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--- computing:logarithm-db [2026/05/04 15:09] – oscar
+++ computing:logarithm-db [2026/08/01 13:02] (current) – removed - external edit (Unknown date) 127.0.0.1
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-====== Logarithm Scale & dB ======
-===== Log Scale =====
-A logarithmic scale uses decades (factors of 10) or octaves (factors of 2) to represent vast ranges of data, such as frequency, on a compact graph. Decades, useful for spanning magnitudes (10, 100, 1000 Hz), represent a 10:1 ratio, while octaves (doubling) are common in audio.
-  * **Decade**: Represents a power of 10 increase (e.g., 10 Hz to 100 Hz is one decade; 100 Hz 1000 Hz is a second decade). Often used in electronics, such as Bode plots to display frequency response over a large range.
-  * **Octave**: Represents a doubling of frequency (e.g., 100 Hz to 200 Hz is one octave; 200 Hz to 400 Hz is another). Used in audio and vibration analysis, derived from music.
-Octave and decade
-An octave is a frequency band from ω1 to ω2 such that
-ω2 / ω1 = 2
-There is an increase in decade from ω1 to ω2 when
-ω2 / ω1 = 10
-===== Motivation for using 20 log10 |H(jω)| =====
-In communications it is standard to measure power gain in decibels,
-|H|dB = 10 log10 (P2/P1)
-Since power is the square of voltage, the voltage gain is
-|H|dB = 20 log10 (V2/V1)
-From now on, we will drop the base of the logarithm; it is understood to be 10.
-Bode plots dB vs. frequency to analyze magnitude and phase Bode Plots and Frequency Response: Logarithmic scales are used to display frequency response over several orders of magnitude. The gain is expressed in decibels dB, calculated as 20*log10|a|), and frequency is plotted logarithmically.
-Logarithmic plots of H(jω), or Bode diagrams of H(jω), are two graphs:
-. A plot of 20 log10 |H(jω)| versus the frequency in log scale, that is, versus log10 ω
-. The phase angle 6 H(jω) versus log10 ω
-The standard representation of the logarithmic
-magnitude of H(jω) is
-log10 |H(jω)| dB
-===== Formulas =====
-{{ :computing:log-formulas.jpg?400 |}}