Mark Borgerding, Founder & Principal Engineer, 3dB Labs
Resampling is the process of adjusting a signal from one sampling rate to another while preserving its spectral content and avoiding aliasing. It requires compromise between accuracy vs. computational cost… unless you find a better way …
At 3dB Labs, we use a novel technique that delivers both high accuracy and high throughput without the usual trade-offs.
Resampling Limitations: DSP theory (Nyquist, Whittaker, and Shannon) shows that perfect interpolation is theoretically possible with FIR filters having infinite length. Engineers must often settle for methods that can be realized in the inconvenient space and time demands of our universe.
Cheap and Awful: The simplest, fastest, and worst method is nearest-neighbor sampling (zero-order hold). Only slightly better is linear interpolation. These work best when the input is massively oversampled, but generally the distortion is unacceptable.
Better, but limited: A bit closer to ideal resampling are polyphase filtering or fast convolution.
- Fast Convolution
FFTs handle long FIR filters more efficiently (cost is logarithmic in FIR length). Different sized forward and inverse FFTs change rate by their ratio. Fast and clean but cannot provide arbitrary rate changes. - Polyphase Filtering
A prototype low-pass filter at slightly different time offsets (read:phases) is a reasonable stand-in for the ideal sinc function. Efficient for low quality filtering but the cost rises sharply as the filter effectiveness improves (narrow transition bandwidth and suppressed aliasing).
Each of these has its strengths, but neither alone provides both excellent signal quality and computational efficiency.
3dB’s Two-Stage “Secret Sauce”
Our resampler combines the two techniques to get their combined strengths without their weaknesses
- Fast Convolution Stage
- Upsample the signal by 2× (with optional anti-alias filtering).
- Create a wide frequency band near the folding frequency with negligible energy
- Polyphase Stage
- Based on a cheap FIR filter (~12 coefficients) with a very wide transition frequency band that coincides with the band of negligible energy
- Interpolates between thousands of phases for near-continuous precision.
Our hybrid approach achieves:
- 97% bandwidth retention of input or output rates, whichever is lower
- Extremely low distortion (aliasing below –85 dB).
- Super-fast — up to hundreds of megasamples per second on one core of a commodity CPU.
Combining the strengths of fast convolution and polyphase filtering makes 3dB resampling flexible, fast, and accurate.
Want to Learn More?
If you’d like to brush up on the fundamentals behind our method, these resources are excellent starting points:
- Understanding DSP by Rick Lyons – a practical introduction to digital signal processing.
- Multirate Signal Processing for Communication Systems by fred harris – dives deep into multirate techniques.
- Contact 3dB Labs
About the Author:
Mark Borgerding is a signal processing engineer and co-founder of 3dB Labs. His love of programming and passion for efficiency helped found 3dB Labs more than twenty years ago and made it a magnet for exceptional engineers. Mark has published in IEEE Transactions on Signal Processing, IEEE Signal Processing Magazine, presented at conferences, and authored a chapter in the book Streamlining Digital Signal Processing, assembled by the legendary Richard Lyons.
