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.
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