DSP - BLOCK MEAN
The arithmetic mean of a block of N consecutive samples. N is a power of two chosen at RUN TIME on the EXP input pin (EXP = 10 means N = 1024), so the division by N is an exact arithmetic shift and the block contains no divider at all. This is the cheapest useful block of the family: one adder, one barrel shifter and one requantiser - no multiplier and no serial arithmetic, so the result of a block is presented exactly 2 clocks after that block’s last sample. IN_DV is the only qualifier and there is deliberately no CE pin. Optional BUSY / INTEGRATING / SAMPLE_COUNT status outputs. Blocks of up to 2^20 samples out of the box, 2^31 if you ask for it.
Introduction
The Block Mean block chops the input stream into consecutive blocks of N samples and, at the end of each block, publishes the arithmetic mean of that block:
$$ S_1 = \sum_{i=0}^{N-1} x_i , \qquad \mathrm{mean} = \frac{S_1}{N} $$
That is the whole block. One accumulator, one shift, one requantisation.
N is a runtime input, not a property. You drive the exponent on the
EXP pin and the block size is $N = 2^{\mathrm{EXP}}$:
| EXP | N | EXP | N |
|---|---|---|---|
| 4 | 16 | 12 | 4096 |
| 6 | 64 | 16 | 65536 |
| 8 | 256 | 20 | 1048576 |
Because N is a power of two, the division by N is an exact arithmetic shift. There is no divider, no reciprocal ROM and no rounding beyond the single final requantisation into your Q format - which is also why the block size can be changed while the design is running, for free.
What it is FOR
The mean is the baseline / DC level of the channel. Subtract it downstream and you have a zero-centred signal. It is the standard baseline estimator in pulse processing, the slow-control telemetry value a CPU wants to read, and the reference a threshold is normally placed against.
Because it is a straight sum divided by a power of two, it is also the cheapest
way to decimate by N with an anti-alias average rather than by dropping
samples: one result per block, at 1/N of the input rate, on OUT_DV.
Cost
One accumulator (input working width + Max Block Exponent bits), one barrel shifter and one requantiser. No multiplier, no divider, no serial arithmetic. It is the cheapest block of the family after Block Sum, which is this block without the final shift.
When to use this instead of Block Statistics
The all-in-one Block Statistics block is not deprecated and computes this same mean among twenty other statistics. The rule is simple:
- you want several statistics of the SAME block - mean and RMS and min/max of the same N samples - use Block Statistics. They share one accumulator and one serial tail, so the second and third statistic are nearly free.
- you want exactly one number - use this block. Then you synthesise only that number: the pin list, the logic and the tail are all that the mean needs, and nothing else reaches the synthesiser.
Two Block Statistics blocks side by side would duplicate the accumulators; two per-operator blocks side by side duplicate them too. One Block Statistics block never does.
Pin Description
IN_DV is high.
'1'. (There is deliberately no CE pin - to stall the block,
gate this.)
OUT_DV clock and on no
other; it holds the previous block’s result until then.
MEAN is updated on this clock and on no other. BUSY is
still high here and falls on the next clock.
OUT_DV pulse, and it falls on the clock after. On a continuous stream it
simply stays high. Present on the symbol only when Enable BUSY = YES.
How many samples have been accumulated so far in the current block: 1 after the first, N after the N-th. It is NOT cleared at the end of a block
- it HOLDS the final count through the tail and past
OUT_DV, until the first sample of the next block takes it back to 1, so on theOUT_DVclock it reads the length of the block being presented. OnlyRESETclears it to 0. Fixed 32 bits. Present on the symbol only when Enable SAMPLE_COUNT = YES.
Properties
Number of INTEGER bits of the input sample (the sign, when present, uses one of them).
Integer bits of the input sample (the sign, when present, uses one of them). 1..64. Default 16.Default: 16
Options: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
Number of FRACTIONAL bits of the input sample, i.e. the bits to the right of the binary point. Total width = integer + fractional bits, and must not exceed 64.
Fractional bits of the input sample. 0..64. Total input width must be 2..64 bits. Default 0.Default: 0
Options: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
Select whether the input sample is signed (two’s complement) or unsigned.
SIGNED (two’s complement) or UNSIGNED input. Default SIGNED. An UNSIGNED input costs one extra bit internally, because a sample has to be promoted to signed before it can be accumulated.Default: SIGNED
Options: UNSIGNED SIGNED
Largest block-size exponent the accumulators are sized for: the block can be up to 2^MaxBlockExponent samples long. The EXP input is clamped to this value at run time. Raising it widens the internal accumulators, and ON THE BLOCKS WHOSE SERIAL ENGINES ARE SIZED FROM THOSE ACCUMULATORS (Coefficient of Variation, SNR, Skewness, Kurtosis, Correlation, Autocorrelation, Linear Regression) it also LENGTHENS THE SERIAL TAIL – even when the runtime EXP is small. Keep it at the largest block you actually use. The default of 20 covers blocks of up to 1048576 samples.
Largest block-size exponent the accumulator is sized for: the block can be up to $2^{\text{MaxBlockExponent}}$ samples long, and theEXP input is
clamped to this value at run time. Raising it widens the internal sum
register by one bit per unit; it does NOT lengthen the latency of this
block, which is a constant 2 clocks. Keep it at the largest block you
actually use. 1..31, default 20, i.e. blocks of up to 1048576 samples
out of the box.
Default: 20
Options: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Number of INTEGER bits of the MEAN output (the sign, when present, uses one of them).
Integer bits of the MEAN output. 1..64, default 16. The mean never leaves the range of a sample, so the input integer bits are always enough.Default: 16
Options: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
Number of FRACTIONAL bits of the MEAN output, i.e. the bits to the right of the binary point. Total width = integer + fractional bits, and must not exceed 64.
Fractional bits of the MEAN output. 0..64, total width 2..64 bits, default 0. Ask for more than the input has if you want sub-LSB resolution on the baseline - the accumulator carries those bits exactly.Default: 0
Options: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
Select whether the MEAN output is signed (two’s complement) or unsigned.
SIGNED or UNSIGNED MEAN output. Default SIGNED. Use SIGNED for a bipolar signal.Default: SIGNED
Options: UNSIGNED SIGNED
YES: the BUSY (high from the first sample of a block until its result is out – it COVERS THE SERIAL TAIL, and its last high clock IS the OUT_DV pulse) pin is present. NO: the pin AND all of its logic are removed BEFORE synthesis, so nothing is paid for it.
YES: theBUSY pin exists. It is high from the first sample of a block
until its result is out, tail included, and its last high clock is the
OUT_DV pulse. NO: the pin and its register are removed before synthesis.
Default NO.
Default: NO
Options: NO YES
YES: the INTEGRATING (high only while the block is ACCUMULATING; it drops as soon as the N-th sample has been taken and the tail starts, so BUSY-and-not-INTEGRATING means ‘computing’) pin is present. NO: the pin AND all of its logic are removed BEFORE synthesis, so nothing is paid for it.
YES: theINTEGRATING pin exists. It is high only while the block is
accumulating, so BUSY high with INTEGRATING low means “the samples are
all in, I am computing”. NO: the pin and its register are removed.
Default NO.
Default: NO
Options: NO YES
YES: the SAMPLE_COUNT (32 bit, how many samples have been accumulated so far in the current block: 1 after the first, N after the N-th. It is NOT cleared at the block end – it holds N until the NEXT block’s first accepted sample takes it back to 1. On a CONTINUOUS stream that happens DURING the serial tail, so at OUT_DV it reads how far into the next block the input has already got, NOT N. To capture the length of the block being presented, latch SAMPLE_COUNT on the clock INTEGRATING falls – that one always reads N) pin is present. NO: the pin AND all of its logic are removed BEFORE synthesis, so nothing is paid for it.
YES: theSAMPLE_COUNT pin exists - a fixed 32 bit count of the samples
accumulated so far in the current block, holding the final count through
the tail and past OUT_DV. NO: the pin and its counter are removed.
Default NO.
Default: NO
Options: NO YES
ROUND: round to nearest when a result has to be requantised into a coarser output format. TRUNCATE: drop the bits (cheaper, adds a negative bias).
ROUND: round to nearest when the result has to be requantised into a coarser output format. TRUNCATE: drop the bits (cheaper, adds a negative bias). Default ROUND.Default: ROUND
Options: TRUNCATE ROUND
YES: clip to the largest representable value of each output format (symmetric for signed formats). NO: wrap around.
YES: clip to the largest representable value of the output format (symmetric bounds for signed formats). NO: wrap around. Only matters when the output format is too narrow for the value - which, for a mean sized like the input, cannot happen. Default YES.Default: YES
Options: NO YES
Accuracy
The accumulator $S_1$ is an exact integer and the division by N is a
shift, so the only error in this block is the single final
requantisation into the Q format you chose for the MEAN pin. There is no
accumulated rounding, no truncated intermediate and no approximation
anywhere in the datapath.
That is not an aspiration. The host regression (tb/block-ops/run_tb.ps1)
demands tolerance ZERO against a Python golden (tb/block-ops/ gen_golden.py) that evaluates the definition above in exact rational
arithmetic - not “within 1 LSB”, not “within a few counts”. Any deviation at
all fails the build.
Accumulation and IN_DV
IN_DV is the only qualifier. It says “this clock carries a sample”: a
sample is accumulated, and counts towards N, exactly on the clocks where
IN_DV is high. Clocks with IN_DV low are ignored completely - whatever
sits on IN during them cannot corrupt the block - while the tail keeps
running, which is what you want: the tail has nothing to do with the input
stream.
Unconnected, IN_DV ties to '1' and EXP ties to 10 (N = 1024), so the
block free-runs with nothing wired except IN.
There is deliberately no CE pin. On the all-in-one Block Statistics block an earlier revision had one, and it did not survive synthesis: with nothing but internal state gated by it, Vitis could reason the frozen path away and delete the port from the generated entity while SciCompiler’s wrapper still wired it, which failed a real Vivado build with [VRFC 10-718] formal port <ce> does not exist in entity. The whole per-operator family was built without one. To stall this block, gate its
IN_DV- a block that only accumulates onIN_DVhas no need to be frozen.
When EXP changes
EXP is clamped to Max Block Exponent and then latched on the first
accepted sample of a block, and held for that whole block. A change
therefore takes effect on the NEXT block: a block in progress always
finishes against the N it was started with, and a block is never emitted
against a different N than the one it was accumulated with. You can sweep
EXP from a register interface while the stream runs and every result stays
self-consistent.
Timing: the latency contract
OUT_DV pulses for one clock, L clocks after the clock on which the N-th
sample of the block was accepted - not when that sample arrives. MEAN is
updated on that same clock and on no other. For this block
$$ L = 2 $$
and it is a constant: there is no serial arithmetic here at all, so L does
not depend on the input width, on the output width or on EXP. The two clocks
are one to enter the final state and one to present the registered result.
The rule that governs the whole family is that the tail of one block must finish before the next block completes, i.e.
$$ 2^{\mathrm{EXP}} \ge L $$
If a block completes while the previous tail is still running, that block’s
result is DROPPED: no OUT_DV for it, the accumulators are unaffected and
later blocks come out correctly, but a result is silently skipped. There is
no error pin for it.
With $L = 2$ that condition is $2^{\mathrm{EXP}} \ge 2$, i.e. EXP $\ge$ 1, so it cannot bite here: the only value that violates it is EXP = 0, a block of a single sample. The blocks where this rule really matters are the ones with a serial tail - Block RMS, Block Variance, Block Std Dev and Block Crest Factor, whose L runs to tens of clocks and whose minimum usable exponent the compiler prints in the compilation log.
Knowing where the block is: BUSY, INTEGRATING and SAMPLE_COUNT
Three optional status outputs, all defaulting to NO. They answer different questions:
INTEGRATING |
BUSY |
|
|---|---|---|
| accumulating the block | 1 | 1 |
| tail computing | 0 | 1 |
| idle | 0 | 0 |
Every output of this block is a register, so each status bit is observed on the clock after the event that sets it:
INTEGRATINGrises on the clock after the FIRST sample of a block is accepted and falls on the clock after the N-th - it is high exactly while the block is ACCUMULATING.BUSYcovers the accumulation and the tail. It rises withINTEGRATING, stays high across the tail, and its LAST HIGH CLOCK IS THEOUT_DVPULSE; it falls on the clock after.- On a continuous stream the next block starts before the previous tail
ends, so
BUSYnever drops andINTEGRATINGdips for exactly one clock per block boundary - which makes it a free block marker. SAMPLE_COUNTis a fixed 32 bits and reads 1 after the first accepted sample, N after the N-th. It is NOT cleared at the block end: it HOLDS N through the tail and pastOUT_DV, until the first sample of the next block takes it back to 1. So on theOUT_DVclock it reads the length of the block being presented - which is the useful thing to latch alongside the result. OnlyRESETclears it to 0.
Q formats
Both ports carry their own fixed point format (integer bits, fractional bits,
sign), the same convention as the Fixed P. family. The result is requantised
into the MEAN format with the selected rounding (nearest / truncate) and
overflow policy (saturate / wrap); saturation is symmetric for signed formats,
as everywhere else in the toolchain.
Sizing is easy here: the mean of a block of samples can never leave the range
of a sample, so the input format is always safe for the output. Give
MEAN more fractional bits than IN if you want sub-LSB resolution on the
baseline - the accumulator carries those bits exactly, they are simply
discarded by the final shift if you do not ask for them.
Verification
The core is regression tested by a host-side csim harness
(tb/block-ops/run_tb.ps1) that runs one simulated clock at a time and
follows OUT_DV. The expected values come from tb/block-ops/gen_golden.py,
which evaluates $S_1/N$ in exact rational arithmetic and shares no algorithm
with the core; the tolerance is 0. Mean coverage includes pseudo-random
and ramp inputs, maximum positive and maximum negative samples, unsigned
input, fractional output formats, truncate instead of round, a deliberately
narrow saturating output format, IN_DV gaps inside the accumulation, an
EXP that changes half way through a block, and an EXP driven above Max
Block Exponent to exercise the clamp. The status outputs are checked
clock by clock against the contract above. A cross-check compiles this
core and the all-in-one block_stats.cpp into the same binary, drives them
with identical stimulus, and compares the two clock by clock.