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Research

StockPulse — Financial Signal Analysis

FFT/FIR-based denoising and automated trend detection applied to real AAPL price time-series.

Difficulty — intermediate Complexity — 6/10 Category — Research
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Overview

A DSP-first take on financial time-series analysis: rather than applying technical indicators directly to noisy price data, this project treats price noise as a signal-processing problem — removing it via both frequency-domain and time-domain filtering, then validating the two approaches agree, before running trend detection.

Architecture

Real AAPL price data → synthetic noise modeling → parallel FFT-domain and FIR time-domain filtering (validated via the convolution-multiplication duality) → moving-average crossover and derivative-based trend/volatility detection.

Key Features

  • A 100-tap Hamming-windowed FIR low-pass filter designed and tuned for financial time-series.
  • Cross-validation between frequency-domain (FFT/IFFT) and time-domain (FIR convolution) filtering, confirming equivalent results.
  • Golden Cross / Death Cross moving-average crossover detection for bullish/bearish trend signals.
  • Derivative-based spike detection for high-volatility market events.

Development Process

  • Modeled artificial noise onto real AAPL price data to create a controlled evaluation signal.
  • Filtered the same signal two independent ways (FFT-domain and FIR-domain) to cross-check correctness.
  • Measured reconstruction accuracy via RMSE before trusting the filtered output for trend detection.
  • Layered trend and volatility detection on top of the validated, denoised signal.

Challenges & Solutions

Challenge

Confirming that frequency-domain and time-domain filtering actually produced equivalent results required more than eyeballing the output.

Solution

Explicitly validated the convolution-multiplication duality theorem between the two approaches and compared RMSE, not just visual inspection.

Results & Impact

Both filtering approaches converged to equivalent denoised signals, and the resulting trend-detection layer successfully surfaced Golden Cross/Death Cross events and volatility spikes from the cleaned data.

Future Improvements

  • Extend to multi-asset comparative analysis.
  • Backtest the crossover signals against actual trading outcomes.
  • Add adaptive filter length selection.