Signal-to-noise ratio

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The signal-to-noise ratio (SNR, S/N) is a measure used in science and engineering to quantify how much a signal has been corrupted by noise. It is defined as the ratio of the power of a signal (meaningful information) to the power of background noise (unwanted signal):

SNR = \frac{P_{signal}}{P_{noise}}

where \( P_{signal} \) is the average power of the signal and \( P_{noise} \) is the average power of the noise. SNR is usually expressed in decibels (dB):

SNR_{dB} = 10 \log_{10} \left( \frac{P_{signal}}{P_{noise}} \right)

Applications

SNR is a critical parameter in various fields such as telecommunications, audio engineering, medical imaging, and data acquisition.

Telecommunications

In telecommunications, SNR is used to measure the quality of a communication channel. A higher SNR indicates a clearer signal, which is essential for effective data transmission.

Audio Engineering

In audio engineering, SNR is used to assess the quality of audio equipment. A higher SNR means that the audio signal is less affected by noise, resulting in clearer sound.

Medical Imaging

In medical imaging, such as MRI and CT scans, SNR is crucial for obtaining clear images. Higher SNR values lead to better image quality, which is essential for accurate diagnosis.

Data Acquisition

In data acquisition systems, SNR is used to evaluate the quality of the acquired data. High SNR ensures that the data is reliable and accurate.

Calculation

The calculation of SNR can vary depending on the context. For example, in digital systems, SNR can be calculated using the bit error rate (BER). In analog systems, it can be calculated using the root mean square (RMS) values of the signal and noise.

Related Concepts

• Noise figure
• Dynamic range
• Total harmonic distortion
• Bit error rate
• Modulation

See Also

• Decibel
• Noise (electronics)
• Signal processing
• Telecommunications
• Audio engineering
• Medical imaging
• Data acquisition