ISTFT

The inverse of STFT: overlap-add synthesis back to the time domain, with the window-envelope normalization, in two kernels riding one GPU submission. Round trips are exact to float precision (the figure’s title carries the measured error).

specux.istft(Z, n_fft=2048, hop_length=None, win_length=None, window="hann",
             center=True, length=None, backend="auto")

import numpy as np

import specux

x = np.random.randn(8, 32768).astype(np.float32)
Z = specux.stft(x, n_fft=1024, hop_length=256)          # complex spectrum
y = specux.istft(Z, n_fft=1024, hop_length=256, length=x.shape[-1])
np.abs(y - x).max()                                     # ~1e-5, float32 roundoff

Parameters

• Z: the complex spectrum, shaped (..., n_fft // 2 + 1, n_frames), as produced by specux.stft(..., output="complex"). The output is (..., time). torch inputs are differentiable (adjoint backward).
• n_fft, hop_length, win_length, window, center: must match the analysis parameters.
• length: crop or bound the output length in samples.
• backend: "auto", "cuda", "cpu", or "metal".

A window/hop combination that violates the NOLA condition, meaning no exact reconstruction exists, raises ValueError instead of returning silently wrong audio [griffin1984].

Determinism

GPU overlap-add uses atomics by default; large n_fft (past the fused kernels) always runs a gather pipeline with no atomics, so it is bitwise-reproducible as-is. specux.deterministic(True) (or torch’s use_deterministic_algorithms) switches the fused path to a bitwise-reproducible ordered gather, at the cost of a larger intermediate buffer:

with specux.deterministic(True):
    y = specux.istft(Z, n_fft=1024, hop_length=256, length=x.shape[-1])

The configured form

specux.ISTFT holds the parameters and broadcasts over any leading shape; to_dict() round-trips the configuration:

t = specux.ISTFT(n_fft=1024, hop_length=256)
y = t(Z, length=x.shape[-1])                   # (..., time)
assert specux.ISTFT(**t.to_dict()) == t

The torch Module for training pipelines is specux.transforms.InverseSpectrogram.

References

• [allen1977]: overlap-add synthesis.
• [griffin1984]: the NOLA condition and least-squares inversion of modified spectra.