Why IIR Allpass Halfband Filters Work So Well for PCM-to-DSD
A practical look at phase, impulse response, computational cost, and why a theoretically imperfect filter can be the better engineering choice.
There is no shortage of technically impressive filters for sample-rate conversion. Long FIR filters can deliver extraordinary stop-band rejection and extremely precise frequency-domain behavior. Yet during the development of our PCM-to-DSD pipeline, we repeatedly returned to a much older and simpler idea: the polyphase IIR allpass halfband filter.
The Engineering Problem
PCM-to-DSD conversion is not simply a matter of increasing the sample rate. A practical real-time player must balance several requirements at once:
- sufficient suppression of unwanted spectral images;
- predictable time-domain behavior;
- low computational cost;
- stable performance at very high output rates;
- and sufficiently low startup latency for interactive playback.
The theoretically most impressive filter is therefore not automatically the best filter for the complete playback system.
Why Halfband Filters Matter
A halfband stage is particularly useful when the sampling rate is increased by a factor of two. Cascading several stages provides a natural route from ordinary PCM rates toward the much higher clock rates required by DSD conversion.
Polyphase allpass structures make these stages computationally inexpensive.
In a real player, computational efficiency is not separate from audio performance. It determines what can be calculated before playback begins and how much safety margin remains during playback.
Frequency Domain vs. Time Domain
Long linear-phase FIR filters can provide exceptionally clean frequency responses, but they also introduce symmetrical pre- and post-ringing around transients.
The IIR allpass approach behaves differently. Its phase response is nonlinear, but it avoids the characteristic pre-ringing of a linear-phase FIR.
Neither description by itself determines what sounds better. The useful question is whether the complete converter behaves predictably under the constraints of actual playback.
What We Found
Across several implementations, differences between competent SRC approaches were smaller than the differences suggested by their theoretical descriptions.
The allpass halfband cascade nevertheless remained attractive because it combined:
- low CPU cost;
- good stop-band performance;
- useful time-domain behavior;
- straightforward multi-stage scaling;
- and fast initialization.
Conclusion
For PCM-to-DSD conversion, filter design cannot be separated from system design.
The allpass halfband filter is interesting not because it wins every theoretical comparison, but because its compromises align unusually well with the requirements of a real-time high-rate DSD player.