Altera CIC MegaCore Function - Manual (Page 21)

Note: A data width of B
out
is required for each integrator and differentiator for no data loss.
For an interpolation filter, the gain at each filter stage is:
Hence the required data width at the ith stage is:
W
i
= [B
in
+ log
2
(G
i
)]
and the data width at the output stage is:
B
out
= [B
in
+ Nlog
2
(RM) - log2(R)]
where B
in
is the input data width.
When the differential delay is one, the bit width at each integrator stage is increased by one to ensure
stability.
For more information about these calculations, refer to Hogenauer, Eugene. An Economical Class of
Digital Filters For Decimation and Interpolation, IEEE Transactions on Acoustics, Speech and Signal
Processing, Vol. ASSP-29, pp. 155-162, April 1981.
Output Rounding
For high rate change factors, the maximum required data width for no data loss is large for many practical
cases. To reduce the output data width to the input level, apply quantization at the end of the output stage.
the CIC filter offers various rounding or saturation options. You can only apply these rounding options to
the output stage of the filter. The data widths at the intermediate stages are not changed.
Table 3-1: Output Rounding Options
Option Description
Trunca
tion
The CIC drops the LSBs. (Equivalent to rounding to minus
infinity.)
Conver
gent
roundi
ng
Also known as unbiased rounding. Rounds to the nearest even
number. If the most significant deleted bit is one, and either the
least significant of the remaining bits or at least one of the other
deleted bits is one, then one is added to the remaining bits.
Round
up
Also known as rounding to plus infinity. Adds the MSB of the
discarded bits for positive and negative numbers via the carry in.
Saturati
on
Puts a limit value (upper limit in the case of overflow, or lower
limit in the case of negative overflow) at the output when the input
exceeds the allowed range. The upper limit is +2n-1 and lower limit
is –2n
UG-CIC
2014.12.15
Output Rounding 3-5
CIC IP Core Functional Description Altera Corporation
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