[time-nuts] was: Odd-order multi Now: fft analyzer woes

[jimlux]

On 1/23/20 4:20 PM, Magnus Danielson wrote:

>> There is still the minor? problem, that from low to high frequencies,
>> many new decades
>> start with elevated noise, but I correct for the increased noise
>> bandwidth. Maybe discrete
>> spurii are then over-represented? I'm unsure how to handle that. When
>> I add a carrier
>> from a signal generator for CAL reasons, that carrier level should not
>> be changed by noise BW
>> correction, assuming that all of the carrier power hits the same bin?
> 
> You should *never* assume that all the carrier power hits the same bin.
> This is known to lead to incorrect measurements, and under-estimating
> the carrier power. I've made the same comment in the P1139 working
> group. The full power of the carrier includes it sidebands, it's the
> power which you would measure wide-band into a power-meter.
> Underestimating the carrier power leads to increase the sideband powers,
> and it can even lead to non-sensible measures as positive dBc values
> that can be had when deep PM suppresses carrier and eventually nulls it
> (Bessel polynomial - B0).


Not only that, but don't forget errors due to the window of your FFT - 
if your frequency isn't dead center in a bin, the power is distributed 
among multiple bins.  And if it is dead center in a bin, there's still 
the window effects.

There's a whole literature on accurate power measurements using FFTs, 
along with a lot of exotic windows (i.e. not a simple raised cosine or 
something like that) that have very good sidelobe performance. For run 
of the mill work, I use a Blackman-Harris window, mostly because it's in 
most libraries and has sidelobes more than 80 dB down (vs rectangular at 
13 dB down, or Hamming at -42 dB). Hamming windows are fine for 1% (8 
bit) systems.

Not all spectrum analyzers which display total power or carrier vs 
sidebands or spurious levels, do a good job of automatically computing 
this kind of thing. You really need to check with some known signals (or 
carefully read the spectrum analyzer ap-notes).  The *worst* are so 
called spectrum analyzer apps and blocks in things like gnuradio, or 
"software spectrum analyzers" implemented on one of the inexpensive SDR 
platforms.

For what it's worth, there are also *power meters* (usually combined 
with a counter) which have a narrow band filter that tracks the input 
signal. The Agilent 53152, for instance, might give you a different 
power reading than an old school power meter like a 437 with a 8480 
series power sensor.

Granted, a lot of this is worrying about millibels (0.01 dB), but as 
Magnus points out, you can come up with unphysical derived measurements 
like spurious signals > total power.



Here's a 200 page catalog of window functions from Sandia:
https://prod-ng.sandia.gov/techlib-noauth/access-control.cgi/2017/174042.pdf

SANDIA REPORT SAND2017-4042

Printed April 2017
Catalog of Window Taper Functions for Sidelobe Control
Armin W. Doerry

It has some excellent explanatory information and examples at the 
beginning and data on dozens of windows, with plots.

It will save you the trouble of getting Fred Harris's IEEE Proceedings 
paper, and the later ones by others like Nuttall.   The Harris paper is 
useful, though.
F. J. Harris, "On the use of windows for harmonic analysis with the 
discrete Fourier transform," in Proceedings of the IEEE, vol. 66, no. 1, 
pp. 51-83, Jan. 1978.
doi: 10.1109/PROC.1978.10837
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1455106&isnumber=31261

there are copies around at places like the MIT website. It's well up 
there on the "cited count" well over 8000.  I could only dream of 
writing such a paper.



I warn you though - You can go down a rabbit hole on this - there are 
people who have tried to reverse engineer the windows used on equipment 
like HP/Agilent/Keysight analyzers, or who have developed windows with 
some peculiarly useful property for some specific signal (low sidelobes 
around known spurs, etc.)

However, this is time-nuts, not window-nuts.