Add TUTHILL ref.

applications/lofar2/model/pfb_os/dsp_study_erko.txt

@@ -65,7 +65,9 @@
 # * [SELESNICK] Ivan Selesnick
 #   . https://eeweb.engineering.nyu.edu/iselesni/EL713/zoom/mrate.pdf
 # * [KIEL] Part 6: Multi-Rate Digital Signal Processing, Gerhard Schmidt
-#   https://dss-kiel.de/images/teaching/lectures/advanced_digital_signal_processing/slides/adsp_06_multirate_processing.pdf
+#   https://dss-kiel.de/images/teaching/lectures/advanced_digital_signal_processing/
+#   slides/adsp_06_multirate_processing.pdf
+# * [TUTHILL] Compensating for oversampling effects in polyphase channelizers, 2015
 #
 # https://ocw.mit.edu/courses/6-341-discrete-time-signal-processing-fall-2005/
 # Youtube: Guitars 4RL
@@ -350,8 +352,9 @@ c) s-plane and z-plane
   domain:
     y(n) = h(k) * x(n) ==> DFT ==> Y(z) = H(z) X(z)
 
-  For DFT this is circular convolution. With suffcient zero padding N >= len(the
-  circular convolution can calculate the linear convolution:
+  For DFT this is circular convolution. With suffcient zero padding N >= len(h)
+  + len(x) - 1 [LYONS 13.10], then the circular convolution can calculate the
+  linear convolution:
 
            N-1
     y[n] = sum h(k) x((n - k) % N)
@@ -1409,7 +1412,7 @@ c) s-plane and z-plane
     filters the DAC output.
 
 
-13) Single channel down converter [HARRIS 6]
+13a) Single channel down converter [HARRIS 6]
 - Analogue I-Q downconverter, yields baseband signal:
     xb[n] = exp(-j w_k n) x[n] = I[n] + j Q[n]
     . I[n] = cos(-w_k n) x[n]
@@ -1435,7 +1438,7 @@ c) s-plane and z-plane
 
       where:
 
-        h_npf[n] = h_lpf[n] exp(j w_k n)  # mix LPF up to BPF [HARRIS Fig. 6.6]
+        h_bpf[n] = h_lpf[n] exp(j w_k n)  # mix LPF up to BPF [HARRIS Fig. 6.6]
 
                    +inf
         H_BPF(z) = sum h_lpf[n] exp(j w_k n) z^-n
@@ -1502,7 +1505,7 @@ c) s-plane and z-plane
     . Shift in D samples and output sum of all branches after every D input
       samples.
     . A time shift of D samples causes a (bin) frequency dependent phase shift
-      of:
+      of [HARRIS Eq 6.10, Eq 9.2]:
 
         theta(w) = (D Ts) * (w_k / Ts)
                  = D * w_k,  with w_k = 2pi k / M
@@ -1518,11 +1521,21 @@ c) s-plane and z-plane
 
     . This can also be interpreted as to calculate bin k for downsampled output
       samples m = 0, 1, ..., calculate the output y for bin k + (mD) % M.
-      Instead of first caluclating the output y for bin k and then multiplying
-      y by exp(-j 2pi k D / M m).
+      Instead of first calculating the output y for bin k and then multiplying
+      y by exp(-j 2pi k D / M m). Hence for a PFB with all bins this implies
+      applying a circular shift of the DFT input by D for every m, to start at
+      index R(m) = (mD) % M [TUTHILL].
 
         exp(j w_k) exp(j w_k D m) = exp(j w_k(1 + mD))
 
+      A wideband PFB with wideband factor wb, that can process fs = wb * fclk
+      using wb parallel lanes. The parallel lanes should have independent
+      circular shift. Therefore R(m) / wb should be an integer then [TUTHILL].
+
+
+13b) Single channel up converter [HARRIS 7]
+
+
 
 
 
@@ -1541,7 +1554,7 @@ c) s-plane and z-plane
     converters in parallel, that share the same downsampling polyphase FIR
     structure, with the coefficients of the H_LPF prototype filter, and use the
     IDFT to calculate all M bins. The PFB output has a commutator that starts
-    at bin 0, so bin k = M-1 is the the newest and output last.
+    at bin 0, so bin k = M-1 is the newest and output last.