What is Signal to Noise Ratio?
In terms of definition, SNR or signal-to-noise ratio is the ratio between the desired information or the power of a signal and the undesired signal or the power of the background noise.
Also, SNR is a measurement parameter in use in the fields of science and engineering that compares the level of the desired signal to the level of background noise. In other words, SNR is the ratio of signal power to the noise power, and its unit of expression is typically decibels (dB). Also, a ratio greater than 0 dB or higher than 1:1, signifies more signal than noise.
Aside from the technical definition of SNR, the way I define it in other terms is by using a comparative. For example, say that you and one other person are inside a large room having a conversation. However, the room is full of other people who are also having conversations. Furthermore, a few of the other individuals also have similar voice patterns to you and the other individual involved in your discussion. As you can imagine, it would be difficult to decipher which person is saying what.
How to Calculate Signal to Noise Ratio
SNR calculations can be either simple or complex, and it depends on the devices in question and your available data. So, if your SNR measurements are already in decibel form, then you can subtract the noise quantity from the desired signal: SNR = S - N. This is because when you subtract logarithms, it is the equivalent of dividing normal numbers. Also, the difference in the numbers equals the SNR. For example, you measure a radio signal with a strength of -10 dB and a noise signal of -50 dB. -10 - (-50) = 40 dB.
As I stated earlier, calculating SNR can be involved, as well. So, for complex calculations, you divide the value of the desired signal by the amount of the noise and then take the common logarithm of the result, i.e., log (S ÷ N). After this, if the signal strength measurements are in watts (power), you will then multiply by 20. However, if they are units of voltage, then you will multiply by 10.
Furthermore, for power, SNR = 20 log (S ÷ N) and for voltage, SNR = 10 log (S ÷ N). Also, the resulting calculation is the SNR in decibels. For example, your measured noise value (N) is 2 microvolts, and your signal (S) is 300 millivolts. The SNR is 10 log (.3 ÷ .000002) or approximately 62 dB.
Example
Calculating Signal-to-Noise Ratio (SNR)
The Signal-to-Noise Ratio (SNR) is a measure of the strength of a signal relative to the background noise. It is a crucial parameter in telecommunications, audio systems, and many other fields, as it indicates the quality of a signal. A higher SNR means a clearer signal with less noise, while a lower SNR indicates more noise relative to the signal.
The general approach to calculating SNR includes:
- Identifying the signal power and noise power (or voltage, depending on the context).
- Knowing the type of measurement (e.g., in decibels or linear scale).
- Applying the formula for SNR to calculate the result.
Signal-to-Noise Ratio Formula
The general formula for SNR is:
\[ \text{SNR} = \frac{{P_s}}{{P_n}} \]Where:
- P_s is the signal power (in watts or milliwatts, depending on the context).
- P_n is the noise power (in watts or milliwatts, depending on the context).
Example:
If the signal power is 20 mW and the noise power is 5 mW, the SNR is:
- Step 1: Divide the signal power by the noise power: \( \text{SNR} = \frac{{20}}{{5}} = 4 \, \text{dB} \).
Converting SNR to Decibels
SNR is often expressed in decibels (dB) for easier comparison and interpretation. To convert a linear SNR value to dB, use the following formula:
\[ \text{SNR (dB)} = 10 \log_{10} (\text{SNR}_{\text{linear}}) \]Where:
- log10 is the base-10 logarithm.
- SNR_linear is the linear SNR ratio.
Example:
If the linear SNR is 100, the SNR in dB is:
- Step 1: Apply the formula: \( \text{SNR (dB)} = 10 \log_{10} (100) = 20 \, \text{dB} \).
Real-life Applications of SNR
Calculating SNR has many practical applications, such as:
- Evaluating the quality of a communication system (e.g., Wi-Fi, mobile networks).
- Assessing the clarity of an audio signal in recording or playback systems.
- Improving signal processing in radio astronomy, medical imaging, and other fields.
Common Units of SNR
SI Unit: The SNR is typically measured in decibels (dB) when comparing signal strength to noise levels.
SNR can also be expressed in a linear scale, where the ratio is directly calculated without using logarithms.
Common Operations with SNR
Linear SNR: SNR in its basic form, calculated as the ratio of signal power to noise power.
Logarithmic SNR: SNR expressed in decibels (dB) to simplify the comparison between signals.
Negative SNR: A negative SNR (often expressed as a negative dB) indicates that the noise is stronger than the signal, which is typically undesirable in communication systems.
| Problem Type | Description | Steps to Solve | Example |
|---|---|---|---|
| Calculating SNR from Signal and Noise Power | Finding the signal-to-noise ratio when given the signal power and noise power. |
|
For a signal power of \( 20 \, \text{mW} \) and a noise power of \( 5 \, \text{mW} \), the SNR is \( \text{SNR} = \frac{{20}}{{5}} = 4 \, \text{dB} \). |
| Calculating SNR from Signal and Noise Voltage | Finding the SNR when given the signal voltage and noise voltage. |
|
For a signal voltage of \( 10 \, \text{V} \) and a noise voltage of \( 2 \, \text{V} \), the SNR is \( \text{SNR} = \left( \frac{{10}}{{2}} \right)^2 = 25 \, \text{dB} \). |
| Converting SNR to dB | Finding the SNR in decibels (dB) when given the linear SNR. |
|
For a linear SNR of 100, the SNR in dB is \( \text{SNR (dB)} = 10 \log_{10} (100) = 20 \, \text{dB} \). |
| Real-life Applications | Applying SNR to solve practical problems in telecommunications, audio systems, and signal processing. |
|
If a communication system has a signal power of \( 50 \, \text{mW} \) and noise power of \( 10 \, \text{mW} \), use the formula \( \text{SNR} = \frac{{50}}{{10}} = 5 \, \text{dB} \) to evaluate the quality of the signal. |
