Spectral Processing¶
Algorithms that operate in the frequency domain via the Short-Time Fourier Transform (STFT).
STFT round-trip¶
The STFT decomposes a signal into overlapping windowed frames, applies an FFT to each, and produces a complex-valued spectrogram. The ISTFT reverses this with overlap-add.
from nanodsp import spectral
from nanodsp.buffer import AudioBuffer
buf = AudioBuffer.from_file("input.wav")
# Analyze
spec = spectral.stft(buf, window_size=2048, hop_size=512)
# Inspect
print(f"Channels: {spec.channels}")
print(f"STFT frames: {spec.num_frames}")
print(f"Frequency bins: {spec.bins}")
mag = spectral.magnitude(spec) # magnitude array
ph = spectral.phase(spec) # phase array
# Reconstruct
reconstructed = spectral.istft(spec)
Window types¶
# Available: "hann", "hamming", "blackman", "bartlett", "rectangular"
spec = spectral.stft(buf, window_size=2048, window="blackman")
out = spectral.istft(spec, window="blackman")
Time stretching¶
Changes duration without changing pitch. Uses the phase vocoder technique (Flanagan & Golden, 1966; Laroche & Dolson, 1999).
spec = spectral.stft(buf, window_size=2048, hop_size=512)
# Half speed (double duration)
slow = spectral.istft(spectral.time_stretch(spec, rate=0.5))
# Double speed (half duration)
fast = spectral.istft(spectral.time_stretch(spec, rate=2.0))
# Phase-locked stretching (cleaner for tonal material)
locked = spectral.phase_lock(spectral.time_stretch(spec, rate=0.75))
slow_clean = spectral.istft(locked)
Spectral pitch shifting¶
Changes pitch without changing duration by combining time stretching with resampling.
# Up 5 semitones
shifted = spectral.pitch_shift_spectral(buf, semitones=5.0)
# Down one octave
low = spectral.pitch_shift_spectral(buf, semitones=-12.0)
Spectral processing¶
spec = spectral.stft(buf, window_size=2048, hop_size=512)
# Gate: silence bins below threshold
cleaned = spectral.spectral_gate(spec, threshold_db=-40.0, noise_floor_db=-80.0)
# Tilt EQ: boost highs, cut lows
tilted = spectral.spectral_emphasis(spec, low_db=-3.0, high_db=3.0)
# Apply a custom mask
import numpy as np
mask = np.ones(spec.bins, dtype=np.float32)
mask[:10] = 0.0 # zero first 10 bins (remove low frequencies)
masked = spectral.apply_mask(spec, mask)
# Reconstruct any of these
result = spectral.istft(cleaned)
Spectral freeze¶
Repeats a single STFT frame indefinitely, creating a sustained "frozen" texture from an instant of the input.
spec = spectral.stft(buf, window_size=2048, hop_size=512)
frozen = spectral.spectral_freeze(spec, frame_index=10, num_frames=200)
sustained = spectral.istft(frozen)
Spectral morphing¶
Interpolates the magnitude spectra of two spectrograms while preserving the phase of the first. Creates smooth timbral transitions.
buf_a = AudioBuffer.from_file("guitar.wav")
buf_b = AudioBuffer.from_file("voice.wav")
spec_a = spectral.stft(buf_a, window_size=2048, hop_size=512)
spec_b = spectral.stft(buf_b, window_size=2048, hop_size=512)
# 50/50 blend of timbres
morphed = spectral.spectral_morph(spec_a, spec_b, mix=0.5)
hybrid = spectral.istft(morphed)
Noise reduction¶
Estimates a noise floor from the first N frames, then attenuates bins at or below it. Works best when the signal starts with noise-only content.
spec = spectral.stft(buf, window_size=2048, hop_size=512)
# Use first 10 frames as noise profile
denoised = spectral.spectral_denoise(spec, noise_frames=10, reduction_db=-20.0)
clean = spectral.istft(denoised)
# More aggressive with smoothing to reduce musical noise artifacts
strong = spectral.spectral_denoise(spec, noise_frames=15, reduction_db=-40.0, smoothing=3)
EQ matching¶
Analyzes the spectral envelope of a target, computes the ratio to the source, and applies it as a filter. Makes one recording's tonal balance match another.
source = AudioBuffer.from_file("my_mix.wav")
reference = AudioBuffer.from_file("pro_mix.wav")
# Match tonal balance
matched = spectral.eq_match(source, reference, window_size=4096, smoothing=8)