Re: FFT test with few kbits

From: Cristiano (cristiano.pi_at_NSquipo.it)
Date: 02/03/04 

Date: Tue, 03 Feb 2004 20:18:42 GMT

Eric Backus wrote:
> "Cristiano" <cristiano.pi@NSquipo.it> wrote in message
> news:IKLSb.229337$_P.7863588@news4.tin.it...
>> Eric Backus wrote:
>>> "Cristiano" <cristiano.pi@NSquipo.it> wrote in message
>>> news:6xASb.169284$VW.6887419@news3.tin.it...
>>>> "Eric Backus" <eric_backus@alum.mit.edu> ha scritto nel messaggio
>>>> news:1075493567.723814@cswreg.cos.agilent.com
>>> I don't see where you're getting that. For your example above, the
>>> mean of the real part of the rest is -0.888888888888. If you do
>>> this many times with different random data, the expected value of
>>> the values other than the first is zero. If you include the first
>>> value, the expected value of everything is 1 (basicly N/2 from the
>>> first point, plus zero for each other point, divided by N/2 which
>>> is the number of points you're averaging).
>>>
>>>
>>>> The mean of the imaginary part varies from about -1.14 to 1.23.
>>>> You seem able to calculate the FFT; have you checked what you've
>>>> said?
>>>
>>> Yes.
>>
>> I'm very surprised of that "yes".
>>
>> We have said that the first number is about N/2 (integer always >0).
>> The sum of the real components from 1 to N/2-1 is always an integer
>> number and it is about 1/2 of the first component, or N/4 it can be
>> <0 or >0.
>>
>> For example, if we get a 300-bit sequence, we could get:
>> component #1 = 148,
>> sum from 1 to 149 of the real components = -78,
>> -78 / 149 = -.523.
>>
>> I don't know how you get 0.
>
> If the sum is N/4 half the time, and -N/4 half the time, then the
> mean value will be zero, right?

No :-) but I think the problem is that my first component is #0 (please, see
my answer to Ernst Lippe).

>>>> As I said in my first post, the KS test over the real part gives
>>>> good p-values, and the same happens for the imaginary part. These
>>>> p-values should be uniformly distributed, but unfortunately it
>>>> doesn't happen.
>>>> The KS test over the p-values gotten from the 1st level KS test is
>>>> bad for t he real part, but incredibly bad for the imaginary part.
>>>> For this reason I used the real part.
>>>
>>> If you're including the first point, which has a much larger real
>>> part and exactly zero imaginary part, that might cause problems? I
>>> guess I don't really know what the problem might be here.
>>
>> I don't include the first point, I use points from 1 to N/2-1.
>
> I'm over my head here, but I can try to guess anyways. My guess is
> that this comes from the real values not being truly independent.
> Clearly, if the real values sum to either N/4 or -N/4, they are not
> independent variables. Perhaps the tests would pass if you used only
> the first N/4-1 DFT outputs instead of N/2-1. But like I said, I'm
> over my head and don't really know.

Thank you anyway for the help.

Cristiano

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