From 542d084b80a4bcd8e34dd30a440fc2598b4fa33f Mon Sep 17 00:00:00 2001
From: OverLordGoldDragon
 <16495490+OverLordGoldDragon@users.noreply.github.com>
Date: Wed, 14 Oct 2020 08:54:34 +0400
Subject: [PATCH] Improve `center_frequency` accuracy, fix edge case

In summary, below are addressed:

 1. Failure to estimate center frequency within two significant figures
 2. Using _negative_ frequency index if wavelet's peak frequency is positive max for even `len(psi)`

Two sig figs should be bare minimum in precise frequency applications. Case (2) should be rare, but more importantly, it fails to make sense, unless I'm missing something.
---
 pywt/_functions.py | 12 ++++++++----
 1 file changed, 8 insertions(+), 4 deletions(-)

diff --git a/pywt/_functions.py b/pywt/_functions.py
index 86033967a..58c34dfe1 100644
--- a/pywt/_functions.py
+++ b/pywt/_functions.py
@@ -153,11 +153,15 @@ def central_frequency(wavelet, precision=8):
     domain = float(x[-1] - x[0])
     assert domain > 0
 
-    index = np.argmax(abs(fft(psi)[1:])) + 2
-    if index > len(psi) / 2:
-        index = len(psi) - index + 2
+    # improve center frequency estimation by sampling DTFT(psi) more granularly
+    pad_factor = 3
+    psi_pad = np.pad(psi, [0, pad_factor * len(psi)])
 
-    return 1.0 / (domain / (index - 1))
+    index = np.argmax(abs(fft(psi_pad))[1:]) + 1  # omit dc, +1 to compensate
+    if index > len(psi_pad) / 2:  # if negative freq, use index of positive
+        index = len(psi_pad) - index
+
+    return 1.0 / ((pad_factor + 1) * domain / index)
 
 
 def scale2frequency(wavelet, scale, precision=8):