Introduction
In signal and acoustic analysis, FFT provides a narrowband spectrum with very high resolution.
However, in practical acoustics, we often need:
- Octave band
- 1/3-octave band
because they are:
- Easier to interpret
- Required by standards
This leads to a key question:
How do we convert a narrowband (FFT) spectrum into octave bands?
Conversion (Narrow โ 1/3ย โ 1 octave)
Narrowband spectrum (refer to Samples/octave band.mmj)
1/3-octave band spectrumย (refer to Samples/octave band.mmj)
1-octave band ย spectrumย (refer to Samples/octave band.mmj)
Narrowband Spectrum
- High resolution (many bins)
- Each bin represents a small frequency range
Octave Band Spectrum
- Grouped frequencies
- Logarithmic spacing
- Energy summed within bands
Conversion = Grouping + Energy Summation โ You must sum energy, not dB values
Why?
Because dB is logarithmic, not physical values:
Therefore:
- Convert dB โ linear
- Sum energies
- Convert back to dB
Conversion Method (FFT-based)
Step 1: Define Band Limits
Each octave (or 1/3-octave) band has:
- Center frequency fc
- Lower bound fl
- Upper bound fu
For 1/3-octave:
Step 2: Select FFT Bins
For each band, find all FFT bins where:
Step 3: Convert to Linear Scale (Physical values)
If FFT is in dB:
Step 4: Sum Energy (Physical values)
Step 5: Convert Back to dB
Conversion Method (Filter-based)
MALMIJAL adopts this method
Instead of FFT grouping:
- Apply band-pass filters
- Measure energy per band
| Conversion Method | Feature |
|---|
| FFT-based | Fast, Flexible |
| Filter-based | Physically accuate (standards) |
Conclusion
Converting narrowband spectra to octave bands is essential for bridging:
- Detailed signal analysis
- Practical acoustic interpretation
Suggested Further Reading
Introduction
In signal and acoustic analysis, FFT provides a narrowband spectrum with very high resolution.
However, in practical acoustics, we often need:
because they are:
This leads to a key question:
How do we convert a narrowband (FFT) spectrum into octave bands?
Conversion (Narrow โ 1/3ย โ 1 octave)
Narrowband spectrum (refer to Samples/octave band.mmj)
1/3-octave band spectrumย (refer to Samples/octave band.mmj)
1-octave band ย spectrumย (refer to Samples/octave band.mmj)
Narrowband Spectrum
Octave Band Spectrum
Conversion = Grouping + Energy Summation โ You must sum energy, not dB values
Why?
Because dB is logarithmic, not physical values:
Therefore:
Conversion Method (FFT-based)
Step 1: Define Band Limits
Each octave (or 1/3-octave) band has:
For 1/3-octave:
Step 2: Select FFT Bins
For each band, find all FFT bins where:
Step 3: Convert to Linear Scale (Physical values)
If FFT is in dB:
Step 4: Sum Energy (Physical values)
Step 5: Convert Back to dB
Conversion Method (Filter-based)
MALMIJAL adopts this method
Instead of FFT grouping:
Conclusion
Converting narrowband spectra to octave bands is essential for bridging:
Suggested Further Reading