Signal-to-Noise Ratio
Signal-to-Noise Ratio (SNR) is the ratio of the power of a desired signal to the power of background noise, expressed in decibels (dB), that quantifies the quality of a signal in a communication or measurement system. A higher SNR indicates a cleaner, more detectable signal relative to noise, while a low SNR indicates the signal is buried in noise. SNR is a critical parameter in audio engineering, telecommunications, radar, medical imaging (MRI), and data acquisition systems, directly determining the fidelity, range, and reliability of signal transmission and detection.
Key Formula
SNR (dB) = 10·log10(P_signal / P_noise) = 20·log10(A_signal / A_noise)
LaTeX: SNR = 10\log_{10}\!\left(\frac{P_{signal}}{P_{noise}}\right) = 20\log_{10}\!\left(\frac{A_{signal}}{A_{noise}}\right) \text{ dB}
| Symbol | Meaning | Unit |
|---|---|---|
| SNR | Signal-to-noise ratio | dB (decibels) |
| P_signal | Power of the desired signal | W or µW |
| P_noise | Power of the noise | W or µW (same unit) |
| A_signal | Amplitude (RMS voltage) of signal | V |
| A_noise | Amplitude (RMS voltage) of noise | V |
Worked Example
Problem
A radio receiver picks up a signal with an RMS voltage of 50 mV and noise with an RMS voltage of 0.5 mV. Calculate the SNR in dB. If the noise doubles to 1 mV, what is the new SNR?
Solution
Step 1: Calculate initial SNR. SNR = 20 × log10(A_signal / A_noise) SNR = 20 × log10(50 mV / 0.5 mV) SNR = 20 × log10(100) SNR = 20 × 2 = 40 dB Step 2: Verify using power ratio. Power ratio = (50/0.5)² = 100² = 10,000 SNR = 10 × log10(10,000) = 10 × 4 = 40 dB ✓ Step 3: New SNR with doubled noise. SNR_new = 20 × log10(50 mV / 1 mV) SNR_new = 20 × log10(50) SNR_new = 20 × 1.699 = 33.98 ≈ 34 dB Step 4: Reduction in SNR. ΔSNR = 40 − 34 = 6 dB (doubling noise reduces SNR by 6 dB).
Answer
Initial SNR = 40 dB; with doubled noise, SNR = 34 dB (a 6 dB reduction)
SNR Values and Their Practical Implications
| SNR (dB) | Quality Level | Power Ratio | Typical Application |
|---|---|---|---|
| < 0 dB | Below noise floor | < 1 | Signal undetectable |
| 0–10 dB | Very poor | 1–10 | Barely detectable; unreliable comms |
| 10–20 dB | Poor to fair | 10–100 | AM radio in weak coverage areas |
| 20–40 dB | Good | 100–10,000 | CD audio, standard telephony |
| 40–60 dB | Very good | 10⁴–10⁶ | Professional audio, FM radio |
| > 60 dB | Excellent | > 10⁶ | Laboratory instruments, MRI scanners |
Interactive Tools
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Related Terms
Signal Processing
Signal processing is the analysis, manipulation, and synthesis of signals — including audio, video, sensor data, and communications waveforms — to extract information or transform them for a desired purpose. It encompasses filtering, compression, modulation, spectral analysis, and noise reduction using both analog and digital techniques. Signal processing underpins technologies such as telecommunications, medical imaging, radar, speech recognition, and multimedia systems.
Fourier Transform
The Fourier Transform decomposes a time-domain signal into its constituent frequency components, expressing it as a superposition of sinusoids of different frequencies, amplitudes, and phases. It provides the frequency-domain representation of a signal and is fundamental to signal processing, communications, image analysis, and solving differential equations. The transform is invertible, meaning the original signal can be perfectly reconstructed from its frequency spectrum.
Power Factor
Power factor is the ratio of real power (watts) to apparent power (volt-amperes) in an AC circuit, representing how effectively electrical power is being converted into useful work. It equals the cosine of the phase angle between the voltage and current waveforms, ranging from 0 (purely reactive) to 1 (purely resistive). A low power factor indicates high reactive power circulation, which increases current for a given load, causing extra losses in transmission lines, and utilities typically penalise industrial consumers for poor power factor below 0.85.
The decibel unit was named after Alexander Graham Bell by engineers at Bell Telephone Laboratories in 1924, with "deci-" indicating one-tenth. The signal-to-noise concept formalised during the development of telephony and radio communications in the 1920s–1940s. Claude Shannon's landmark 1948 paper "A Mathematical Theory of Communication" placed SNR at the centre of information theory through the Shannon–Hartley channel capacity theorem.