The main purpose of upsampling before digital to analog conversion is to move quantization noise far beyond the audible spectrum to be able to filter it out by simple second-order low pass analog filter. So dithering may be an overkill in this case.


dithering and noise shaping are techniques that are applicable to any operation that has quantization (a.k.a. "rounding")happening to the data. you dither and noiseshape in conjunction with rounding after an arithmetic operation.

dithering has the expense of generating a random number (or two) and massaging it to get the properties of dither that you want. noise shaping has the expense of a filter in the feedback path (the filter might be very simple, maybe even just a delay of one sample).

upsampling is done a few different ways, perhaps with polyphase filtering using a different set of FIR coefficients for each fractional delay (you would have 8 fractional delays if you are upsampling by 8x). this FIR multiply-accumulate operation is the same as a dot product. when the accumulation is done, you will likely need to quantize the word to be a shorter word going out. you might want to dither and noiseshape the word getting quantized. might not be necessary.

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  • $\begingroup$ You are talking about implementation. Now I'm trying to implement upsampling in FPGA using single long FIR filter instead of a series of half-band filters. And it seems to work. Obviously this operation require quantization. I just ask do I really need some additional steps like dithering on such high frequencies. Especially if I plan to use analog post-filtering. Quantization noise consists of harmonics of sampling frequency, isn't it? $\endgroup$ – e_asphyx Dec 23 '16 at 2:40
  • $\begingroup$ no. images resulting from uniform sampling is not the same as quantization error. two different things. the uniform sampling is like quantizing along the $t$-axis and the quantization that is related to dithering and noise shaping is quantizing along the vertical axis. $\endgroup$ – robert bristow-johnson Dec 23 '16 at 5:12
  • $\begingroup$ The nature of imaging effect is quite clear for me. The spectrum becomes infinitely mirrored when we replace time-continuous signal with a series of modulated δ impulses (in theory). Spectrum becomes aliased if these images are overlapped (not our case). I'm talking about quantization noise only and its relation to sampling frequency. Does resampling affect quantization noise spectrum too? $\endgroup$ – e_asphyx Dec 23 '16 at 11:40
  • $\begingroup$ is what you want, the transfer function of the quantization error input to the output? that is the only relationship that $f_\text{s}$ has to quantization and noise shaping. $\endgroup$ – robert bristow-johnson Dec 23 '16 at 17:45

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