How Do You Convert Narrowband Spectrum To Broad Bands?
In signal and acoustic analysis, FFT provides a narrowband spectrum with very high resolution.
However, in practical acoustics, we often need broad band such as
- 1-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?
Narrow band → 1/3 octave → 1 octave
Narrowband spectrum (refer to Samples/octave band.mmj)
1/3-octave band spectrum (refer to Samples/octave band.mmj)
1-octave band spectrum (refer to Samples/octave band.mmj)
Narrowband Spectrum
- High resolution (many bins)
- Each bin represents a small frequency range
Octave Band Spectrum
- Frequency bands
- Logarithmic spacing
- Energy summed within bands
Conversion = Grouping + Energy Summation → You must sum energy, not dB values
Why?
Because dB is logarithmic, not physical values
Therefore
- Convert dB → 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 filtering at each center frequency
- 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
#You may also be interested in these topics:
How Do You Convert Narrowband Spectrum To Broad Bands?
In signal and acoustic analysis, FFT provides a narrowband spectrum with very high resolution.
However, in practical acoustics, we often need broad band such as
because they are
This leads to a key question
How do we convert a narrowband (FFT) spectrum into octave bands?
Narrow band → 1/3 octave → 1 octave
Narrowband spectrum (refer to Samples/octave band.mmj)
1/3-octave band spectrum (refer to Samples/octave band.mmj)
1-octave band spectrum (refer to Samples/octave band.mmj)
Narrowband Spectrum
Octave Band Spectrum
Conversion = Grouping + Energy Summation → 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
#You may also be interested in these topics: