Add type 3 polyphase, see FLIEGE.

applications/lofar2/model/pfb_os/dsp_study_erko.txt

@@ -69,6 +69,7 @@
 #   slides/adsp_06_multirate_processing.pdf
 # * [TUTHILL] Compensating for oversampling effects in polyphase channelizers, 2015
 # * [BUNTON] Multi-resolution FX Correlator, ALMA memo 447, 2003
+# * [FLIEGE] Multirate DSP
 #
 # https://ocw.mit.edu/courses/6-341-discrete-time-signal-processing-fall-2005/
 # Youtube: Guitars 4RL
@@ -1357,7 +1358,7 @@ c) s-plane and z-plane
        where Hq(z^Q) is the z-transform of hq[n]:
 
            hq[n] = h(nQ + q),  +q for counter clockwise with delays z^(-1)
-                               [VAIDYANATHAN Eq 4.3.8]
+                               [VAIDYANATHAN Eq 4.3.8, CROCHIERE Eq 3.29]
 
                   +inf
            Hq(z) = sum hq[n] z^(-n),  0 <= q <= Q - 1
@@ -1401,11 +1402,20 @@ c) s-plane and z-plane
        where:
            p = Q - 1 - q
 
-           rp[n] = h(nQ - p),  -p for clockwise with advances z^(+1)
-
            Rp(z) = H{Q-1-p}(z),   so flipud Hq phases, but keep coefficient order
                                   per phase
 
+  . Type III polyphase [FLIEGE 1.1.2, CROCHIERE 3.3.3]
+    - p = Q - q = -q  (With Q % Q = 0)
+    - rp[n] = h(nQ - p)  [CROCHIERE Eq. 3.35],  -p for clockwise with advances
+      z^(+1)
+    - CROCHIERE does not mention type II and VAIDYANATHAN does not mention type
+      III. FLIEGE mentions all three types. The advantage of type I and III is
+      that they both begin with x[n=0] at branch p = q = 0 with H0, so they
+      yield same result except for a delay. The purpose of type III is then
+      that it yields a fold of the branches, so that DFT can be used instead of
+      IDFT, because DFT(x) = IDFT(fold(x)). The purpose of type II is ?.
+
   . Type I polyphase does not imply Direct Form FIR and type II polyphase is
     not the same as Transposed Direct Form FIR [CROCHIERE 3.3.3]:
     * Type I uses delay line z^(-1) and +q in hq[n] = h(nQ + q) and yields