diff --git a/applications/lofar2/model/pfb_os/dsp_study_erko.txt b/applications/lofar2/model/pfb_os/dsp_study_erko.txt index 16f6a0ba4eb874270a3c67f577feaecf3cd5194c..0454633f9c8ec1132f48cf0604c2f7bf922ffdfe 100644 --- a/applications/lofar2/model/pfb_os/dsp_study_erko.txt +++ b/applications/lofar2/model/pfb_os/dsp_study_erko.txt @@ -41,6 +41,12 @@ # . https://webaudio.github.io/Audio-EQ-Cookbook/Audio-EQ-Cookbook.txt # . Configure the Coefficients for Digital Biquad Filters in TLV320AIC3xxx Family (pdf) # * [WOLFSOUND] https://thewolfsound.com/ +# * [NOISESHAPING] +# . "Digital Signal Processing Oversampled Analog to Digital Conversion with +# Noise Shaping", D. Richard Brown III +# . "Realisering van Digitale Signaalbewerkende Systemen, Toepassingen", +# 5N290, TUE, P.C.M. Sommen, slide 19, 20, +# 1) Linear Time Invariant (LTI) system [LYONS 1.6] @@ -910,6 +916,42 @@ Fractional time delay [CROCHIERE 6.3] - Up sampling M --> LPF --> z^(-L) --> down sampling M yields semi allpass filter and delay of L / M samples +Oversampling ADC and DAC +- Every oversampling factor of 4 yields 1 extra bit, because then 1 / 4 of the + quantisation power remains in the low pass band, and factor 4 in power is + factor 2 in voltage level. +- The higher sampling rate relaxes the analogue LPF by using the extra BW of + 3 / 4 fs / 2 as transition band. A digital LPF then filters the wanted 1 / 4 + fs / 2 low pass band and thus also removes the quantisation noise in the + stop band, which yields the extra bit. + +Noise shaping +- Noise shaping is based on quantisation error feedback. At low frequencies + the feedback error is still related to the input, so the feedback will + compensate the error for lower frequencies, but worsen it for higher + frequencies. An LPF filters the higher frequencies and thus increases the + effective number of bits of the low pass output, by about 1 bit for first + order feedback. +- ADC: [NOISESHAPING Brown] + For an ADC noise shaping requires feedback in the analogue domain, because + after quantization the error information is only available when comparing + the digitized input with the analogue input. Noise shaping of digital input + is not possible (e.g. 8b input using LSBit feedback from 24b LPF output), + because the digital input has fixed resolution and therefore the feedback + error can not contain more accurate information about the (analogue) input. + Therefore LPF in the digital domain are never combined with noise shaping. + The analogue feedback of the quantized value uses a DAC and tracks the + analogue input signal. With a 1 bit DAC it becomes a sigma-delta ADC. The + feedback signal jumps between too high or too low, which thus contains the + more detailed accuracy on the analogue input signal level that leads to the + extra bits for oversampling. +- DAC: [NOISESHAPING TUE] + For a DAC noise shaping uses feedback in the digital domain. The round + off LSbits of the LPF output are fed back to the input, so that the noise + power is shaped towards higher frequencies. This noise power at higher + frequences will be filtered by the analoge LPF that filters the DAC + output. + Appendix A) Signal operators [JOS1 7.2]