[R] significance of spectal peak with spectrum()

[Uwe Ligges]

Sebastian Leuzinger wrote:

> the null hypothesis would be: one particular frequency peak is not 
> significantly different from the background noise.

So you want to know, e.g., whether there is something going on at 1000 
Hz? This is difficult: If you are considering the periodogram to be a 
density, then you do not know the distribution of the value of a single 
frequency, because it depends on the stuff going on at other frequencies.

Second point is (and already asked): "Kind of [background] noise"?

The only really easy test is for the Null "signal is white noise", hence 
H1 is "at least one non-white-noisy frequency".

[If somebody knows a really good book or papers that cover other cases 
than the trivial one mentioned above, I am very interested to hear about 
them, BTW.]

If you have another kind of noise (such as blue or pink noise), things 
become even worse.

Uwe Ligges


> On Friday 16 September 2005 09:28, you wrote:
> 
>>Sebastian Leuzinger wrote:
>>
>>>Hello, has anybody got a simple recepie to test the significance level of
>>>the peaks after using spectrum() ?
>>
>>What is you null hypothesis?
>>
>>- Kind of noise?
>>- One particular frequency is noisy or all noisy?
>>- ...
>>
>>Uwe Ligges
>>
>>
>>>(R-version 2.0.1, linux SuSE9.3)