Hi

Using an FFT on real data, I noticed that the magnitudes (root sum 
square of real & imag) of the bins was not equal when the input signal 
comprises tones of equal sizes.  OK, there's a bit of noise and the 
numbers move about a bit, and there's some analog signal equalisation 
which isn't as good as it could be.

But when I plot the output, while there is an overall trend, there is 
also a clear alternation in magnitudes - the odd numbered bins are 
smaller than the even.

This occurs only when using multiple tones.  If I use single tones the 
measured magnitudes follow the overall trend as expected, but there's no 
alternation.

Anyone seen this before?

Cheers
-- 
Syd

Did you use any window function?

On 26.07.2012 11:06, Syd Rumpo wrote:
> Hi
>
> Using an FFT on real data, I noticed that the magnitudes (root sum
> square of real & imag) of the bins was not equal when the input signal
> comprises tones of equal sizes.  OK, there's a bit of noise and the
> numbers move about a bit, and there's some analog signal equalisation
> which isn't as good as it could be.
>
> But when I plot the output, while there is an overall trend, there is
> also a clear alternation in magnitudes - the odd numbered bins are
> smaller than the even.
>
> This occurs only when using multiple tones.  If I use single tones the
> measured magnitudes follow the overall trend as expected, but there's no
> alternation.
>
> Anyone seen this before?
>
> Cheers

On 26/07/2012 11:29, Andre wrote:
> Did you use any window function?
>
> On 26.07.2012 11:06, Syd Rumpo wrote:
>> Hi
>>
>> Using an FFT on real data, I noticed that the magnitudes (root sum
>> square of real & imag) of the bins was not equal when the input signal
>> comprises tones of equal sizes.  OK, there's a bit of noise and the
>> numbers move about a bit, and there's some analog signal equalisation
>> which isn't as good as it could be.
>>
>> But when I plot the output, while there is an overall trend, there is
>> also a clear alternation in magnitudes - the odd numbered bins are
>> smaller than the even.
>>
>> This occurs only when using multiple tones.  If I use single tones the
>> measured magnitudes follow the overall trend as expected, but there's no
>> alternation.
>>
>> Anyone seen this before?
>>
>> Cheers

No window, each tone comprises a whole number of cycles.

Cheers
-- 
Syd

On 26.07.2012 12:42, Syd Rumpo wrote:
> On 26/07/2012 11:29, Andre wrote:
>> Did you use any window function?
>>
>> On 26.07.2012 11:06, Syd Rumpo wrote:
>>> Hi
>>>
>>> Using an FFT on real data, I noticed that the magnitudes (root sum
>>> square of real & imag) of the bins was not equal when the input signal
>>> comprises tones of equal sizes.  OK, there's a bit of noise and the
>>> numbers move about a bit, and there's some analog signal equalisation
>>> which isn't as good as it could be.
>>>
>>> But when I plot the output, while there is an overall trend, there is
>>> also a clear alternation in magnitudes - the odd numbered bins are
>>> smaller than the even.
>>>
>>> This occurs only when using multiple tones.  If I use single tones the
>>> measured magnitudes follow the overall trend as expected, but there's no
>>> alternation.
>>>
>>> Anyone seen this before?
>>>
>>> Cheers
>
> No window, each tone comprises a whole number of cycles.
>
> Cheers
I guess this could be the problem, in case you have a "step" when 
cycling your signal (which is what the FFT does)...

>On 26.07.2012 12:42, Syd Rumpo wrote:
>> On 26/07/2012 11:29, Andre wrote:
>>> Did you use any window function?
>>>
>>> On 26.07.2012 11:06, Syd Rumpo wrote:
>>>> Hi
>>>>
>>>> Using an FFT on real data, I noticed that the magnitudes (root sum
>>>> square of real & imag) of the bins was not equal when the input
signal
>>>> comprises tones of equal sizes.  OK, there's a bit of noise and the
>>>> numbers move about a bit, and there's some analog signal equalisation
>>>> which isn't as good as it could be.
>>>>
>>>> But when I plot the output, while there is an overall trend, there is
>>>> also a clear alternation in magnitudes - the odd numbered bins are
>>>> smaller than the even.
>>>>
>>>> This occurs only when using multiple tones.  If I use single tones
the
>>>> measured magnitudes follow the overall trend as expected, but there's
no
>>>> alternation.
>>>>
>>>> Anyone seen this before?
>>>>
>>>> Cheers
>>
>> No window, each tone comprises a whole number of cycles.
>>
>> Cheers

also consider the power due quantisation noise that may concentrate in
spikes(harmonics) if your tones correlate with sampling frequency.

try some tones that don't correlate

Kadhiem

 

>> multiple tones

this could be a result of nonlinear distortion. But it would require
knowing more details to come up with a good theory.

Anyway, some hints:
- do you observe the same, if you cut the amplitude in half for the total
input signal?
- Do you leave sufficient headroom for your type of ADC? For example,
sigma-delta converters shouldn't use the whole input range, as the
converter needs some of it for its own internal magic.
- have you looked at the peaks (or more generally, amplitude probability
density) of the input signal?

On Thu, 26 Jul 2012 11:42:52 +0100, Syd Rumpo <u...@neonica.co.uk>
wrote:

>On 26/07/2012 11:29, Andre wrote:
>> Did you use any window function?
>>
>> On 26.07.2012 11:06, Syd Rumpo wrote:
>>> Hi
>>>
>>> Using an FFT on real data, I noticed that the magnitudes (root sum
>>> square of real & imag) of the bins was not equal when the input signal
>>> comprises tones of equal sizes.  OK, there's a bit of noise and the
>>> numbers move about a bit, and there's some analog signal equalisation
>>> which isn't as good as it could be.
>>>
>>> But when I plot the output, while there is an overall trend, there is
>>> also a clear alternation in magnitudes - the odd numbered bins are
>>> smaller than the even.
>>>
>>> This occurs only when using multiple tones.  If I use single tones the
>>> measured magnitudes follow the overall trend as expected, but there's no
>>> alternation.
>>>
>>> Anyone seen this before?
>>>
>>> Cheers
>
>No window, each tone comprises a whole number of cycles.
>
>Cheers

Hi Syd Rumpo,
  At first I thought your problem was FFT leakage.
But if you have exactly an integer number of cycles 
of the tones within your input sequence, then the spec 
magnitudes of those tones should be proportional 
to the peak time-domain amplitude of the input tones.

Humm, ...you're correct in being concerned (worried) 
about your spectral results.  Something's wrong there.

When you say that your tones have "equal sizes", 
what do you mean?  If your input signal sequence is 
the output of an A/D converter, then how do you know you 
have exactly an integer number of cycles 
of the tones within your FFT input sequence?

Also, when you say "some analog signal equalisation
isn't as good as it could be", that statement adds all 
sorts of uncertainty in our minds concerning the nature 
of your input signal.

[-Rick-]
 
 

If you are using an equalization filter and a sigma delta a/d converter then you have to
make sure you are waiting long enough for the system to reach steady state before capturing the
data. A sigma delta converter has a decimation filter with an impulse response up to 100 samples
long. I'm guessing you know this already but thought I'd mention it anyway. The equalization
filter is unknown to us but if it is doing anything interesting at low frequencies then it could
also have a long impulse response. 

Thanks to all who replied, your insights were a useful guide.  The 
culprit was a fairly large regular square pulse occurring before the FFT 
window whose harmonics were interfering.

Yes, it was a debug pulse used for 'scope triggering, breaking through 
onto the analog signal.  In other words, I put it there and forgot about it.

Cheers
-- 
Syd