Explain oversampling and noise shaping for ADC and DAC

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]