scipy.fftpack计算特定长度数组FFT时程序冻结问题咨询

Answer #

This isn't exactly a "bug" (the program isn't crashing—it's just taking an extremely long time), but it is a known performance limitation in older versions of Scipy's FFT implementation. Here's why it's happening:

The Cooley-Tukey FFT algorithm (used by Scipy's fftpack) works best when the input array length can be factored into small prime numbers (like 2, 3, 5, 7). When the length has large prime factors, the algorithm can't use its efficient radix-based splits and falls back to a naive O(n²) DFT calculation. For arrays of ~1.5 million elements, this naive approach can take hours to finish—making it look like the program has frozen.

Let's break down your test lengths:

• 1492827: This number factors into smaller primes (3 × 497609; even if 497609 is prime, it's small enough that the FFT can handle it efficiently with mixed-radix methods).
• 1492828: Factors into 4 × 373207, where 373207 is a large prime. This triggers the slow naive DFT path.
• 1492826: Factors into 2 × 746413, another large prime—same slow path issue.

Your environment (Scipy 1.1.0 on Python 2.7) is an older stack where this limitation was more noticeable. Later Scipy versions (1.2+) introduced improvements to handle large-prime-length arrays more efficiently, reducing this hang-like behavior.

Fixes to try:

• Pad to a highly composite length: Adjust your array length to the next "highly composite number" (a number with many small prime factors, e.g., 1500000 = 2⁶ × 3 × 5⁶). Pad your array with zeros to reach this length, and the FFT will run in seconds instead of hours.
• Upgrade Scipy: If you're stuck on Python 2.7, you can still upgrade to Scipy 1.2.3 (the last version supporting Python 2.7), which has better FFT performance for these edge cases.
• Try NumPy's FFT: In some scenarios, numpy.fft.fft handles large-prime-length arrays more gracefully than older Scipy fftpack versions.

内容的提问来源于stack exchange，提问作者Basj