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Signal metrics evaluate the quality of source separation, speech enhancement, and audio restoration using reference-based measurements.

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Function Signature

signal_metric(
    pred_x,
    gt_x
)

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Parameters

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pred_x
numpy.ndarray
required
Predicted/enhanced audio signal. Accepted shapes:
  • 1D array: (samples,) - automatically expanded to (1, samples)
  • 2D array: (channels, samples)
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gt_x
numpy.ndarray
required
Ground truth/reference audio signal. Accepted shapes:
  • 1D array: (samples,) - automatically expanded to (1, samples)
  • 2D array: (channels, samples)
Length Handling: If signals have different lengths, both are automatically truncated to the shorter length.

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Returns

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sdr
float
Signal-to-Distortion Ratio in dB (higher is better)
  • Measures overall signal quality
  • Combines artifacts, interference, and noise
  • Typical range: -10 to 30 dB
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sir
float
Signal-to-Interference Ratio in dB (higher is better)
  • Measures separation from interfering sources
  • Important for source separation tasks
  • Typical range: 0 to 40 dB
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sar
float
Signal-to-Artifacts Ratio in dB (higher is better)
  • Measures processing artifacts introduced
  • Important for enhancement quality
  • Typical range: 0 to 30 dB
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si_snr
float
Scale-Invariant Signal-to-Noise Ratio in dB (higher is better)
  • Scale-independent signal quality measure
  • Robust to amplitude differences
  • Widely used in speech enhancement
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ci_sdr
float
Convolutive-Invariant Signal-to-Distortion Ratio in dB (higher is better)
  • Invariant to filtering/convolution operations
  • Uses 512-tap filter by default
  • Better for reverberant conditions

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Usage Examples

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Basic Usage

import numpy as np
from versa import signal_metric

# Load audio signals
reference = np.random.random(16000)  # Replace with actual reference
enhanced = np.random.random(16000)   # Replace with actual enhanced audio

# Calculate all signal metrics
results = signal_metric(
    pred_x=enhanced,
    gt_x=reference
)

print(f"SDR: {results['sdr']:.2f} dB")
print(f"SIR: {results['sir']:.2f} dB")
print(f"SAR: {results['sar']:.2f} dB")
print(f"SI-SNR: {results['si_snr']:.2f} dB")
print(f"CI-SDR: {results['ci_sdr']:.2f} dB")

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Multi-Channel Audio

import numpy as np
from versa import signal_metric

# Multi-channel signals (e.g., stereo)
reference = np.random.random((2, 48000))  # 2 channels
enhanced = np.random.random((2, 48000))

results = signal_metric(
    pred_x=enhanced,
    gt_x=reference
)

print(f"Multi-channel SDR: {results['sdr']:.2f} dB")

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Different Length Signals

import numpy as np
from versa import signal_metric

# Signals with different lengths
reference = np.random.random(20000)
enhanced = np.random.random(18000)  # Shorter

# Automatically truncated to min length (18000)
results = signal_metric(
    pred_x=enhanced,
    gt_x=reference
)

print(f"SDR: {results['sdr']:.2f} dB")

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Speech Enhancement Evaluation

import numpy as np
import soundfile as sf
from versa import signal_metric

# Load clean and enhanced speech
clean_speech, sr = sf.read("clean.wav")
enhanced_speech, sr = sf.read("enhanced.wav")

# Evaluate enhancement quality
results = signal_metric(
    pred_x=enhanced_speech,
    gt_x=clean_speech
)

print("Speech Enhancement Results:")
print(f"  SDR: {results['sdr']:.2f} dB")
print(f"  SI-SNR: {results['si_snr']:.2f} dB (scale-invariant)")
print(f"  SAR: {results['sar']:.2f} dB (artifacts)")

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Source Separation Evaluation

import numpy as np
import soundfile as sf
from versa import signal_metric

# Load reference and separated source
reference_vocals, sr = sf.read("vocals_ref.wav")
separated_vocals, sr = sf.read("vocals_separated.wav")

# Evaluate separation quality
results = signal_metric(
    pred_x=separated_vocals,
    gt_x=reference_vocals
)

print("Source Separation Results:")
print(f"  SDR: {results['sdr']:.2f} dB")
print(f"  SIR: {results['sir']:.2f} dB (interference rejection)")
print(f"  CI-SDR: {results['ci_sdr']:.2f} dB (convolution-invariant)")

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Metric Details

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SDR (Signal-to-Distortion Ratio)

Formula: Ratio of target signal power to distortion power Interpretation:
  • Measures overall quality including all types of errors
  • Higher values indicate better quality
  • Combines SIR and SAR information
Use Cases:
  • Overall system performance
  • General quality assessment
  • Benchmark comparisons

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SIR (Signal-to-Interference Ratio)

Formula: Ratio of target signal to interference from other sources Interpretation:
  • Specifically measures separation performance
  • High SIR means good source isolation
  • Low SIR indicates source leakage
Use Cases:
  • Source separation evaluation
  • Multi-speaker scenarios
  • Music source separation

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SAR (Signal-to-Artifacts Ratio)

Formula: Ratio of target signal to processing artifacts Interpretation:
  • Measures algorithm-introduced distortions
  • High SAR means clean processing
  • Low SAR indicates processing artifacts
Use Cases:
  • Enhancement algorithm quality
  • Codec evaluation
  • Processing artifact detection

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SI-SNR (Scale-Invariant SNR)

Formula: SNR computed after optimal scaling Interpretation:
  • Invariant to signal amplitude
  • Focuses on waveform shape similarity
  • Popular in neural network training
Advantages:
  • No sensitivity to volume differences
  • Differentiable (good for training)
  • Robust metric for speech tasks
Use Cases:
  • Speech enhancement
  • Neural network training loss
  • Speaker separation

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CI-SDR (Convolutive-Invariant SDR)

Formula: SDR after optimal filtering (512-tap filter) Interpretation:
  • Invariant to linear filtering/convolution
  • Handles room acoustics effects
  • More robust than SDR in reverb
Use Cases:
  • Reverberant environments
  • Far-field speech processing
  • Acoustic echo cancellation

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Interpretation Guidelines

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Quality Ranges

MetricExcellentGoodFairPoor
SDR> 18 dB12-18 dB6-12 dB< 6 dB
SIR> 20 dB15-20 dB10-15 dB< 10 dB
SAR> 15 dB10-15 dB5-10 dB< 5 dB
SI-SNR> 15 dB10-15 dB5-10 dB< 5 dB
CI-SDR> 15 dB10-15 dB5-10 dB< 5 dB

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Task-Specific Benchmarks

Speech Enhancement:
  • Target SI-SNR improvement: 10-20 dB
  • Typical SDR: 10-18 dB
  • SAR importance: High
Music Source Separation:
  • Good SDR: 6-12 dB (vocals), 8-14 dB (accompaniment)
  • SIR importance: Critical
  • State-of-the-art: 8-10 dB SDR
Speaker Separation:
  • Target SI-SNR: 12-18 dB
  • SIR importance: Very high
  • CI-SDR useful for reverberant conditions

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Implementation Details

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Backends

  • SDR, SIR, SAR: Uses mir_eval.separation.bss_eval_sources
  • SI-SNR: Uses fast_bss_eval.si_sdr_loss
  • CI-SDR: Uses ci_sdr.pt.ci_sdr_loss

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Computation Parameters

  • Permutation: compute_permutation=False (assumes correct channel order)
  • CI-SDR filter length: 512 taps (default)
  • SI-SNR zero mean: Controlled by backend default

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Dependencies

pip install mir_eval fast_bss_eval ci_sdr torch

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Use Cases

  • Speech Enhancement: Noise reduction, dereverberation
  • Source Separation: Music, speech, environmental sounds
  • Echo Cancellation: Acoustic echo removal
  • Beamforming: Multi-microphone processing
  • Codec Evaluation: Audio compression quality
  • Model Training: Loss functions and validation

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Notes

Channel Ordering: Assumes predicted and reference channels are aligned. Enable permutation if channel order is unknown.
Negative Values: Negative dB values indicate predicted signal is worse than the input mixture.
Shape Requirements: Input must be 1D or 2D. Higher dimensional arrays will cause errors.

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