From: jack@larc.nasa.gov (Jack Dunn)
Newsgroups: comp.dsp
Subject: Re: Windows for High Res Spectral Analysis
Date: 21 Jan 1993 12:37:50 GMT
Organization: ASEB/SySD LaRC NASA
Distribution: world
Reply-To: jack@larc.nasa.gov
NNTP-Posting-Host: headless.larc.nasa.gov

In article 14930@nstn.ns.ca, tcreasy@fox.nstn.ns.ca (Tim Creasy) writes:
>
>SUMMARY:
>
>I am looking for feedback from the net about applying windows to 
>discrete-time samples for high resolution spectral analysis.  
>I need to resolve a spectrum accurately at more than 90dB 
>below the level of the fundamental signal.
>
>
>THE PROBLEM:
>
>I am testing a 16 bit A-D converter for SNR and Harmonic Distortion.
>This involves appling a spectrally pure sine wave of known frequency 
>to the input, and capturing the digital samples at the output into 
>memory on a single board computer.  Then I perform an FFT, enabling 
>me to analyze the output in the frequency domain.
>
>I soon encountered the problem of spectral leakage.  If there is
>a discontinuity in amplitude between the first and last time sample,
>the fundamental tone does not fall neatly in an FFT bin, but spreads out 
>over a large number of bins, totally obscuring any harmonics at the
>-90dB level and below.
>
>One way of overcoming this is to phase lock the sinusoidal source to 
>the sampling clock (not possible with my set up), or equivalently,
>truncate the time data so that there remains an integer number of sine 
>waves in the sample interval.  But this is not satisfactory because 
>now the number of time samples is not a power of two, so the Fourier 
>Transform is slow.
>
>The more common way is to multiply the time data by a window before
>performing the FFT.  This effectively makes the input waveform
>(and possibly its derivatives) continuous at its endpoints.  But 
>I know windowing must also have a side effect of distorting the
>output spectrum, especially at the low levels I am talking about.
>Apparently the familiar Hanning and Hamming windows are not good 
>enough for this application.  To date, I have achieved best results 
>with a four-term Blackmann-Harris window.  This is where I need help!
>
>
>QUESTIONS
>
>1. How much distortion can I expect the Blackmann-Harris window to 
>   put into my resulting spectrum?  Will the levels of the harmonics
>   be affected?  Can I trust it at the -90 to -100dB level?
>
>2. Are there better windows to use?  (I have never seen anyone mention
>   5 or 6-term windows, but I can't see why they wouldn't exist AND
>   be better than the 3 or 4 term variety.  More computing power is 
>   not a big issue here.)
>   
>3. Has anyone heard of a Rosenfeld window?  What are its coefficients?
>   (I noticed that Analogic Inc. uses this window in their ADC tests.)
>
>
>THANKS...
>
>....in advance for answers to any of the above, or for any tips or
>tidbits from your experiences with this type of problem.
>
>Please reply either to the net or to me, tcreasy@appliedmicro.ns.ca
>
>----
>
>Tim Creasy
>Hardware Designer
>Applied Microelectronics Institute
>Halifax, NS, Canada


Who should read the book Digital Signal Processing by
Oppenheim and Shafer.. In my version
there is a chapter on Power Spectrum Estimation, chapter 11.
This chapter describes how to do what you want.
Basicly you should apply the window to the estimate of the 
correlation estimate, then the power spectrum
is calulated from the correlation.

Jack Dunn