PCM to DSD Conversion
This core converts multi-bit PCB into 1-bit Sigma-Delta bit-stream, commercially called DSD. For the reasons mentioned in the article for the opposite type of conversion, DSD is quite popular for direct digital to analogue conversion. All that is needed is a suitable low-pass filter to convert the bit-stream into an analogue audio signal. This type of filter is always a trade-off between time and frequency domain properties. A trade-off between transient response distortion versus sufficient attenuation of high-frequency quantization noise and non-linear components, but that is a different story.
A DSD stream is usually produced in two steps. The first one is up-sampling of the PCM signal to a sufficiently high sampling rate. The second stage is a noise-shaper with a 1-bit quantizer, which actually converts multi-bit PCM into 1-bit stream. Noise shapers are complicated feedback structures which, depending on some other constraints, can do a lot of unwanted things. Apart from nicely shaped quantization noise they can also produce a range of non-harmonically related components called idle tones or limit cycles or become completely unstable. 1-bit noise-shapers are usually only conditionally stable and there has to be a whole infrastructure of stability assurance measures and optimizations. Also dithering of 1-bit noise-shapers is sub-optimal while maintaining reasonable modulation indexes. All and all, it is not entirely trivial to get a decently performing noise-shaper working in a real application and we spent a lot of time optimizing various architectures.
3rd to 7th order SDM modulator
64x to 256x oversampling ratio
TPDF dithered quantizer
Optional output shift register for analogue FIR filter
Our preferred modulator architecture is a 5th order noise-shaper with no local feedbacks running at 128x or 256x ratio, giving the best balance between noise frequency distribution and computational resources needed. Our optimizations and over-modulation protection allows for momentary modulation index exceeding 0.9 without losing stability. This is quite useful for handling inter-sample peaks and overshoots often found in modern recordings. A shift register at the output is just a little bonus when the final low-pass filtering is done using an analogue FIR filter.