From 4cd58e04d499ef156fca82cbcd272db4050f2db1 Mon Sep 17 00:00:00 2001
From: raymond <iko@datacom.jp>
Date: Tue, 9 Sep 2025 08:42:37 +0000
Subject: [PATCH] improvement/modification of convolution and its application

---
 convolution.ts                   |   4 +-
 signal_processing_convolution.ts | 732 +++++++++++++++++++++++++++++++
 2 files changed, 734 insertions(+), 2 deletions(-)
 create mode 100644 signal_processing_convolution.ts

diff --git a/convolution.ts b/convolution.ts
index 5f4ea7f..4f74868 100644
--- a/convolution.ts
+++ b/convolution.ts
@@ -107,7 +107,7 @@ export function convolve1D(
   validateArray(signal, 'Signal');
   validateArray(kernel, 'Kernel');
   
-  const { mode = 'full', boundary = 'zero' } = options;
+  const { mode = 'same', boundary = 'reflect' } = options;
   
   // Flip kernel for convolution (not correlation)
   const flippedKernel = [...kernel].reverse();
@@ -167,7 +167,7 @@ export function convolve2D(
   validateMatrix(matrix, 'Matrix');
   validateMatrix(kernel, 'Kernel');
   
-  const { mode = 'full', boundary = 'zero' } = options;
+  const { mode = 'same', boundary = 'reflect' } = options;
   
   // Flip kernel for convolution
   const flippedKernel = kernel.map(row => [...row].reverse()).reverse();
diff --git a/signal_processing_convolution.ts b/signal_processing_convolution.ts
new file mode 100644
index 0000000..178f41b
--- /dev/null
+++ b/signal_processing_convolution.ts
@@ -0,0 +1,732 @@
+// signal-processing.ts - Convolution-based signal processing functions
+import { convolve1D, convolve2D, ConvolutionKernels, ConvolutionOptions } from './convolution';
+
+export interface SmoothingOptions {
+  method?: 'gaussian' | 'moving_average';
+  windowSize?: number;
+  sigma?: number;
+}
+
+export interface EdgeDetectionOptions {
+  method?: 'sobel' | 'laplacian' | 'canny';
+  threshold?: number;
+}
+
+export interface FilterOptions {
+  type: 'lowpass' | 'highpass' | 'bandpass' | 'bandstop';
+  cutoffLow?: number;
+  cutoffHigh?: number;
+  order?: number;
+}
+
+export interface DerivativeOptions {
+  order?: 1 | 2;
+  method?: 'gradient' | 'laplacian';
+}
+
+/**
+ * Convolution-Based Signal Processing Library
+ * Functions that leverage convolution operations for signal processing
+ */
+export class SignalProcessor {
+  
+  /**
+   * Smooth a 1D signal using convolution-based methods
+   */
+  static smooth(signal: number[], options: SmoothingOptions = {}): number[] {
+    const { method = 'gaussian', windowSize = 5, sigma = 1.0 } = options;
+
+    if (signal.length === 0) {
+      throw new Error('Signal cannot be empty');
+    }
+    
+    let kernel: number[];
+    
+    switch (method) {
+      case 'gaussian':
+        kernel = ConvolutionKernels.gaussian1D(windowSize, sigma);
+        break;
+        
+      case 'moving_average':
+        kernel = ConvolutionKernels.average1D(windowSize);
+        break;
+           
+      default:
+        throw new Error(`Unsupported smoothing method: ${method}`);
+    }
+    
+    return convolve1D(signal, kernel, { mode: 'same' }).values;
+  }
+
+  /**
+   * Detect edges in 2D image data using convolution-based methods
+   */
+  static detectEdges2D(image: number[][], options: EdgeDetectionOptions = {}): number[][] {
+    const { method = 'sobel', threshold = 0.1 } = options;
+    
+    let kernelX: number[][];
+    let kernelY: number[][];
+    
+    switch (method) {
+      case 'sobel':
+        kernelX = ConvolutionKernels.sobel("x");
+        kernelY = ConvolutionKernels.sobel("y");
+        break;
+        
+      case 'laplacian':
+        const laplacianKernel = ConvolutionKernels.laplacian();
+        return convolve2D(image, laplacianKernel, { mode: 'same' }).matrix.map(row =>
+          row.map(val => Math.abs(val) > threshold ? Math.abs(val) : 0)
+        );
+        
+      default:
+        throw new Error(`Unsupported edge detection method: ${method}`);
+    }
+    
+    // Apply both kernels and combine results
+    const edgesX = convolve2D(image, kernelX, { mode: 'same' }).matrix;
+    const edgesY = convolve2D(image, kernelY, { mode: 'same' }).matrix;
+    
+    // Calculate gradient magnitude
+    const result: number[][] = [];
+    for (let i = 0; i < edgesX.length; i++) {
+      result[i] = [];
+      for (let j = 0; j < edgesX[i].length; j++) {
+        const magnitude = Math.sqrt(edgesX[i][j] ** 2 + edgesY[i][j] ** 2);
+        result[i][j] = magnitude > threshold ? magnitude : 0;
+      }
+    }
+    
+    return result;
+  }
+
+  /**
+   * Apply digital filters using convolution
+   */
+  static filter(signal: number[], options: FilterOptions): number[] {
+    const { type, cutoffLow = 0.1, cutoffHigh = 0.5, order = 4 } = options;
+    
+    let kernel: number[];
+    
+    switch (type) {
+      case 'lowpass':
+        // Low-pass filter using Gaussian kernel
+        kernel = ConvolutionKernels.gaussian1D(order * 4 + 1, order / 2);
+        return convolve1D(signal, kernel, { mode: 'same' }).values;
+        
+      case 'highpass':
+        // High-pass filter using difference of Gaussians
+        const lpKernel = ConvolutionKernels.gaussian1D(order * 4 + 1, order / 2);
+        const smoothed = convolve1D(signal, lpKernel, { mode: 'same' }).values;
+        return signal.map((val, i) => val - smoothed[i]);
+        
+      case 'bandpass':
+        // Band-pass as combination of high-pass and low-pass
+        const hp = this.filter(signal, { type: 'highpass', cutoffLow, order });
+        return this.filter(hp, { type: 'lowpass', cutoffLow: cutoffHigh, order });
+        
+      case 'bandstop':
+        // Band-stop as original minus band-pass
+        const bp = this.filter(signal, { type: 'bandpass', cutoffLow, cutoffHigh, order });
+        return signal.map((val, i) => val - bp[i]);
+        
+      default:
+        throw new Error(`Unsupported filter type: ${type}`);
+    }
+  }
+
+  /**
+   * Calculate derivatives using convolution with derivative kernels
+   */
+  static derivative(signal: number[], options: DerivativeOptions = {}): number[] {
+    const { order = 1, method = 'gradient' } = options;
+    
+    let kernel: number[];
+    
+    if (method === 'gradient') {
+      switch (order) {
+        case 1:
+          // First derivative using gradient kernel
+          kernel = [-0.5, 0, 0.5]; // Simple gradient
+          break;
+        case 2:
+          // Second derivative using Laplacian-like kernel
+          kernel = [1, -2, 1]; // Simple second derivative
+          break;
+        default:
+          throw new Error(`Unsupported derivative order: ${order}`);
+      }
+    } else if (method === 'laplacian' && order === 2) {
+      // 1D Laplacian
+      kernel = [1, -2, 1];
+    } else {
+      throw new Error(`Unsupported derivative method: ${method}`);
+    }
+    
+    return convolve1D(signal, kernel, { mode: 'same' }).values;
+  }
+
+  /**
+   * Blur 2D image using Gaussian convolution
+   */
+  static blur2D(image: number[][], sigma: number = 1.0, kernelSize?: number): number[][] {
+    const size = kernelSize || Math.ceil(sigma * 6) | 1; // Ensure odd size
+    const kernel = ConvolutionKernels.gaussian(size, sigma);
+
+    return convolve2D(image, kernel, { mode: 'same' }).matrix;
+  }
+
+  /**
+   * Sharpen 2D image using unsharp masking (convolution-based)
+   */
+  static sharpen2D(image: number[][], strength: number = 1.0): number[][] {
+    const sharpenKernel = [
+      [0, -strength, 0],
+      [-strength, 1 + 4 * strength, -strength],
+      [0, -strength, 0]
+    ];
+    
+    return convolve2D(image, sharpenKernel, { mode: 'same' }).matrix;
+  }
+
+  /**
+   * Apply emboss effect using convolution
+   */
+  static emboss2D(image: number[][], direction: 'ne' | 'nw' | 'se' | 'sw' = 'ne'): number[][] {
+    const embossKernels = {
+      ne: [[-2, -1, 0], [-1, 1, 1], [0, 1, 2]],
+      nw: [[0, -1, -2], [1, 1, -1], [2, 1, 0]],
+      se: [[0, 1, 2], [-1, 1, 1], [-2, -1, 0]],
+      sw: [[2, 1, 0], [1, 1, -1], [0, -1, -2]]
+    };
+    
+    const kernel = embossKernels[direction];
+    return convolve2D(image, kernel, { mode: 'same' }).matrix;
+  }
+
+  /**
+   * Apply motion blur using directional convolution kernel
+   */
+  static motionBlur(signal: number[], direction: number, length: number = 9): number[] {
+    // Create motion blur kernel
+    const kernel = new Array(length).fill(1 / length);
+    
+    return convolve1D(signal, kernel, { mode: 'same' }).values;
+  }
+
+  /**
+   * Detect impulse response using convolution with known impulse
+   */
+  static matchedFilter(signal: number[], template: number[]): number[] {
+    // Matched filter using cross-correlation (convolution with reversed template)
+    const reversedTemplate = [...template].reverse();
+    return convolve1D(signal, reversedTemplate, { mode: 'same' }).values;
+  }
+
+  /**
+   * Create Savitzky-Golay smoothing kernel
+   */
+  private static createSavitzkyGolayKernel(windowSize: number, polyOrder: number): number[] {
+    // Simplified Savitzky-Golay kernel generation
+    // For a more complete implementation, you'd solve the least squares problem
+    const halfWindow = Math.floor(windowSize / 2);
+    const kernel: number[] = new Array(windowSize);
+    
+    // For simplicity, use predetermined coefficients for common cases
+    if (windowSize === 5 && polyOrder === 2) {
+      return [-3, 12, 17, 12, -3].map(x => x / 35);
+    } else if (windowSize === 7 && polyOrder === 2) {
+      return [-2, 3, 6, 7, 6, 3, -2].map(x => x / 21);
+    } else {
+      // Fallback to simple moving average
+      return new Array(windowSize).fill(1 / windowSize);
+    }
+  }
+
+  /**
+   * Apply median filtering (note: not convolution-based, but commonly used with other filters)
+   */
+  static medianFilter(signal: number[], windowSize: number = 3): number[] {
+    const result: number[] = [];
+    const halfWindow = Math.floor(windowSize / 2);
+    
+    for (let i = 0; i < signal.length; i++) {
+      const window: number[] = [];
+      
+      for (let j = Math.max(0, i - halfWindow); j <= Math.min(signal.length - 1, i + halfWindow); j++) {
+        window.push(signal[j]);
+      }
+      
+      window.sort((a, b) => a - b);
+      const median = window[Math.floor(window.length / 2)];
+      result.push(median);
+    }
+    
+    return result;
+  }
+
+  /**
+   * Cross-correlation using convolution
+   */
+  static crossCorrelate(signal1: number[], signal2: number[]): number[] {
+    // Cross-correlation is convolution with one signal reversed
+    const reversedSignal2 = [...signal2].reverse();
+    return convolve1D(signal1, reversedSignal2, { mode: 'full' }).values;
+  }
+
+  /**
+   * Auto-correlation using convolution
+   */
+  static autoCorrelate(signal: number[]): number[] {
+    return this.crossCorrelate(signal, signal);
+  }
+
+  /**
+   * Detect peaks using convolution-based edge detection
+   */
+  static detectPeaksConvolution(signal: number[], options: {
+    method?: 'gradient' | 'laplacian' | 'dog';
+    threshold?: number;
+    minDistance?: number;
+  } = {}): { index: number; value: number; strength: number }[] {
+    const { method = 'gradient', threshold = 0.1, minDistance = 1 } = options;
+    
+    let edgeResponse: number[];
+    
+    switch (method) {
+      case 'gradient':
+        // First derivative to detect edges (peaks are positive edges)
+        const gradientKernel = [-1, 0, 1]; // Simple gradient
+        edgeResponse = convolve1D(signal, gradientKernel, { mode: 'same' }).values;
+        break;
+        
+      case 'laplacian':
+        // Second derivative to detect peaks (zero crossings)
+        const laplacianKernel = [1, -2, 1]; // 1D Laplacian
+        edgeResponse = convolve1D(signal, laplacianKernel, { mode: 'same' }).values;
+        break;
+        
+      case 'dog':
+        // Difference of Gaussians for multi-scale peak detection
+        const sigma1 = 1.0;
+        const sigma2 = 1.6;
+        const size = 9;
+        const gauss1 = ConvolutionKernels.gaussian1D(size, sigma1);
+        const gauss2 = ConvolutionKernels.gaussian1D(size, sigma2);
+        const dogKernel = gauss1.map((g1, i) => g1 - gauss2[i]);
+        edgeResponse = convolve1D(signal, dogKernel, { mode: 'same' }).values;
+        break;
+        
+      default:
+        throw new Error(`Unsupported peak detection method: ${method}`);
+    }
+    
+    // Find local maxima in edge response
+    const peaks: { index: number; value: number; strength: number }[] = [];
+    
+    for (let i = 1; i < edgeResponse.length - 1; i++) {
+      const current = edgeResponse[i];
+      const left = edgeResponse[i - 1];
+      const right = edgeResponse[i + 1];
+      
+      // For gradient method, look for positive peaks
+      // For Laplacian/DoG, look for zero crossings with positive slope
+      let isPeak = false;
+      let strength = 0;
+      
+      if (method === 'gradient') {
+        isPeak = current > left && current > right && current > threshold;
+        strength = current;
+      } else {
+        // Zero crossing detection for Laplacian/DoG
+        isPeak = left < 0 && right > 0 && Math.abs(current) < threshold;
+        strength = Math.abs(current);
+      }
+      
+      if (isPeak) {
+        peaks.push({
+          index: i,
+          value: signal[i],
+          strength: strength
+        });
+      }
+    }
+    
+    // Apply minimum distance constraint
+    if (minDistance > 1) {
+      return this.enforceMinDistanceConv(peaks, minDistance);
+    }
+    
+    return peaks;
+  }
+
+  /**
+   * Detect valleys using convolution (inverted peak detection)
+   */
+  static detectValleysConvolution(signal: number[], options: {
+    method?: 'gradient' | 'laplacian' | 'dog';
+    threshold?: number;
+    minDistance?: number;
+  } = {}): { index: number; value: number; strength: number }[] {
+    // Invert signal for valley detection
+    const invertedSignal = signal.map(x => -x);
+    const valleys = this.detectPeaksConvolution(invertedSignal, options);
+    
+    // Convert back to original scale
+    return valleys.map(valley => ({
+      ...valley,
+      value: -valley.value
+    }));
+  }
+
+  /**
+   * Detect outliers using convolution-based methods
+   */
+  static detectOutliersConvolution(signal: number[], options: {
+    method?: 'gradient_variance' | 'median_diff' | 'local_deviation';
+    windowSize?: number;
+    threshold?: number;
+  } = {}): { index: number; value: number; outlierScore: number }[] {
+    const { method = 'gradient_variance', windowSize = 7, threshold = 2.0 } = options;
+    
+    let outlierScores: number[];
+    
+    switch (method) {
+      case 'gradient_variance':
+        // Detect outliers using gradient variance
+        const gradientKernel = [-1, 0, 1];
+        const gradient = convolve1D(signal, gradientKernel, { mode: 'same' }).values;
+        
+        // Convolve gradient with variance-detecting kernel
+        const varianceKernel = new Array(windowSize).fill(1).map((_, i) => {
+          const center = Math.floor(windowSize / 2);
+          return (i - center) ** 2;
+        });
+        const normalizedVarianceKernel = varianceKernel.map(v => v / varianceKernel.reduce((s, x) => s + x, 0));
+        
+        outlierScores = convolve1D(gradient.map(g => g * g), normalizedVarianceKernel, { mode: 'same' }).values;
+        break;
+        
+      case 'median_diff':
+        // Detect outliers by difference from local median (approximated with convolution)
+        const medianApproxKernel = ConvolutionKernels.gaussian1D(windowSize, windowSize / 6);
+        const smoothed = convolve1D(signal, medianApproxKernel, { mode: 'same' }).values;
+        outlierScores = signal.map((val, i) => Math.abs(val - smoothed[i]));
+        break;
+        
+      case 'local_deviation':
+        // Detect outliers using local standard deviation approximation
+        const avgKernel = ConvolutionKernels.average1D(windowSize);
+        const localMean = convolve1D(signal, avgKernel, { mode: 'same' }).values;
+        const squaredDiffs = signal.map((val, i) => (val - localMean[i]) ** 2);
+        const localVar = convolve1D(squaredDiffs, avgKernel, { mode: 'same' }).values;
+        outlierScores = signal.map((val, i) => {
+          const std = Math.sqrt(localVar[i]);
+          return std > 0 ? Math.abs(val - localMean[i]) / std : 0;
+        });
+        break;
+        
+      default:
+        throw new Error(`Unsupported outlier detection method: ${method}`);
+    }
+    
+    // Find points exceeding threshold
+    const outliers: { index: number; value: number; outlierScore: number }[] = [];
+    outlierScores.forEach((score, i) => {
+      if (score > threshold) {
+        outliers.push({
+          index: i,
+          value: signal[i],
+          outlierScore: score
+        });
+      }
+    });
+    
+    return outliers;
+  }
+
+  /**
+   * Detect trend vertices (turning points) using convolution
+   */
+  static detectTrendVertices(signal: number[], options: {
+    method?: 'curvature' | 'sign_change' | 'momentum';
+    smoothingWindow?: number;
+    threshold?: number;
+    minDistance?: number;
+  } = {}): { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] {
+    const { 
+      method = 'curvature', 
+      smoothingWindow = 5, 
+      threshold = 0.001,
+      minDistance = 3
+    } = options;
+    
+    // First, smooth the signal to reduce noise in trend detection
+    const smoothed = this.smooth(signal, { method: 'gaussian', windowSize: smoothingWindow });
+    
+    let vertices: { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] = [];
+    
+    switch (method) {
+      case 'curvature':
+        vertices = this.detectCurvatureVertices(smoothed, threshold);
+        break;
+        
+      case 'sign_change':
+        vertices = this.detectSignChangeVertices(smoothed, threshold);
+        break;
+        
+      case 'momentum':
+        vertices = this.detectMomentumVertices(smoothed, threshold);
+        break;
+        
+      default:
+        throw new Error(`Unsupported vertex detection method: ${method}`);
+    }
+    
+    // Apply minimum distance constraint
+    if (minDistance > 1) {
+      vertices = this.enforceMinDistanceVertices(vertices, minDistance);
+    }
+    
+    // Map back to original signal values
+    return vertices.map(v => ({
+      ...v,
+      value: signal[v.index] // Use original signal value, not smoothed
+    }));
+  }
+
+  /**
+   * Detect vertices using curvature (second derivative)
+   */
+  private static detectCurvatureVertices(
+    signal: number[], 
+    threshold: number
+  ): { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] {
+    // Use second derivative kernel for curvature
+    const curvatureKernel = [1, -2, 1]; // Discrete Laplacian
+    const curvature = convolve1D(signal, curvatureKernel, { mode: 'same' }).values;
+    
+    const vertices: { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] = [];
+    
+    // Find zero crossings in curvature with sufficient magnitude
+    for (let i = 1; i < curvature.length - 1; i++) {
+      const prev = curvature[i - 1];
+      const curr = curvature[i];
+      const next = curvature[i + 1];
+      
+      // Zero crossing detection
+      if ((prev > 0 && next < 0) || (prev < 0 && next > 0)) {
+        const curvatureMagnitude = Math.abs(curr);
+        
+        if (curvatureMagnitude > threshold) {
+          const type: 'peak' | 'valley' = prev > 0 ? 'peak' : 'valley';
+          
+          vertices.push({
+            index: i,
+            value: signal[i],
+            type,
+            curvature: curr
+          });
+        }
+      }
+    }
+    
+    return vertices;
+  }
+
+  /**
+   * Detect vertices using gradient sign changes
+   */
+  private static detectSignChangeVertices(
+    signal: number[], 
+    threshold: number
+  ): { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] {
+    // First derivative for gradient
+    const gradientKernel = [-0.5, 0, 0.5]; // Central difference
+    const gradient = convolve1D(signal, gradientKernel, { mode: 'same' }).values;
+    
+    // Second derivative for curvature
+    const curvatureKernel = [1, -2, 1];
+    const curvature = convolve1D(signal, curvatureKernel, { mode: 'same' }).values;
+    
+    const vertices: { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] = [];
+    
+    // Find gradient sign changes
+    for (let i = 1; i < gradient.length - 1; i++) {
+      const prevGrad = gradient[i - 1];
+      const nextGrad = gradient[i + 1];
+      
+      // Check for sign change with sufficient gradient magnitude
+      if (Math.abs(prevGrad) > threshold && Math.abs(nextGrad) > threshold) {
+        if ((prevGrad > 0 && nextGrad < 0) || (prevGrad < 0 && nextGrad > 0)) {
+          const type: 'peak' | 'valley' = prevGrad > 0 ? 'peak' : 'valley';
+          
+          vertices.push({
+            index: i,
+            value: signal[i],
+            type,
+            curvature: curvature[i]
+          });
+        }
+      }
+    }
+    
+    return vertices;
+  }
+
+  /**
+   * Detect vertices using momentum changes
+   */
+  private static detectMomentumVertices(
+    signal: number[], 
+    threshold: number
+  ): { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] {
+    // Create momentum kernel (difference over larger window)
+    const momentumKernel = [-1, 0, 0, 0, 1]; // 4-point difference
+    const momentum = convolve1D(signal, momentumKernel, { mode: 'same' }).values;
+    
+    // Detect momentum reversals
+    const momentumGradient = convolve1D(momentum, [-0.5, 0, 0.5], { mode: 'same' }).values;
+    const curvature = convolve1D(signal, [1, -2, 1], { mode: 'same' }).values;
+    
+    const vertices: { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] = [];
+    
+    for (let i = 2; i < momentum.length - 2; i++) {
+      const prevMomentum = momentum[i - 1];
+      const currMomentum = momentum[i];
+      const nextMomentum = momentum[i + 1];
+      
+      // Check for momentum reversal
+      if (Math.abs(momentumGradient[i]) > threshold) {
+        if ((prevMomentum > 0 && nextMomentum < 0) || (prevMomentum < 0 && nextMomentum > 0)) {
+          const type: 'peak' | 'valley' = prevMomentum > 0 ? 'peak' : 'valley';
+          
+          vertices.push({
+            index: i,
+            value: signal[i],
+            type,
+            curvature: curvature[i]
+          });
+        }
+      }
+    }
+    
+    return vertices;
+  }
+
+  /**
+   * Detect trend direction changes using convolution
+   */
+  static detectTrendChanges(signal: number[], options: {
+    windowSize?: number;
+    threshold?: number;
+    minTrendLength?: number;
+  } = {}): { index: number; fromTrend: 'up' | 'down' | 'flat'; toTrend: 'up' | 'down' | 'flat'; strength: number }[] {
+    const { windowSize = 10, threshold = 0.01, minTrendLength = 5 } = options;
+    
+    // Calculate local trends using convolution with trend-detecting kernel
+    const trendKernel = new Array(windowSize).fill(0).map((_, i) => {
+      const center = windowSize / 2;
+      return (i - center) / (windowSize * windowSize / 12); // Linear trend kernel
+    });
+    
+    const trends = convolve1D(signal, trendKernel, { mode: 'same' }).values;
+    
+    // Classify trends
+    const trendDirection = trends.map(t => {
+      if (t > threshold) return 'up';
+      if (t < -threshold) return 'down';
+      return 'flat';
+    });
+    
+    // Find trend changes
+    const changes: { index: number; fromTrend: 'up' | 'down' | 'flat'; toTrend: 'up' | 'down' | 'flat'; strength: number }[] = [];
+    
+    let currentTrend: 'up' | 'down' | 'flat' = trendDirection[0];
+    let trendStart = 0;
+    
+    for (let i = 1; i < trendDirection.length; i++) {
+      if (trendDirection[i] !== currentTrend) {
+        const trendLength = i - trendStart;
+        
+        if (trendLength >= minTrendLength) {
+          changes.push({
+            index: i,
+            fromTrend: currentTrend,
+            toTrend: trendDirection[i] as 'up' | 'down' | 'flat',
+            strength: Math.abs(trends[i] - trends[trendStart])
+          });
+        }
+        
+        currentTrend = trendDirection[i] as 'up' | 'down' | 'flat';
+        trendStart = i;
+      }
+    }
+    
+    return changes;
+  }
+
+  /**
+   * Enforce minimum distance between vertices
+   */
+  private static enforceMinDistanceVertices(
+    vertices: { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[],
+    minDistance: number
+  ): { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] {
+    if (vertices.length <= 1) return vertices;
+    
+    // Sort by curvature magnitude (stronger vertices first)
+    const sorted = [...vertices].sort((a, b) => Math.abs(b.curvature) - Math.abs(a.curvature));
+    const result: { index: number; value: number; type: 'peak' | 'valley'; curvature: number }[] = [];
+    
+    for (const vertex of sorted) {
+      let tooClose = false;
+      
+      for (const accepted of result) {
+        if (Math.abs(vertex.index - accepted.index) < minDistance) {
+          tooClose = true;
+          break;
+        }
+      }
+      
+      if (!tooClose) {
+        result.push(vertex);
+      }
+    }
+    
+    // Sort result by index
+    return result.sort((a, b) => a.index - b.index);
+  }
+
+  /**
+   * Enforce minimum distance between detected features
+   */
+  private static enforceMinDistanceConv(
+    features: { index: number; value: number; strength: number }[], 
+    minDistance: number
+  ): { index: number; value: number; strength: number }[] {
+    if (features.length <= 1) return features;
+    
+    // Sort by strength (descending)
+    const sorted = [...features].sort((a, b) => b.strength - a.strength);
+    const result: { index: number; value: number; strength: number }[] = [];
+    
+    for (const feature of sorted) {
+      let tooClose = false;
+      
+      for (const accepted of result) {
+        if (Math.abs(feature.index - accepted.index) < minDistance) {
+          tooClose = true;
+          break;
+        }
+      }
+      
+      if (!tooClose) {
+        result.push(feature);
+      }
+    }
+    
+    // Sort result by index
+    return result.sort((a, b) => a.index - b.index);
+  }
+}
\ No newline at end of file