The formula to calculate the harmonics to noise ratio (HNR) is:
\[ HNR = 10 \cdot \log_{10} \left( \frac{P_h}{P_n} \right) \]
Where:
Harmonics to Noise Ratio (HNR) is a measure used in signal processing to quantify the ratio of the power of harmonic components to the power of noise within a signal. This ratio is often expressed in decibels (dB). A higher HNR indicates a cleaner signal with more harmonic content relative to noise, while a lower HNR indicates a noisier signal. HNR is commonly used in various fields such as audio engineering, telecommunications, and acoustics to assess the quality and clarity of signals.
Example 1:
Calculation:
\[ HNR = 10 \cdot \log_{10} \left( \frac{100}{10} \right) = 10 \cdot \log_{10} (10) = 10 \cdot 1 = 10 \text{ dB} \]
Example 2:
Calculation:
\[ HNR = 10 \cdot \log_{10} \left( \frac{200}{20} \right) = 10 \cdot \log_{10} (10) = 10 \cdot 1 = 10 \text{ dB} \]
