From 46a62ee4b236ae1c322dc9194a5f2c77964ac746 Mon Sep 17 00:00:00 2001
From: Eric Kooistra <kooistra@astron.nl>
Date: Tue, 9 Jul 2024 16:15:58 +0200
Subject: [PATCH] Improve multirate section.
---
applications/lofar2/model/pfb_os/dsp_study_erko.txt | 12 ++++++------
1 file changed, 6 insertions(+), 6 deletions(-)
diff --git a/applications/lofar2/model/pfb_os/dsp_study_erko.txt b/applications/lofar2/model/pfb_os/dsp_study_erko.txt
index e949822ecd..d6141fb1fb 100644
--- a/applications/lofar2/model/pfb_os/dsp_study_erko.txt
+++ b/applications/lofar2/model/pfb_os/dsp_study_erko.txt
@@ -1029,8 +1029,8 @@ c) s-plane and z-plane
. Up sampling : x[n] --> up Q --> H(z^Q) --> y[m], is equivalent to:
H(z) --> up Q
- . Down sampling : x[n] --> H(z^Q) --> down --> y[m], is equivalent to:
- x[n] --> down Q --> H(z) --> y[m]
+ . Down sampling : x[n] --> H(z^Q) --> down Q --> y[m], is equivalent to:
+ x[n] --> down Q --> H(z) --> y[m]
. H_i(z^Q) is upsampled-by-Q version of H(z), so with Q-1 zero coefficients
in the H(z) power series, starting at phase i.
@@ -1100,8 +1100,8 @@ c) s-plane and z-plane
the original spectrum must be less than pi / D. This is the non-aliasing
condition for the downsampling operator.
- . Discarding samples folds the spectrum around multiples of pi / D =
- fxNyquist / D. First the LPF has to remove all folds.
+ . Discarding samples copies the spectrum around multiples of 2pi / D. First
+ the LPF has to remove all copies.
. Do not calculate samples that will be thrown away.
- Upsampling + LPF = interpolation:
@@ -1118,9 +1118,9 @@ c) s-plane and z-plane
X_U(e^jw) = X(exp(jw U))
- . Inserting zeros replicates the spectrum around multiples of pi / U. Then
+ . Inserting zeros replicates the spectrum around multiples of 2pi / U. Then
the LPF has to remove all replicas and by that it interpolates to fill in
- the zeros.
+ the zeros. To remove the replicas, the LPF pass band is pi / L.
. Do not calculate samples that will be inserted as zeros.
. Using zero order hold would be a naive approach, because then all samples
need to be calculated and the LPF then needs to compensate for the non-flat
--
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