Introduction

In real-world DSP systems—embedded sensing, instrumentation, audio processing, vibration monitoring, and RF-adjacent pipelines—engineers routinely face narrowband tonal interference, harmonic spurs, and frequency-drifting noise components contaminating time-domain measurements.

Typical workflows rely on manual spectrum inspection and heuristic tuning: visually identifying peaks, guessing problematic frequencies, and iteratively adjusting filters until the output “looks cleaner.” While workable for simple stationary tones, this approach becomes unreliable when interference drifts over time, appears intermittently, or overlaps with broadband noise.

This article presents a deterministic and auditable workflow for spectral characterization and automated filter synthesis—focused on engineering repeatability rather than black-box optimization—and explains how SignalForge structures that pipeline end-to-end.

Why DSP Filtering Fails in Practice

Many real-world filtering failures are not caused by inappropriate filter structures, but by incorrect spectral identification and non-repeatable tuning.

Common failure modes include:

  • false tonal detection caused by random PSD ripples
  • missed interference due to frequency drift over time
  • unstable high-Q notch coefficient placement
  • over-filtering that suppresses meaningful signal components
  • lack of quantitative verification beyond visual inspection

A robust DSP workflow must begin with correct spectral characterization, proceed to stable synthesis, and finish with objective performance validation.

PSD and STFT: Complementary Analysis Tools

Power Spectral Density (PSD)

PSD is highly effective at revealing stationary narrowband energy concentrations and remains the primary tool for detecting tonal interference.

However, PSD alone can fail when:

  • tones drift slowly in frequency
  • interference appears intermittently
  • short transients distort long-window estimates
  • harmonic families blur into complex peaks

Short-Time Fourier Transform (STFT)

STFT introduces time resolution, allowing engineers to:

  • track frequency drift trajectories
  • isolate intermittent bursts
  • distinguish persistent tones from transient noise

A deterministic workflow combines PSD’s stable energy estimation with STFT’s temporal structure detection.

Deterministic Tonal and Harmonic Characterization

Rather than subjective visual tuning, deterministic characterization produces explicit spectral facts:

  • candidate tonal frequencies and their strength
  • temporal persistence across STFT windows
  • harmonic structure consistency
  • confidence-weighted prioritization of interference sources

This structured representation enables repeatable filter synthesis and verification.

Example: Mixed Tonal and Harmonic Interference Case

Consider a signal containing:

  • a dominant narrowband tonal interferer
  • multiple harmonic spurs
  • low-level broadband noise

Raw Spectral Signature

(Insert PSD plot showing dominant tone + harmonics here)
Figure 1 — PSD revealing primary tonal peak and harmonic structure

Time-Frequency Behavior

(Insert STFT heatmap showing drift/persistence here)
Figure 2 — STFT illustrating temporal persistence and slight frequency drift

Using combined PSD and STFT analysis, SignalForge deterministically identifies:

  • the fundamental tonal frequency
  • harmonic relationships
  • persistence confidence
  • drift envelope when present

This avoids both false positives and missed interference components.

Automated Stable Notch Synthesis

Based on deterministic characterization, SignalForge automatically synthesizes:

High-Q IIR Notch Filters

  • numerically stable pole-zero placement
  • normalized coefficient sets
  • multi-notch compositions for harmonic suppression
  • stability-verified designs

FIR Shaping Filters (when appropriate)

  • controlled ripple and stopband attenuation
  • predictable frequency response
  • deployable coefficient outputs

All coefficients are exported in C-compatible format for direct firmware integration.

Verification Through Quantitative Metrics

To enforce engineering rigor, each design is validated using:

  • tonal suppression depth
  • notch-aware SNR before/after measurements
  • spectral consistency checks
  • pass/fail compliance evaluation

(Insert PSD before/after comparison here)
Figure 3 — Spectral response before and after automated notch suppression

Verification metrics replace subjective “looks cleaner” judgments with measurable performance.

Reproducible Engineering Outputs

Each pi