Exponential Moving Average (EMA)

Keywords: #filter #lowpass #averaging

This repository contains a VHDL implementation of an Exponential Moving Average (EMA). The EMA is a simple recursive filter commonly used for smoothing input data and identifying trends. It weights recent data points more heavily than older ones, controlled by a smoothing factor.

Features

• Computes the EMA using the formula: [ \text{EMA}(n) = \alpha \cdot x(n) + (1 - \alpha) \cdot \text{EMA}(n-1) ]
• Fixed-point arithmetic with customizable data width and smoothing factor precision.
• Synchronous operation with clock and reset signals.

Entity Declaration

Ports

Name	Direction	Width	Description
clk	Input	1 bit	Clock signal.
init	Input	1 bit	Synchronous reset signal.
data	Input	DATA_WIDTH bits	Input data to the EMA filter (signed).
average	Output	DATA_WIDTH bits	Filtered EMA output (signed).

Generics

Name	Type	Default	Description
DATA_WIDTH	Integer	16	Width of input and output data in bits.
ALPHA_BITS	Integer	8	Bit width for the smoothing factor (alpha).

Architecture

The design computes the EMA in the following steps:

1. Parameterization: The smoothing factor (alpha) is defined in fixed-point representation.
   • Example: For 8-bit ALPHA_BITS, alpha = 128 corresponds to ( \alpha = 0.5 ).
2. Recursive Calculation: Uses the EMA formula with fixed-point arithmetic.
3. Output Update: The result is updated synchronously on each clock cycle.

Usage

1. Customization: Adjust the generics DATA_WIDTH and ALPHA_BITS in the ExponentialAverage entity to fit your design requirements.
2. Integration: Instantiate the entity in your top-level design, connect the ports, and configure the input data and clock/reset signals.

Example Instantiation

ExponentialAverage_inst : entity work.ExponentialAverage
    generic map (
        DATA_WIDTH => 16,
        ALPHA_BITS => 8
    )
    port map (
        clk     => clk,
        init    => init,
        data    => data,
        average => average
    );

3. Simulation: Use a VHDL simulation tool (e.g., ModelSim, GHDL) to verify the functionality. Provide a time-varying input signal to observe the smoothed EMA output.

Applications

•	Data smoothing (e.g., temperature sensors, financial data).
•	Noise reduction in signals.
•	Real-time control systems.

Acknowledgements

This README.md created with the assistance of Claude.ai