feat: implement mlx.core.blackman

[Vlor999]

Description

This PR implements the Blackman window function (mlx.core.blackman), completing the standard trio of window functions (Hanning, Hamming, Blackman) and improving feature parity with NumPy.

Implementation Details

• C++: Implemented in mlx/ops.cpp.
  • Optimization: Instead of computing two separate cosine terms ($\cos(x)$ and $\cos(2x)$ ), I utilized the double-angle identity: $\cos(2x) = 2\cos^2(x) - 1$.
  • Performance: This reduces the computational cost to a single transcendental cos operation followed by cheap polynomial arithmetic ($0.34 - 0.5\cos(x) + 0.16\cos^2(x)$ ).
  • Edge Cases: Explicitly handles M < 1 (empty) and M = 1 (returns [1.0]), matching NumPy's behavior exactly.
• Python Bindings: Exposed via nanobind with nb::sig for proper type hinting and full LaTeX documentation.

Test Plan

Verified locally against NumPy for numerical accuracy and edge cases.

Verification script:

import mlx.core as mx
import numpy as np

# 1. Standard Case
M = 100
mx_blackman = mx.blackman(M)
np_blackman = np.blackman(M)

assert np.allclose(mx_blackman, np_blackman, atol=1e-6), "Mismatch in values"

# 2. Edge Case M=1
# Verified that both return [1.0]
assert mx.blackman(1).item() == 1.0
assert np.blackman(1).item() == 1.0

# 3. Edge Case M=0
assert mx.blackman(0).size == 0

print("✅ All verifications passed against numpy.blackman")

Unit Tests:

Added test_blackman in python/tests/test_ops.py.

Checklist

Put an x in the boxes that apply.

• I have read the CONTRIBUTING document
• I have run pre-commit run --all-files to format my code / installed pre-commit prior to committing changes
• I have added tests that prove my fix is effective or that my feature works
• I have updated the necessary documentation (if needed)

[angeloskath]

Looks good as well.

Feel free to fix the conflicts and then I can run the tests and merge.

[Vlor999]

Thanks
I've corrected all the issues.

[Vlor999]

Hi team! 👋
Just a gentle ping on this PR. Let me know if there's anything else you need from my side or if you'd like any changes to the implementation! 🚀

[angeloskath]

Hi @Vlor999, sorry for the delay.

Out of curiosity is there a specific project that needs these window functions? They are becoming a bit complicated and I am wondering if they are worth it. Looking for instance at the i0 function and the Kaiser window 🤔

[Vlor999]

Hi @Vlor999, sorry for the delay.

Out of curiosity is there a specific project that needs these window functions? They are becoming a bit complicated and I am wondering if they are worth it. Looking for instance at the i0 function and the Kaiser window 🤔

I'm currently building a fully GPU-accelerated STFT (Short-Time Fourier Transform) pipeline MLX.

The goal is to provide a fast, autograd-compatible alternative to CPU-bound libraries like librosa or scipy. By keeping the framing, windowing, and mx.fft operations entirely within the MLX graph, this will enable highly parallelized audio preprocessing directly integrated into neural network training loops.

[angeloskath]

👍