IIR Filters vs FFT for Octave Band Analysis
Two common paths to octave and third-octave bands are recursive filter banks and FFT bin summation. Both can be accurate, but their trade-offs are different.
The IIR filter-bank approach
IIR bandpass filters are designed per band and run directly on the time-domain signal. This matches analog standards and gives continuous output with minimal latency, which is ideal for streaming or meter-like displays.
- Pros: low CPU, low latency, good match to IEC/ANSI analog prototypes.
- Cons: phase is non-linear, careful coefficient design is required, sensitive to coefficient precision.
A 4th-order or 6th-order Butterworth bandpass per band is common. Use SOS form to keep stability and numeric accuracy.
The FFT/STFT approach
FFT analysis slices the signal into windows, computes a spectrum, and then sums the power of bins inside each octave band. With proper windowing and overlap, FFT-based bands can be accurate and easy to parallelize.
- Pros: linear-phase processing (per frame), easy to extend to wideband metrics, flexible re-binning.
- Cons: higher latency, windowing artifacts, careful bin-edge interpolation needed for precision.
If you compute a 1/3-octave spectrum from FFT bins, account for partial-bin contributions and window energy normalization.
Side-by-side trade-offs
| Criteria | IIR filter bank | FFT bin summation |
|---|---|---|
| Latency | Very low, streaming-ready | At least one window length |
| CPU per sample | Constant, scales with bands | Batch cost, scales with FFT size |
| Standard compliance | Easy to match analog prototypes | Requires careful window correction |
| Phase response | Non-linear phase | Linear phase per frame |
| Resolutions | Fixed band edges | Flexible re-binning |
When to choose each method
- Choose IIR filters for real-time monitoring, embedded systems, or when you need strict IEC alignment.
- Choose FFT if you already compute spectra, need wideband metrics, or want to post-process the same FFT into multiple views.
- Hybrid pipelines are common: use FFT for analysis and IIR for real-time display or alerting.
Implementation notes
For FFT bands, use a consistent window (Hann is common), overlap enough to stabilize levels, and correct for window energy. For IIR banks, verify each band edge and confirm the aggregate band energy matches broadband RMS within tolerance.