DSP TOOLBOX · CONSOLIDATION

FIR vs IIR
Phase, Ringing & Trade-offs

We already know how FIR and IIR filters are built. Now the useful question is not “which is better?” but “where do we want to pay the cost?”

FIR: delayed INPUT samples × coefficients → ADD IIR: input path + previous OUTPUT fed back → recursive memory

Same toolbox, different architecture. Effects below are deliberately exaggerated so we can see and hear them.

1. Why IIR feels closer to analogue

IIR · recursive

y[n] = b₀x[n] + b₁x[n−1] + … − a₁y[n−1] − a₂y[n−2]

The system has state: previous outputs participate in the next calculation. This makes IIR a natural digital counterpart to many analogue filter behaviours, where components and feedback networks store energy.

FIR · stored samples

y[n] = Σ h[k]x[n−k]

Store discrete input samples, multiply by coefficients, then add. With suitable coefficient symmetry, FIR can provide linear phase — particularly useful in digital systems.

Not a hard divide: analogue ≠ IIR and digital ≠ FIR. Both are digital structures. Recursive IIR designs simply map naturally from many classic analogue filter families.

2. Watch a transient go through the filter

Switch between the original, an exaggerated minimum-phase/IIR-style response and a symmetric linear-phase FIR response.

ORIGINAL

3. How can a filter ring before the sound?

Minimum phase

The main transient can occur immediately, followed by the response. The trade-off is frequency-dependent phase rotation.

Linear phase

A symmetric FIR response has energy on both sides of its centre. The entire signal is delayed, allowing the response to extend before and after the delayed transient.

It is NOT predicting the future. input arrives → FIR delays signal → symmetric response surrounds the delayed transient

4. More FIR taps buy precision — and cost time

FIR TAP COUNT

REFERENCE SAMPLE RATE

FILTER LENGTHstored coefficients

GROUP DELAY(N−1)/2

LATENCY

Longer kernels can realise finer transitions, but symmetric linear-phase FIRs also incur greater group delay.

5. Hear the trade-off

Short synthetic transient; ringing is intentionally exaggerated. Output starts low.

AUDITION OUTPUT−18 dB

READY

6. The cost moves — it does not disappear

	IIR / minimum-phase	Linear-phase FIR
Latency	Usually very low	Can be substantial
Efficiency	Very efficient	May require many taps
Phase	Frequency-dependent rotation	Relative phase can be preserved
Ringing	Primarily after impulse	Can occur before + after delayed impulse
Feedback	Recursive	Not required
Analogue-style design	Natural fit	Less directly analogous
Convolution	—	Potentially enormous FIR

Neither is inherently “higher quality”. Choose the compromise that suits the job. And FIR does not automatically mean linear phase: minimum-phase FIRs exist too.

7. Which would you reach for?

Live vocal monitoring

Latency matters enormously.

Phase-sensitive crossover / parallel processing

Relative phase may matter.

Convolution reverb

You want the measured h[n] of a whole system.

NEXT PRIMITIVE

MEASURE → COMPARE

So far we have mainly changed audio. Next we extract information from audio.

audio → MEASURE → peak / RMS / envelope ↓ COMPARE ↓ threshold ↓ control signal

That opens the door to meters, gates, compressors, transient detectors, envelope followers and automatic gain control.

FIR vs IIRPhase, Ringing & Trade-offs