Fix IndexError in THD() for low/fractional fundamental frequencies

[youdie006]

Repro

THD() raises IndexError when the fundamental is low enough that its FFT bin rounds up:

import numpy as np
from waveform_analysis import THD

fs, N = 12000, 12000
t = np.arange(N) / fs
sig = np.sin(2 * np.pi * 6 * t)
THD(sig, fs, freq=5.994)

    ampl = abs(f[i * h])
IndexError: index 6006 is out of bounds for axis 0 with size 6001

This is the case described in #38 (fundamental low, rounded bin on the wrong side).

Root cause

THD() computes the number of harmonics from the continuous fundamental:

num_harmonics = int((fs/2)/frequency)

but indexes each harmonic with the rounded fundamental bin i = int(round(frequency * N / fs)):

for h in range(2, num_harmonics + 1):
    ampl = abs(f[i * h])

When the fractional bin rounds up, i * num_harmonics overshoots the rfft length len(f) = N//2 + 1, so the last harmonic's bin lands past Nyquist and the index is out of bounds. In the repro, i = round(5.994) = 6, num_harmonics = 1001, and i * 1001 = 6006 > 6001.

Fix

Guard the index before use and stop the loop:

if i * h >= len(f):
    break

Physics oracle: a harmonic at bin >= len(f) corresponds to a frequency >= fs/2, above Nyquist, which cannot exist in the sampled spectrum, so it must be excluded. break (not continue) is correct because h increases monotonically -- once one harmonic is out of range, every later one is too. Harmonics whose bin is in range are summed exactly as before, so results for normal signals are unchanged (existing test_sine/test_sawtooth/test_freq_parameter still pass).

Test

Added a regression test that reproduces #38 and asserts a finite THD:

def test_low_fundamental_no_indexerror(self):
    fs = 12000
    signal = sine_wave(6, fs)
    result = THD(signal, fs, freq=5.994)
    assert np.isfinite(result)
    assert result >= 0

Before the fix it raises IndexError: index 6006 is out of bounds for axis 0 with size 6001; after, it returns a finite ratio.

Thanks to @khaut for reporting.

---

AI-assisted: this change was prepared with the help of an AI coding assistant and reviewed by me.

Summary by CodeRabbit

• Bug Fixes

  • Fixed an issue where THD calculations could fail for low-frequency signals due to out-of-range harmonic analysis.
  • THD analysis now safely stops at the available frequency range, including frequencies above Nyquist.

• Tests

  • Added regression coverage confirming low, fractional frequencies produce finite, nonnegative THD results.

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📝 Walkthrough

Walkthrough

THD now stops harmonic analysis before it accesses FFT bins beyond the spectrum. A regression test covers a low fractional frequency that rounds to an FFT-bin boundary.

Changes

THD harmonic bounds

Layer / File(s)	Summary
Bounded harmonic analysis and regression coverage waveform_analysis/thd.py, tests/test_thd.py	THD stops when the harmonic-bin index reaches the FFT result length. The regression test verifies a finite, nonnegative result for a low fractional fundamental frequency.

Estimated code review effort: 2 (Simple) | ~5 minutes

Merge Risk: ⚪ Minimal · up to 1d0b4

The change prevents THD() from indexing harmonics beyond the Nyquist limit while preserving in-range calculations, with a focused regression test covering the failure case. No actionable merge-blocking risk remains beyond normal checks and review.

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly and concisely describes the fix for the IndexError in THD() caused by low or fractional fundamental frequencies.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 80.44%. Comparing base (6bfa59b) to head (647d8d8).

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #42      +/-   ##
==========================================
+ Coverage   80.34%   80.44%   +0.09%     
==========================================
  Files          12       12              
  Lines         407      409       +2     
==========================================
+ Hits          327      329       +2     
  Misses         80       80              

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