QuanTAlib/lib/trends_FIR/blma/Blma.md

BLMA: Blackman Window Moving Average

If you want to filter noise, don't just average it - window it.

Property	Value
Category	Trend (FIR MA)
Inputs	Source (close)
Parameters	period
Outputs	Single series (Blma)
Output range	Tracks input
Warmup	period bars
PineScript	blma.pine
Signature	blma_signature

• BLMA is a FIR filter that applies a triple-cosine Blackman window function from digital signal processing to financial time series.
• Best suited as a long-term trend filter due to its superior noise suppression (-58 dB sidelobes) at the cost of ~N/2 lag.
• Similar: WMA, TRIMA | Complementary: Trend confirmation | Trading note: Blackman-windowed MA; low sidelobe leakage for clean spectral response.
• Validated against reference implementations using the standard Blackman window formula.

The Blackman Window Moving Average (BLMA) applies a triple-cosine window function from digital signal processing to financial time series. Originally developed by Ralph Beebe Blackman at Bell Labs in the 1950s for spectral analysis, this filter provides superior noise suppression compared to standard moving averages by minimizing spectral leakage.

Historical Context

In the early days of signal processing, engineers struggled with spectral leakage where energy from one frequency bleeds into others during analysis. Simple rectangular windows (like SMA) caused significant leakage. Blackman proposed a window function with tapered edges that drastically reduced this effect. In trading, "leakage" manifests as market noise distorting the trend signal. BLMA adapts this DSP innovation to create a trend filter that is remarkably smooth yet responsive to significant moves.

Architecture & Physics

BLMA is a Finite Impulse Response (FIR) filter. Unlike Exponential Moving Averages (IIR) which have infinite memory, BLMA considers only the last N bars.

The "physics" of BLMA relies on its bell-shaped weighting curve. The weights are highest in the center of the window and taper to zero at both ends (newest and oldest data). This symmetry means BLMA has a lag of approximately N/2, but it effectively suppresses high-frequency noise (jitter) that often plagues other averages.

The Zero-Edge Effect

Because the Blackman window tapers to zero at the edges (w[0] \approx 0 and w[N-1] \approx 0), the most recent price data has very little immediate impact on the indicator value. This creates a "smoothness" that filters out sudden spikes, but it also introduces a specific type of lag where the indicator is slow to react to a sudden trend reversal until the price move enters the "fat" part of the window (the center).

Mathematical Foundation

The Blackman window weights w(n) for a period N are calculated as:

w(n) = 0.42 - 0.5 \cos\left(\frac{2\pi n}{N-1}\right) + 0.08 \cos\left(\frac{4\pi n}{N-1}\right)

Where 0 \le n \le N-1.

The BLMA value is the weighted average:

BLMA_t = \frac{\sum_{i=0}^{N-1} P_{t-i} \cdot w(i)}{\sum_{i=0}^{N-1} w(i)}

Performance Profile

Operation Count (Streaming Mode, Scalar)

Constructor (one-time weight precomputation):

Operation	Count	Cost (cycles)	Subtotal
COS	2N	40	80N
MUL	4N	3	12N
ADD/SUB	3N	1	3N
Total (init)	—	—	~95N cycles

For period=20: ~1,900 cycles (one-time).

Hot path (per bar):

Operation	Count	Cost (cycles)	Subtotal
MUL	N	3	3N
ADD	N	1	N
DIV	1	15	15
Total	2N + 1	—	~4N + 15 cycles

For period=20: ~95 cycles per bar.

Hot path breakdown:

• Weighted sum: ∑(buffer[i] × weights[i]) → N MUL + N ADD
• Normalization: sum / wSum → 1 DIV (wSum precomputed)

Batch Mode (SIMD)

The convolution is highly vectorizable:

Operation	Scalar Ops	SIMD Ops (AVX2)	Speedup
Weighted products	N	N/8	8×
Horizontal sum	N	log₂(8)	~N/3×

Batch efficiency (512 bars, period=20):

Mode	Cycles/bar	Total	Notes
Scalar streaming	~95	~48,640	O(N) per bar
SIMD batch	~25	~12,800	Vectorized dot product
Improvement	~4×	~36K saved	—

Quality Metrics

Metric	Score	Notes
Accuracy	10/10	Precise DSP windowing
Timeliness	4/10	Significant lag (N/2) due to symmetric window
Overshoot	10/10	Never overshoots (FIR property)
Smoothness	10/10	Excellent noise suppression (-58dB side-lobes)

Zero-Allocation Design

The implementation uses a pre-calculated weights array and a circular buffer (RingBuffer) to store price history. The Update method performs the weighted sum without allocating any new memory on the heap. For the static Calculate method, stackalloc is used for weights and temporary buffers for small periods (up to 256), ensuring high performance.

Validation

BLMA is validated against a reference implementation using the standard Blackman window formula.

Library	Status	Notes
QuanTAlib	✅	Matches theoretical formula.
PineScript	✅	Matches PineScript reference logic.

Common Pitfalls

• Lag: BLMA has more lag than EMA or WMA because it suppresses the most recent data. It is a smoothing filter, not a leading indicator.
• Warmup: During the first N bars, the window expands dynamically. The full noise-suppression characteristics are only achieved after N bars.