15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
---------------------------------------------------------------
| | | | | | | | | | | | | | | | |
| Exponent | S | Mantissa | (Q)
|------------------|---|----------------------------------------|
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
---------------------------------------------------------------
| | | | | | | | | | | | | | | | |
| 0 0 0 0 | Log of Power in Sample | (LOG)
|--------------|------------------------------------------------|
To convert these legacy format floating I and Q samples to voltages:
1. Create a 12-bit signed integer in which bits 0 ... 9 are copied from the Mantissa field,
and bits 10 and 11 are either 01 or 10 depending on whether S is 0 or 1.
2. Multiply this number by 2**(exponent-40), where the exponent
field is interpreted as
an unsigned 5-bit integer.
3. Multiply by the maximum voltage.
The resulting value has 12-bits of precision and a dynamic range of approximately 190 dB.
The large dynamic range is necessary to cover the full range of data. In summary:
=
× , × 2
40
The resulting voltage span is ± 4 × V
MAX
. The extra factor of 4 is built into the format so
that transient excursions above the full scale input voltage can be encoded properly.
A High-SNR packed floating format is also available that oers nearly the same dynamic
range, but provides a 6 dB improvement in SNR, that is, a commensurate improvement in
sub-clutter visibility of -78 dB versus -72 dB.
15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
---------------------------------------------------------------
| | | | | | | | | | | | | | | | |
| Exponent | S | Mantissa | High–SNR
|------------------|---|----------------------------------------|
The High-SNR packed format is similar to the legacy packed format except that it uses one
extra mantissa bit and one fewer exponent bit. The dynamic range lost in the exponent is
recovered through a formatting trick known as "soft
underflow", that is, the mantissa is
allowed to become unnormalized when the exponent is 0.
To decode this format when the exponent is non-zero, first create a 13-bit signed integer in
which bits zero through ten are copied from the Mantissa field, and bits eleven and twelve
are either 01 or 10 depending on whether S is 0 or 1. Then, multiply this by 2**(exponent-25),
where the exponent
field is interpreted as an unsigned 4-bit integer.
Chapter 8 – Host Computer Commands
265
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