# Trends (FIR)

> "FIR filters are always stable. The question is how many coefficients you need."  Digital Signal Processing folklore

Finite Impulse Response (FIR) trend indicators. These use fixed-length windows with explicit coefficients. No feedback loops, no recursion. Output depends only on current and past inputs. Always stable. Linear phase possible. SIMD-friendly batch computation.

## Indicator Status

| Indicator | Full Name | Status | Description |
| :--- | :--- | :---: | :--- |
| [ALMA](lib/trends_FIR/alma/Alma.md) | Arnaud Legoux MA |  | Gaussian window with offset parameter. Smooth with configurable lag. |
| [BLMA](lib/trends_FIR/blma/Blma.md) | Blackman MA |  | Blackman window. Excellent side-lobe suppression (-58 dB). |
| [BWMA](lib/trends_FIR/bwma/Bwma.md) | Bessel-Weighted MA |  | Bessel window function. Good frequency resolution. |
| [Conv](lib/trends_FIR/conv/Conv.md) | Convolution MA |  | Generic convolution with custom kernel. Building block for others. |
| [DWMA](lib/trends_FIR/dwma/Dwma.md) | Double Weighted MA |  | WMA of WMA. Smoother than single WMA. Triangular-like response. |
| [GWMA](lib/trends_FIR/gwma/Gwma.md) | Gaussian Weighted MA |  | Centered Gaussian bell curve. No overshoot. Ã controls width. |
| [HAMMA](lib/trends_FIR/hamma/Hamma.md) | Hamming MA |  | Hamming window. -43 dB side lobes. Good general purpose. |
| [HANMA](lib/trends_FIR/hanma/Hanma.md) | Hanning MA |  | Hanning (raised cosine). Zero at edges. Smooth roll-off. |
| [HMA](lib/trends_FIR/hma/Hma.md) | Hull MA |  | Reduced lag via weighted average differencing. Can overshoot. |
| [HWMA](lib/trends_FIR/hwma/Hwma.md) | Holt-Winters MA |  | Triple exponential smoothing. Tracks level, velocity, acceleration. |
| [LSMA](lib/trends_FIR/lsma/Lsma.md) | Least Squares MA |  | Linear regression endpoint. Extrapolates trend. |
| [PWMA](lib/trends_FIR/pwma/Pwma.md) | Pascal Weighted MA |  | Pascal's triangle coefficients. Binomial distribution weights. |
| [SGMA](lib/trends_FIR/sgma/Sgma.md) | Savitzky-Golay MA |  | Polynomial fit. Preserves higher moments. Shape-preserving. |
| [SINEMA](lib/trends_FIR/sinema/Sinema.md) | Sine-Weighted MA |  | Sine wave weighting. Smooth bell-shaped emphasis. |
| [SMA](lib/trends_FIR/sma/Sma.md) | Simple MA |  | Equal weights. Baseline reference. Lag = (N-1)/2. |
| [TRIMA](lib/trends_FIR/trima/Trima.md) | Triangular MA |  | Triangular weights. SMA of SMA. Emphasizes middle. |
| [WMA](lib/trends_FIR/wma/Wma.md) | Weighted MA |  | Linear weights. Recent prices weighted more. Lag < SMA. |

**Status Key:**  Implemented | =Ë Planned

## Selection Guide

| Use Case | Recommended | Why |
| :--- | :--- | :--- |
| Baseline comparison | SMA | Simple, well-understood. Reference for lag/smoothness. |
| Reduced lag | HMA, WMA, LSMA | HMA aggressive. WMA moderate. LSMA extrapolates. |
| Minimal overshoot | GWMA, TRIMA | Gaussian and triangular weights are gentle. |
| Spectral purity | BLMA, HAMMA | Window functions designed for frequency analysis. |
| Shape preservation | SGMA | Polynomial fit preserves peaks and valleys. |
| Configurable response | ALMA, Conv | ALMA has offset/sigma. Conv accepts any kernel. |
| Trend extrapolation | LSMA, HWMA | LSMA extends regression. HWMA tracks velocity. |

## FIR vs IIR Comparison

| Aspect | FIR (This Category) | IIR (trends_IIR) |
| :--- | :--- | :--- |
| Stability | Always stable | Can be unstable if poorly designed |
| Phase | Linear phase possible | Nonlinear phase (causes distortion) |
| Coefficients | Many (N = period) | Few (2-4 typically) |
| Memory | Higher | Lower |
| Computation | O(N) per sample, SIMD-friendly | O(1) per sample, recursive |
| Lag | Fixed for given N | Can be lower for same smoothness |
| Overshoot | Generally low | Can overshoot (especially JMA, HMA) |

## Window Function Characteristics

| Window | Main Lobe Width | Side Lobe (dB) | Best For |
| :--- | :--- | :--- | :--- |
| Rectangular (SMA) | Narrow | -13 | Frequency resolution |
| Hanning | Medium | -31 | General purpose |
| Hamming | Medium | -43 | Better side-lobe rejection |
| Blackman | Wide | -58 | Excellent side-lobe rejection |
| Gaussian | Configurable | Configurable | Tunable trade-off |

Narrower main lobe = better frequency resolution. Lower side lobes = less spectral leakage.