HLS
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Introduction

The Rolling Variance block calculates the Mean, Variance, and Sigma (standard deviation) in real time. Each sample provided to the DATA_IN input will update (after a pipeline delay of 5 clock cycles) the three output values.

Pin Description

DATA_IN Input 8/16/24/32 bit BIT VECTOR
Input data for statistical calculation. Signed integer input. Size is configured by the “Input Data Size” property (8, 16, 24, or 32 bits).
Default: Must be connected
PLEN Input 16 bit BIT VECTOR
Window size selector (power-of-2 encoding). Specifies the number of samples in the rolling window as $N = 2^{PLEN}$. Valid range depends on the “Memory Size” property. See the PLEN encoding table above.
Default: Must be connected
CLK Input 1 bit BIT
System clock input. All operations are synchronous to this clock. Default: Board acquisition clock.
Default: Default Board Clock
RESET Input 1 bit BIT
Synchronous reset. Clears all internal accumulators and restarts the preroll period. Default: Global reset.
Default: Default Board Reset
MEAN Output Configurable bit BIT VECTOR
Rolling mean (average) output. Fixed-point or integer format as configured by “Mean data type” property. Updated every clock cycle with 5-cycle latency.
VAR Output Configurable bit BIT VECTOR
Rolling variance output. Fixed-point or integer format as configured by “Variance data type” property. Updated every clock cycle with 5-cycle latency.
SIGMA Output Configurable bit BIT VECTOR
Rolling standard deviation output (square root of variance). Fixed-point or integer format as configured by “Sigma data type” property. Note: Only valid when “Enable Sigma” property is checked. Enabling sigma requires additional FPGA resources for square root calculation.
DV Output 1 bit BIT

Data Valid output.

  • High (1): Mean, Variance, and Sigma outputs contain valid data
  • Low (0): Outputs are invalid (during preroll or after PLEN change) Remains low for 2x Memory Size samples after reset or PLEN change.

Properties

Property window

Input Data Size BIT_SIZE

Number of bit of the input vector

Input data size in bits. Available values: 8, 16, 24, 32, default 16.

Default: 16

Options: 8 16 24 32

Enable Sigma EN_SIGMA

Instantiate the square root module inside the core to calculate in realtime the sigma

Enable Sigma (standard deviation) calculation. When enabled, instantiates a square root module inside the core. Warning: Significantly increases FPGA resource usage. Default: Disabled.

Default: False

Mean data type MEAN_DATA_OUT_TYPE

Select data output type for mean

Output data type for Mean. Available values: fixed 32.32, fixed 32.16, fixed 32.8, fixed 24.8, fixed 16.16, int 16, int 32, int 64, fixed 56.8, fixed 48.16. Default: fixed 24.8.

Default: fixed 24.8

Options: fixed 32.32 fixed 32.16 fixed 32.8 fixed 24.8 fixed 16.16 int 16 int 32 int 64 fixed 56.8 fixed 48.16

Variance data type VAR_DATA_OUT_TYPE

Select data output type for variance

Output data type for Variance. Available values: fixed 32.32, fixed 32.16, fixed 32.8, fixed 24.8, fixed 16.16, int 16, int 32, int 64, fixed 56.8, fixed 48.16. Default: fixed 24.8.

Default: fixed 24.8

Options: fixed 32.32 fixed 32.16 fixed 32.8 fixed 24.8 fixed 16.16 int 16 int 32 int 64 fixed 56.8 fixed 48.16

Output data type for sigma SIGMA_DATA_OUT_TYPE

Select data output type for sigma

Output data type for Sigma (standard deviation). Only used when “Enable Sigma” is checked. Available values: fixed 32.32, fixed 32.16, fixed 32.8, fixed 24.8, fixed 16.16, int 16, int 32, int 64, fixed 56.8, fixed 48.16. Default: fixed 16.16.

Default: fixed 16.16

Options: fixed 32.32 fixed 32.16 fixed 32.8 fixed 24.8 fixed 16.16 int 16 int 32 int 64 fixed 56.8 fixed 48.16

Memory size BUFFER_LEN

Maximun number of samples in the rolling window

Maximum number of samples in the rolling window buffer. Determines the maximum valid PLEN value. Available values: 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536. Default: 1024.

Default: 1024

Options: 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536

Usage

Mathematical Foundation

The variance is calculated using two running accumulators: one for the sum of values ($\sum x$) and another for the sum of squares ($\sum x^2$). This enables efficient incremental computation without storing all samples explicitly.

Variance Formula

The variance over N samples is computed as:

$$ \sigma^2 = \frac{\sum x^2}{N} - \left(\frac{\sum x}{N}\right)^2 $$

This is equivalent to the standard variance formula:

$$ \sigma^2 = \frac{1}{N}\sum_{i=1}^{N}(x_i - \bar{x})^2 $$

where $\bar{x}$ is the mean:

$$ \bar{x} = \frac{\sum x}{N} $$

The standard deviation (sigma) is simply the square root of the variance:

$$ \sigma = \sqrt{\sigma^2} $$

Rolling Window Algorithm

To achieve the rolling (sliding window) effect, incoming samples are stored in a circular buffer. The algorithm maintains two accumulators that are updated incrementally:

  1. For each new sample $x_{new}$:

    • Add $x_{new}$ to sum
    • Add $x_{new}^2$ to sum2

  2. For the oldest sample $x_{old}$ (N samples behind):

    • Subtract $x_{old}$ from sum
    • Subtract $x_{old}^2$ from sum2

This ensures that variance is always computed over the last N samples, providing the desired rolling window effect with O(1) complexity per sample.

Window Size Encoding (PLEN)

The window size N is encoded as a power of 2, specified by the PLEN input. This encoding allows efficient division using bit-shift operations instead of actual division.

PLEN Window Size (N) Formula
0 INVALID -
1 INVALID -
2 INVALID -
3 8 $2^3$
4 16 $2^4$
5 32 $2^5$
6 64 $2^6$
7 128 $2^7$
8 256 $2^8$
9 512 $2^9$
10 1024 $2^{10}$
11 2048 $2^{11}$
12 4096 $2^{12}$
13 8192 $2^{13}$
14 16384 $2^{14}$
15 32768 $2^{15}$
16 65536 $2^{16}$

Important: The “Memory Size” property must be greater than or equal to the selected window size. For example, with Memory Size = 1024, valid PLEN values are 3 to 10.

Data Valid Signal (DV)

The DV output indicates when the Mean, Variance, and Sigma outputs contain valid data. When PLEN is changed (or at startup), DV is held low for at least 2 times the buffer size specified in the “Memory Size” property. This preroll period ensures the accumulators are properly initialized.

Fixed-Point Output Formats

Output data formats use fixed-point representation for fractional precision. The format notation fixed X.Y means:

  • X bits: Integer part (including sign)
  • Y bits: Fractional part
  • Total bus width: X + Y bits

Example: fixed 24.8 = 24-bit integer + 8-bit fractional = 32-bit total

Resources & Timing

  • Latency: 5 clock cycles

  • Throughput: 1 sample per clock cycle (II=1)

HLS-based implementation. Resource usage varies with configuration.