[med-svn] [python-mne] 337/353: ENH : new stft_norm2 to compute stft norm taking into account negative freqs

[Yaroslav Halchenko]

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yoh pushed a commit to tag 0.4
in repository python-mne.

commit 0d0bf8cc34372872497a65cbee20fea3c89132cd
Author: Alexandre Gramfort <alexandre.gramfort at inria.fr>
Date:   Wed Aug 1 18:15:16 2012 +0200

    ENH : new stft_norm2 to compute stft norm taking into account negative freqs
---
 mne/time_frequency/stft.py            | 22 ++++++++++++++++++++++
 mne/time_frequency/tests/test_stft.py |  9 +++------
 2 files changed, 25 insertions(+), 6 deletions(-)

diff --git a/mne/time_frequency/stft.py b/mne/time_frequency/stft.py
index 4b9c949..917a0d2 100644
--- a/mne/time_frequency/stft.py
+++ b/mne/time_frequency/stft.py
@@ -201,3 +201,25 @@ def stftfreq(wsize, sfreq=None):
     if sfreq is not None:
         freqs *= float(sfreq)
     return freqs
+
+
+def stft_norm2(X):
+    """Compute L2 norm of STFT transform
+
+    It takes into account that stft only return positive frequencies.
+    As we use tight frame this quantity is conserved by the stft.
+
+    Parameters
+    ----------
+    X : 3D complex array
+        The STFT transforms
+
+    Returns
+    -------
+    norms2 : array
+        The squared L2 norm of every raw of X.
+    """
+    X2 = np.abs(X) ** 2
+    # compute all L2 coefs and remove freq zero once.
+    norms2 = (2. * X2.sum(axis=2).sum(axis=1) - np.sum(X2[:, 0, :], axis=1))
+    return norms2
diff --git a/mne/time_frequency/tests/test_stft.py b/mne/time_frequency/tests/test_stft.py
index 11d08f3..42b3c08 100644
--- a/mne/time_frequency/tests/test_stft.py
+++ b/mne/time_frequency/tests/test_stft.py
@@ -3,7 +3,7 @@ from scipy import linalg
 from numpy.testing import assert_almost_equal, assert_array_almost_equal
 from nose.tools import assert_true
 
-from ..stft import stft, istft, stftfreq
+from ..stft import stft, istft, stftfreq, stft_norm2
 
 
 def test_stft():
@@ -29,12 +29,9 @@ def test_stft():
 
         assert_array_almost_equal(x, xp, decimal=6)
 
-        # Symmetrize X to get also negative frequencies to guarantee
         # norm conservation thanks to tight frame property
-        X = np.concatenate([X[:, 1:, :][:, ::-1, :], X], axis=1)
-
-        assert_almost_equal(linalg.norm(X.ravel()), linalg.norm(x.ravel()),
-                            decimal=2)
+        assert_almost_equal(np.sqrt(stft_norm2(X)),
+                            map(linalg.norm, x), decimal=2)
 
         # Try with empty array
         x = np.zeros((0, T))

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