📊 SNR Tutorial
Step 1 of 10

Signal-to-Noise Ratio

Learn to measure audio quality in 10 minutes.

What you'll learn

→ What SNR actually measures

→ The math behind decibels

→ A critical bug in common implementations

→ How to estimate SNR from real audio

What is a Signal?

A signal is what you want to hear. Let's create a 440 Hz tone (musical note A).

Time → Pure Signal (440 Hz)
💡 Notice the clean, regular wave pattern. This is a pure tone with no interference.

What is Noise?

Noise is what you don't want to hear. It's random—no pattern, unpredictable.

Time → Random Noise
💡 Noise has no repeating pattern. It sounds like static or hiss.

The Reality: Mixed Audio

In the real world, you hear signal + noise combined. Use the slider to see how noise affects the signal.

Noise Level 30%
⚡ Key insight: You only observe the mixed signal. The challenge is figuring out how much is signal vs noise!

The Math: Power & Decibels

SNR measures the ratio of signal power to noise power.

SNR = 10 × log₁₀(Psignal / Pnoise) dB
What is Power?

Power = average of squared values

P = mean(x²)
Why Decibels?

Ratios can be huge (10x, 100x, 1000x). dB compresses the scale.

Quick Reference
30 dB 1000× Excellent
20 dB 100× Good
10 dB 10× Poor
0 dB 1× Signal = Noise

Interactive SNR Calculator

Adjust the signal and noise levels to see how SNR changes.

Signal Amplitude 1.0
Noise Amplitude 0.3
Psignal = 0.500 · Pnoise = 0.045 · Ratio = 11.1×
10.5 dB
Signal-to-Noise Ratio
POOR

🐛 The Critical Bug

Here's code found in production systems. Can you spot the bug?

def calculate_snr(audio, noise):
    signal_power = mean(audio ** 2)  # ← THE BUG
    noise_power = mean(noise ** 2)
    return 10 * log10(signal_power / noise_power)

Real-World Estimation

In practice, you only have the mixed audio. How do you estimate SNR?

💡 The Key Insight

Speech has pauses. Music has quiet moments. During silence, you only hear noise!

■ Red = noise only ■ Blue = signal + noise
The Percentile Method
  1. Split audio into short frames (25ms each)
  2. Calculate energy of each frame
  3. Find frames with lowest energy (bottom 10%)
  4. These are your "noise frames"
  5. Estimate noise power from these frames
⚠️ Limitation: This fails for continuous signals with no pauses!

Quick Quiz

Test your understanding with 3 questions.

Q1 OF 3

Signal power = 0.5, Noise power = 0.005. What is the SNR?

📋 Quick Reference

THE FORMULA
SNR = 10 × log₁₀( (Ptotal - Pnoise) / Pnoise )
⚠️ Use (total - noise), not just total
Quality Thresholds
≥ 30 dB EXCELLENT Studio recording
≥ 20 dB GOOD Clear phone call
≥ 15 dB ACCEPTABLE Office background
≥ 10 dB POOR Noisy environment
< 10 dB VERY POOR Hard to understand
Key Takeaways

→ SNR = ratio of signal power to noise power (in dB)

→ Every +10 dB = 10× more signal power

→ Common bug: using (S+N)/N instead of S/N

→ Estimate noise from quiet frames (percentile method)

🎉

Tutorial Complete!

You've mastered the fundamentals of SNR.

3/3
Quiz Score
You now understand:

✓ What SNR measures and why it matters

✓ The math behind power and decibels

✓ The critical bug in common implementations

✓ How to estimate SNR without ground truth

Done