Hi,
  A signal is composed of the sum of two sinusoids, and none of them has a
period matching the transform size. There is DFT leakage after the FFT. Is
there any other solution than windowing?
Thank you.

On Thursday, October 11, 2012 9:21:57 PM UTC-4, commsignal wrote:
> Hi,
> 
>   A signal is composed of the sum of two sinusoids, and none of them has a
> 
> period matching the transform size. There is DFT leakage after the FFT. Is
> 
> there any other solution than windowing?
> 
> Thank you.

I'm not real sure of your question. Are you asking how to find the amplitude coefs for just two
frequencies and hoping windowing will make your estimate better? If there is any or much noise
in your two signals? If not, a simple 2 x 2 matrix problem on the coefs will yield your values.
If you have a lot of noise, the issues are much harder. Please clarify your problem and we can
likely help you more.

Clay

>On Thursday, October 11, 2012 9:21:57 PM UTC-4, commsignal wrote:
>> Hi,
>> 
>>   A signal is composed of the sum of two sinusoids, and none of them has
>a
>> 
>> period matching the transform size. There is DFT leakage after the FFT.
I>s
>> 
>> there any other solution than windowing?
>> 
>> Thank you.
>
>I'm not real sure of your question. Are you asking how to find the
amplitud>e coefs for just two frequencies and hoping windowing will make your
estima>te better? If there is any or much noise in your two signals? If not, a
sim>ple 2 x 2 matrix problem on the coefs will yield your values. If you have
a> lot of noise, the issues are much harder. Please clarify your problem and
>we can likely help you more.
>
>Clay
>

Actually I was thinking of taking e^(j omega_1 n)*(a QAM signal) + e^(j
omega_2)*(another QAM signal) into frequency domain and trying to see what
happens there. But omega_1 and omega_2 destroy the periodicity. Can their
effects be removed, even in case I know omega_1 and omega_2?

On 10/11/12 9:48 PM, commsignal wrote:
...
> Actually I was thinking of taking
> e^(j omega_1 n)*(a QAM signal) + e^(j omega_2)*(another QAM signal)
> into frequency domain and trying to see what
> happens there. But omega_1 and omega_2 destroy the periodicity. Can their
> effects be removed, even in case I know omega_1 and omega_2?

so you want to look at the spectrums of the two QAM signals and are 
worrying how much the window leakage (remember, no window means the 
rectangular window) of one interferes with the other?

if the windows are well defined, you can actually predict how much 
spectral leakage of one modulated QAM is at any other specific 
frequency.  it might not be impossible to detangle two.  it's like two 
equations and two unknowns (the values of the two QAM signals).

but usually we want to minimize the spillage from one to the other, so 
that's when windowing is often applied.  the window most people use to 
control spectral leakage is the Kaiser since it gives you a pretty 
dependable tradeoff control trading off the sharpness of the window's 
main lobe with the spillage amount.  i think the parameter is called 
"beta".  it's in O&S.

how far are omega_1 and omega_2 apart in DFT bins?  the size of the 
window in bins (or samples) and the DFT length are the parameters that 
determines how wide (in samples) the window needs to be.

-- 

r b-j                  r...@audioimagination.com

"Imagination is more important than knowledge."

Hello,

more often than not, your channels are arranged on a grid that allows
integer multiples over a realistic measurement length.

Let's say, I want to observe 1 ms of signal. 
A typical channel raster is 200 kHz. In other words, any frequency offset
that is allowed by some hypothetical radio standard comes in multiples of
200 cycles over my observation length => no problem.

With a bit of "frequency planning", you can set up a simulation with cyclic
signals and avoid FFT windowing completely.

If for some reason the numbers don't work out, it's usually no problem to
tweak them a little until they do. For example, dealing with OFDM symbols,
I adjust my cyclic prefix lengths so that I get -exactly- 14 symbols in 1
ms.

On Thu, 11 Oct 2012 20:21:57 -0500, "commsignal"
<58672@dsprelated> wrote:

>  A signal is composed of the sum of two sinusoids, and none of them has a
>period matching the transform size. There is DFT leakage after the FFT. Is
>there any other solution than windowing?

"Notch Fourier Transform"; Yoshiaki Tadokoro and Kenichi Abe, 
IEEE TRANSACTIONS ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING,
VOL. ASSP-35, NO. 9, September 1987.