Denoise

Wavelet Trend Filter What it is A denoised price line whose smoothing is derived from measured noise, not a period you pick — plus the tool's signature number, the noise fraction (what share of the recent move is noise vs structure). Most published "wavelet denoising improves prediction" results denoise the whole series including future bars, which is lookahead-contaminated and impossible live. This tool refuses that: it runs a Haar wavelet transform over a trailing power-of-two window and keeps only the endpoint as today's value, fixed at close and never revised. Strictly causal, non-repainting, no forecast. How it's built The engine is a five-step Donoho-Johnstone wavelet shrinkage, run every bar over a trailing window (default 128 bars): a Haar DWT (shortest support, fewest boundary coefficients — the right choice for short causal series); noise scale σ = MAD(finest detail coefficients)/0.6745 (robust to outliers); the universal threshold λ = σ·√(2 ln n) with an optional multiplier; soft or hard shrinkage of the detail coefficients; and an inverse transform, keeping the endpoint. Optional symmetric reflection padding reduces edge distortion. Because the threshold self-scales from measured noise, a quiet tape is smoothed less and a noisy tape more — automatically, on any timeframe. Derived reads: noise fraction = 1 − var(denoised)/var(raw) over the window (share the transform removed), ranked into a percentile; trend slope in noise-σ units; and a signal-to-noise strength = slope (σ) × structure share (1 − noise fraction), the single "is this trend real?" number. How you read it — and the honest actionable signal The noise fraction gates everything. A bold chop/structure ribbon along the bottom of the chart shows the whole regime spectrum (green = structure/low noise/trend trustworthy, red = chop/high noise/stand aside), and a ±1σ noise envelope around the denoised line makes the removed noise visible — so it's obviously not just a moving average. The actionable markers are structure-gated: a green ▲ / red ▼ prints when the denoised slope turns up/down and the tape has structure (low noise); in chop the tool withholds and marks the turn with a small caution dot instead. A hysteresis on the structure state keeps the signals from re-firing as noise oscillates. This is not a blind crossover generator — it goes quiet exactly when the tape is too noisy to trust, which is when ordinary signals whipsaw. The panel's "Read" row states the current call in plain English ("up-trend · structure ✓", "chop — stand aside"). Exports & alerts EXP_Denoised · EXP_NoiseSigma · EXP_NoiseFrac (0–1) · EXP_Slope (σ) · EXP_SNR (trend strength) · EXP_Stance (+1 up·structure / −1 down·structure / 0). Alerts: noise fraction entering top / bottom quartile (chop / structure) · denoised slope turning up / down · confirmed up-trend / down-trend with structure present.

Indicator

by Market_Logic_India

Daubechies D4 Denoising [LB]Concept The Daubechies D4 Wavelet Denoising indicator applies a multi‑level discrete wavelet transform using the compactly supported Daubechies D4 wavelet (Ingrid Daubechies, 1992) combined with Donoho's universal threshold (Donoho & Johnstone, 1994). It separates price into approximation (trend) and detail (noise) coefficients, attenuates noise via soft thresholding, and reconstructs a denoised price curve that directly overlays the chart. Mathematical Foundation The Daubechies D4 wavelet is defined by four scaling coefficients h and four wavelet coefficients g , forming quadrature mirror filters that satisfy perfect reconstruction. At each level, the input array a is circularly convolved with h and g , then downsampled by two to produce the approximation a' and detail d' : a' = SUM_m h * a d' = SUM_m g * a This process is iterated J times. The universal threshold lambda is estimated for each detail array independently using the median absolute deviation (MAD) of the coefficients : sigma = MAD / 0.6745 lambda = sigma * sqrt(2 * log N) Soft thresholding is then applied to each detail coefficient x : threshold(x) = sign(x) * max(|x| - lambda, 0) Finally, the denoised signal is reconstructed by upsampling, convolution with synthesis filters, and summation of approximation and detail contributions. What Problem Does It Solve ? Classical moving averages and low‑pass filters eliminate noise at the cost of significant lag and do not adapt to the local structure of the data. The Daubechies D4 wavelet denoising preserves sharp transitions (edges) while removing high‑frequency noise, offering a lag‑free, adaptive smoothing that respects the multi‑scale nature of price action. How To Interpret Denoised line above price – the smoothed trend is stronger than the current raw price; underlying momentum remains positive despite transient dips. Denoised line below price – the smoothed trend is weaker; price is correcting within a larger structure. Denoised line flattening or changing direction – a regime shift may be underway; the multi‑scale trend is losing or gaining momentum. Parameters Source – price field to denoise (default close). Decomposition Levels – number of wavelet decomposition iterations. Higher levels remove lower‑frequency components, producing a smoother but more slowly reacting line. Window Length (power of 2) – analysis window size. Must be a power of two for the dyadic decomposition; the indicator automatically adjusts to the largest valid power of two if an invalid value is entered. Reference Daubechies I., "Ten Lectures on Wavelets", Society for Industrial and Applied Mathematics, 1992. Donoho D.L. & Johnstone I.M., "Ideal Spatial Adaptation by Wavelet Shrinkage", Biometrika, Vol. 81, No. 3, pp. 425‑455, 1994.

Indicator

by luis_barlier

In-depth global business and economic analysis Comprehensive trading education and market insights