The formula to calculate the dB per octave is:
\[ \text{dB/Octave} = \frac{\text{End Level} - \text{Start Level}}{\log_2\left(\frac{\text{End Frequency}}{\text{Start Frequency}}\right)} \]
Where:
Let's say the start frequency is 100 Hz, the end frequency is 800 Hz, the start level is 50 dB, and the end level is 30 dB. Using the formula:
\[ \text{dB/Octave} = \frac{30 - 50}{\log_2\left(\frac{800}{100}\right)} \]
We get:
\[ \text{dB/Octave} = \frac{-20}{3} = -6.67 \]
So, the dB per octave is -6.67.
Definition: dB per octave is a measure of how much a signal's power decreases as the frequency doubles.
Formula: \( \text{dB per octave} = 10 \log_{10} \left( \frac{P_2}{P_1} \right) \)
Example: \( \text{dB per octave} = 10 \log_{10} \left( \frac{50}{100} \right) \)
Formula: \( \text{dB per octave} = \frac{\text{dB per decade}}{3.32} \)
Example: \( \text{dB per octave} = \frac{20}{3.32} \)
Definition: A slope of 6 dB per octave indicates that the signal's power decreases by 6 dB each time the frequency doubles.
Definition: A slope of 3 dB per octave indicates that the signal's power decreases by 3 dB each time the frequency doubles.
Formula: \( \text{Octaves} = \log_{2} \left( \frac{f_2}{f_1} \right) \)
Formula: \( f_c = f_1 \times 2^{\frac{n}{b}} \)
Example: \( f_c = 1000 \times 2^{\frac{1}{3}} \)
Definition: 1 octave per minute indicates that the frequency doubles every minute.
