Date: Fri, 29 Mar 2024 12:37:10 +0000 (GMT)
Message-ID: <410790026.187.1711715830995@[172.30.0.157]>
Subject: Exported From Confluence
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W=
here To Find This Example
Select Help > Open Examples... from the menus and type either =
the example name listed above or one of the keywords at the bottom of this =
page.
You can also open the project directly from this page using this button.=
Make sure to select the Help > Enable Guided Help from=
the menus before clicking this button.
Open Install Ex=
ample
Design Notes
Fixed-Point Magnitude Calculation
This example demonstrates a magnitude estimator whose hardware complexit=
y is much simpler and faster than that of the full-precision exact calculat=
ion using a square-root operation. Magnitude estimators are used in many fi=
xed-point ASIC designs for received signal strength indicators (RSSI) and d=
emodulation algorithms.
The magnitude of a complex number, I + jQ, is defined as sqrt(I^2 + Q^2)=
and is approximated as:
Mag ~=3D A * max(|I|,|Q|) + B * min(|I|,|Q|)
where A and B are two constants whose values can be set such that either=
the RMS error, peak error and/or implementation complexity is reduced with=
in acceptable levels. Some of the most common values for A and B are given =
below, together with the associated errors:
A B Average Error RMS Error Peak Error
(linear) (dB) (dB)
1.0 0.5 -0.086775 -20.7 -18.6
1.0 0.25 0.006456 -27.6 -18.7
1.0 0.4 -0.049482 -25.1 -22.3
0.94754 0.39248 0.000547 -32.6 -25.6 (min RMS error)
0.96043 0.39782 -0.013049 -31.4 -28.1 (min peak error)
Note that the first two choices are very simple to implement in hardware=
(using shifts and adds), while the others are more complex.
This project calculates the magnitude of the input in three different wa=
ys:
1. The exact calculation uses a CMAG block to compute the magnitude of a=
complex input.
2. The floating-point approximation uses the algorithm above and double-=
precision arithmetic.
3. The fixed-point approximation uses fixed-point arithmetic for the alg=
orithm above. In this case, bit and decimal widths should be selected such =
that loss of information due to the real to fixed-point conversion is withi=
n acceptable limits. For example, the bit and decimal widths for the SCALE =
parameter in the SCALE_FP block should be set such that the selected values=
for A and B are represented by these widths.
Sys=
tem Diagram - System Diagram 1
Graph - Magnitud=
e
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