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diff --git a/kaldi_io/src/kaldi/matrix/matrix-functions-inl.h b/kaldi_io/src/kaldi/matrix/matrix-functions-inl.h
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+// matrix/matrix-functions-inl.h
+
+// Copyright 2009-2011 Microsoft Corporation
+//
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+//
+// (*) incorporates, with permission, FFT code from his book
+// "Signal Processing with Lapped Transforms", Artech, 1992.
+
+
+
+#ifndef KALDI_MATRIX_MATRIX_FUNCTIONS_INL_H_
+#define KALDI_MATRIX_MATRIX_FUNCTIONS_INL_H_
+
+namespace kaldi {
+
+//! ComplexMul implements, inline, the complex multiplication b *= a.
+template<typename Real> inline void ComplexMul(const Real &a_re, const Real &a_im,
+                                            Real *b_re, Real *b_im) {
+  Real tmp_re = (*b_re * a_re) - (*b_im * a_im);
+  *b_im = *b_re * a_im + *b_im * a_re;
+  *b_re = tmp_re;
+}
+
+template<typename Real> inline void ComplexAddProduct(const Real &a_re, const Real &a_im,
+                                                   const Real &b_re, const Real &b_im,
+                                                   Real *c_re, Real *c_im) {
+  *c_re += b_re*a_re - b_im*a_im;
+  *c_im += b_re*a_im + b_im*a_re;
+}
+
+
+template<typename Real> inline void ComplexImExp(Real x, Real *a_re, Real *a_im) {
+  *a_re = std::cos(x);
+  *a_im = std::sin(x);
+}
+
+
+} // end namespace kaldi
+
+
+#endif // KALDI_MATRIX_MATRIX_FUNCTIONS_INL_H_
+