day.
>> I input a 'frequency' of 365 (which in my mind is the period). On the
> output
>> of 'spectrum' would this mean that every element of the \$spec array is
> scaled
>> by 1/365? There is a corresponding frequency array on the output from
>> 'spectrum'. If the frequency is 365 and an element in the frequency
> array
>> output from 'spectrum' is .1 am I to assume that the period is 36.5 and
> a
>> corresponding sin wave would be sin(2 * pi * 36.5/365)?
>
> Well, although I am not an expert in this matter I try to explain my
> humble understanding of spectrum results.
>
> sss<-spectrum(sunspots)
> sss\$freq[which.max(sss\$spec)]
> [1] 0.09166667
> 1/sss\$freq[which.max(sss\$spec)]
> [1] 10.90909
>
> you can see that maximum of spec value is for this time series at freq
> 0.09 and 1/0.09 is almost eleven. Knowing that sunspots have periodicity
> 11 years I assume that for each series I can get an information about its
> periodicity by 1/freq. E.g. if your series is days 1/freq means period in
> days.
>
> Regards
> Petr
>
>>
>> Thank you in advance for helping me clear up some confusion.
>>
>> Kevin
>>
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--
Stephen Sefick
Research Scientist