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CIC decimation output is strange (Output word length and negative fractional length)

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I'm implementing fixed point CIC decimation filter with following requirements --
  • Decimation factor: 20
  • Number of CIC stages: 4
  • Input and output bit width of the CIC: Signed 12-bit
Based on the above requirement, I created a CIC filter
cicDecimOut = dsp.CICDecimator(DecimationFactor=20,...
NumSections=4,...
FixedPointDataType="Specify word lengths",...
SectionWordLengths=12,...
OutputWordLength=12);
As an input, 12-bit signed data generated as follow.
x = randi([-2048 2047], 100000, 1);
in = fi(x,1,12);
Now the singned 12-bit input data plug-in to the CIC decimation filter.
out = cicDecimOut(in)
out =
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However, checking the out shows the following at the end,
Two questions I have --
  1. I was expecting signed 12-bit output as I set the OutputWordLength=12. However, out is much larger than 12-bit range. Why this happened. Not sure I was missing something. How could I fix this?
  2. FractionLength is a negative value (-18). Can this be 0 as I wanted to see signed 12-bit? How could I compare this out with the values from the real RTL implementation?

Accepted Answer

Andy Bartlett
Andy Bartlett on 11 Dec 2023
Edited: Andy Bartlett on 12 Dec 2023
In the documentation for CIC Decimator, take a look at the algorithm section.
In that section, take a look at Gain Correction and Output Data Type subsections.
Those sections explain that the block will amplify the input signal by an effective gain value Gain.
In your example, the Gain is as follows.
R_decimation_factor = 20;
M_differential_delay = 1;
N_number_of_sections = 4;
Gain = (R_decimation_factor * M_differential_delay)^N_number_of_sections
Gain = 160000
A fixed-point representation of that gain would use 18 bits.
GainFi = fi( Gain, 0, ceil(log2(Gain)), 0)
GainFi =
160000 DataTypeMode: Fixed-point: binary point scaling Signedness: Unsigned WordLength: 18 FractionLength: 0
So given your 12 bit integer valued input, a full precision output would be 30 bits.
inExample = upperbound(numerictype(1,12,0));
yFullPrecisionExample = inExample * GainFi
yFullPrecisionExample =
327520000 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 30 FractionLength: 0
You've requested that the output be only 12 bits. So the block must throw away 18 bits from the 30 bits that the full precision output would have. The block is design to throw those bits away from the least significant end which reduces precision, but avoids overflows.
nty = numerictype(1,12,-18 );
yExample = removefimath( fi( yFullPrecisionExample, nty, 'RoundingMethod','Floor') )
yExample =
327417856 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 12 FractionLength: -18
For this specific example, dropping the least significant 18 bits
% Type Real World Notation: Integer Mantissa
% Value and Pow2 Exponent
% numerictype(1,30,0) 327520000 = 010011100001011000111100000000 * 2^0
% numerictype(1,12,-18) 327417856 = 010011100001 * 2^18
Dropping the least significant 18 bits produces a relatively modest error for this specific example.
absoluteError = abs( double( yExample ) - double( yFullPrecisionExample ) )
absoluteError = 102144
relativeErr = absoluteError / double( yFullPrecisionExample )
relativeErr = 3.1187e-04
errorInParts = ceil(1/relativeErr)
errorInParts = 3207
The output is accurate to 1 part in 3207, which is in the vicinity of what would be expected for a signed 12 bits fixed point type if well scaled.
Compare using Stored Integer Value and/or Real-World Value
Fixed-point signals always have two values.
For binary-point types as being discussed here, the Fixed-Point Scaling Equation is
V = Q * 2^-FractionLength
where
V is the Real-World Value (RWV) in units prefered by the human engineers
Q is the Stored-Integer (SI) value
When modeling, it is usally far easier to work with Real-World Values (RWV). Fixed-Point Designer works with the real-world values by default. Designer automatically manages all the book keeping related to scaling and storage data types.
The actual embedded implementation produced by Coders will efficiently operate on the stored integers (SI) to produce the high level math desired by the engineers.
When using generic tools on the embedded device such as target debuggers, signals will typically be shown using the stored integer values.
When values for a signal being tested or examined are provided in both real-world value form and stored-integer value form, naturally, it is necessary convert in either direction, SI to RWV or RWV to SI.
Convert RWV to SI
Given a fixed-point fi object produce it's stored integer value.
si_approach_1 = yExample.storedInteger
si_approach_1 = int16 1249
si_approach_2 = yExample.storedIntegerToDouble
si_approach_2 = 1249
si_approach_3 = stripscaling(yExample)
si_approach_3 =
1249 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 12 FractionLength: 0
Notice that si_approach_3 is a fi object with trivial scaling (FractionLength == 0). With trivial scaling, RWV == SI.
Convert SI to RWV
Given a stored integer value and knowledge of the scaling to be applied, it is straightforward to produce a scaled fixed-point fi object or a double holding the real-world value.
RWV in double
si_from_target = int16(1518)
si_from_target = int16 1518
rwv1_in_double = double(si_from_target) * yExample.Slope % Note: Slope = 2^-FractionLength
rwv1_in_double = 397934592
Apply scaling knowledge to a raw SI to create a fixed-point fi object.
Reinterpcast is the key tool to use to apply the scaling information, but preserve the stored integer value.
si_in_raw_fi = fi( si_from_target, 1, 12, 0 )
si_in_raw_fi =
1518 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 12 FractionLength: 0
nty = numerictype( yExample )
nty = DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 12 FractionLength: -18
rwv2_in_fi = reinterpretcast( si_in_raw_fi, nty)
rwv2_in_fi =
397934592 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 12 FractionLength: -18
check_si_still_same = rwv2_in_fi.storedIntegerToDouble
check_si_still_same = 1518
  3 Comments
Jay
Jay on 11 Dec 2023
Edited: Jay on 11 Dec 2023
One minor question is the Gain in your code. In MATLAB document, the Gain term is given by (R x M)^N, e.g., the product of R and M, while it was written by (R + M)^N in your example, e.g., the sum of R and M. I assume this is a typo while it doesn't change the number of bits to represent a fixed-point number?
R_decimation_factor = 20;
M_differential_delay = 1;
N_number_of_sections = 4;
Gain = (R_decimation_factor + M_differential_delay)^N_number_of_sections
Gain = 194481
Andy Bartlett
Andy Bartlett on 12 Dec 2023
Hi Jay,
Good catch. You are correct. The formula should be multiply and not add. I updated the answer. Numbers are a bit different, but the overall message of needing to drop 18 LS bits from the ideal 30 bits to get down to 12 is the same.

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