Why Do We Use Log Scale in Frequency Plots?
When analyzing frequency spectra (like FFT), we often use a logarithmic scale instead of a linear one.
But why?
What Is Log Scale?
A log scale represents values using orders of magnitude instead of equal steps.
Example
Linear scale
Log scale
- 100 = 1, 101 = 10, 102 = 100, 103 = 1000
Intuition
“Log scale compresses large differences”
Problem with Linear Scales
In real signals
- Some frequencies are very strong
- Other frequencies are very weak
On a linear scale
- Strong spectral peaks dominate
- Weak signals disappear
Why Log Scale Is Useful
Log scale solves this problem. It allows both strong and weak components to be visible
Key Benefits
1. Wide Dynamic Range
- Displays large and small values together
2. Better Visualization
- Reveals hidden frequency components
3. Easier Comparison
- Relative differences are clearer
Log Scale in Magnitude (dB)
Decibels (dB)
The decibel (dB) is a logarithmic measure of a ratio between two quantities. The formula depends on whether the quantity is power or magnitude.
Power-Based Definition
Magnitude-Based Definition
Meaning
- Converts power or magnitude to logarithmic scale
- Makes differences easier to interpret
Log Scale in Frequency domain Axis
Sometimes frequency domain axis is also logarithmic:
Used when
- Wide frequency range
- Octave band analysis uses frequency bands that are equally spaced on a logarithmic scale.
Example
- Audio: 20 Hz ~ 20 kHz
A-weighting 1/3-octave band analysis of white noise (from 25 to 10kHz center frequencies), Fs = 30kHz
Real-World Applications
- Audio analysis (human hearing is logarithmic)
- Vibration analysis
- RF / communication systems
MALMIJAL Workflow
Using Log Scale
- Generate/Load a signal
- Apply FFT / PSD
- Switch magnitude to dB scale
- Check magnitude
Generate signal
Apply FFT
Switch magnitude to dB scale
Check magnitude in dB
MALMIJAL Features
- FFT / Power Spectrum
- PSD (Power Spectral Density)
- FRF (Frequency Response Function)
- Octave Band Analysis
Key Takeaways
- Log scale handles large dynamic ranges
- Makes weak signals visible
- dB scale is standard in signal analysis
- Essential for real-world data
Conclusions
Log scale is an essential tool in frequency analysis for effectively representing signals with a wide dynamic range.
- In a linear scale, strong components can overshadow weaker ones, but a log scale allows both strong and weak signals to be observed simultaneously.
- Using dB (decibel) representation makes it easier to compare signal magnitudes intuitively and interpret differences clearly.
- Additionally, for wide frequency ranges, a logarithmic axis helps better visualize frequency characteristics.
In summary,
log scale is a fundamental representation in real-world signal analysis, enabling effective comparison and revealing hidden details across a wide range of signal magnitudes.
Suggested Further Reading
##You may also find these topics helpful:
Why Do We Use Log Scale in Frequency Plots?
When analyzing frequency spectra (like FFT), we often use a logarithmic scale instead of a linear one.
But why?
What Is Log Scale?
A log scale represents values using orders of magnitude instead of equal steps.
Example
Linear scale
Log scale
Intuition
“Log scale compresses large differences”
Problem with Linear Scales
In real signals
On a linear scale
Why Log Scale Is Useful
Log scale solves this problem. It allows both strong and weak components to be visible
Key Benefits
1. Wide Dynamic Range
2. Better Visualization
3. Easier Comparison
Log Scale in Magnitude (dB)
Decibels (dB)
The decibel (dB) is a logarithmic measure of a ratio between two quantities. The formula depends on whether the quantity is power or magnitude.
Power-Based Definition
Magnitude-Based Definition
Log Scale in Frequency domain Axis
Sometimes frequency domain axis is also logarithmic:
Used when
Example
A-weighting 1/3-octave band analysis of white noise (from 25 to 10kHz center frequencies), Fs = 30kHz
Real-World Applications
MALMIJAL Workflow
Using Log Scale
Generate signal
Apply FFT
Switch magnitude to dB scale
Check magnitude in dB
MALMIJAL Features
Key Takeaways
Conclusions
Log scale is an essential tool in frequency analysis for effectively representing signals with a wide dynamic range.
In summary,
log scale is a fundamental representation in real-world signal analysis, enabling effective comparison and revealing hidden details across a wide range of signal magnitudes.
Suggested Further Reading
##You may also find these topics helpful: