diff --git a/.github/scripts/python.sh b/.github/scripts/python.sh
index 22098ec08..3f5701281 100644
--- a/.github/scripts/python.sh
+++ b/.github/scripts/python.sh
@@ -85,4 +85,4 @@ make -j2 install
 cd $GITHUB_WORKSPACE/build/python
 $PYTHON setup.py install --user --prefix=
 cd $GITHUB_WORKSPACE/python/gtsam/tests
-$PYTHON -m unittest discover
+$PYTHON -m unittest discover -v
diff --git a/gtsam/basis/Fourier.h b/gtsam/basis/Fourier.h
index 6943150d7..d264e182d 100644
--- a/gtsam/basis/Fourier.h
+++ b/gtsam/basis/Fourier.h
@@ -40,9 +40,13 @@ class GTSAM_EXPORT FourierBasis : public Basis<FourierBasis> {
   static Weights CalculateWeights(size_t N, double x) {
     Weights b(N);
     b[0] = 1;
-    for (size_t i = 1, n = 1; i < N; i += 2, n++) {
-      b[i] = cos(n * x);
-      b[i + 1] = sin(n * x);
+    for (size_t i = 1, n = 1; i < N; i++) {
+      if (i % 2 == 1) {
+        b[i] = cos(n * x);
+      } else {
+        b[i] = sin(n * x);
+        n++;
+      }
     }
     return b;
   }
diff --git a/python/CMakeLists.txt b/python/CMakeLists.txt
index a5fdc80a6..4254a21c6 100644
--- a/python/CMakeLists.txt
+++ b/python/CMakeLists.txt
@@ -166,5 +166,6 @@ add_custom_target(
         COMMAND
           ${CMAKE_COMMAND} -E env # add package to python path so no need to install
           "PYTHONPATH=${GTSAM_PYTHON_BUILD_DIRECTORY}/$ENV{PYTHONPATH}"
-          ${PYTHON_EXECUTABLE} -m unittest discover -s "${GTSAM_PYTHON_BUILD_DIRECTORY}/gtsam/tests"
-          DEPENDS ${GTSAM_PYTHON_DEPENDENCIES})
+          ${PYTHON_EXECUTABLE} -m unittest discover -v -s .
+          DEPENDS ${GTSAM_PYTHON_DEPENDENCIES}
+          WORKING_DIRECTORY "${GTSAM_PYTHON_BUILD_DIRECTORY}/gtsam/tests")
diff --git a/python/gtsam/preamble/basis.h b/python/gtsam/preamble/basis.h
index d07a75f6f..56a07cfdd 100644
--- a/python/gtsam/preamble/basis.h
+++ b/python/gtsam/preamble/basis.h
@@ -10,3 +10,5 @@
  * Without this they will be automatically converted to a Python object, and all
  * mutations on Python side will not be reflected on C++.
  */
+
+#include <pybind11/stl.h>
diff --git a/python/gtsam/tests/test_basis.py b/python/gtsam/tests/test_basis.py
new file mode 100644
index 000000000..5d3c5ace3
--- /dev/null
+++ b/python/gtsam/tests/test_basis.py
@@ -0,0 +1,96 @@
+"""
+GTSAM Copyright 2010-2019, Georgia Tech Research Corporation,
+Atlanta, Georgia 30332-0415
+All Rights Reserved
+
+See LICENSE for the license information
+
+Basis unit tests.
+Author: Frank Dellaert & Gerry Chen (Python)
+"""
+import unittest
+
+import numpy as np
+
+import gtsam
+from gtsam.utils.test_case import GtsamTestCase
+from gtsam.symbol_shorthand import B
+
+
+class TestBasis(GtsamTestCase):
+    """
+    Tests FitBasis python binding for FourierBasis, Chebyshev1Basis, Chebyshev2Basis, and Chebyshev2.
+    
+    It tests FitBasis by fitting to a ground-truth function that can be represented exactly in
+    the basis, then checking that the regression (fit result) matches the function.  For the
+    Chebyshev bases, the line y=x is used to generate the data while for Fourier, 0.7*cos(x) is
+    used.
+    """
+    def setUp(self):
+        self.N = 2
+        self.x = [0., 0.5, 0.75]
+        self.interpx = np.linspace(0., 1., 10)
+        self.noise = gtsam.noiseModel.Unit.Create(1)
+
+    def evaluate(self, basis, fitparams, x):
+        """
+        Until wrapper for Basis functors are ready,
+        this is how to evaluate a basis function.
+        """
+        return basis.WeightMatrix(self.N, x) @ fitparams
+
+    def fit_basis_helper(self, fitter, basis, f=lambda x: x):
+        """Helper method to fit data to a specified fitter using a specified basis."""
+        data = {x: f(x) for x in self.x}
+        fit = fitter(data, self.noise, self.N)
+        coeff = fit.parameters()
+        interpy = self.evaluate(basis, coeff, self.interpx)
+        return interpy
+
+    def test_fit_basis_fourier(self):
+        """Fit a Fourier basis."""
+
+        f = lambda x: 0.7 * np.cos(x)
+        interpy = self.fit_basis_helper(gtsam.FitBasisFourierBasis,
+                                        gtsam.FourierBasis, f)
+        # test a basis by checking that the fit result matches the function at x-values interpx.
+        np.testing.assert_almost_equal(interpy,
+                                       np.array([f(x) for x in self.interpx]),
+                                       decimal=7)
+
+    def test_fit_basis_chebyshev1basis(self):
+        """Fit a Chebyshev1 basis."""
+
+        f = lambda x: x
+        interpy = self.fit_basis_helper(gtsam.FitBasisChebyshev1Basis,
+                                        gtsam.Chebyshev1Basis, f)
+        # test a basis by checking that the fit result matches the function at x-values interpx.
+        np.testing.assert_almost_equal(interpy,
+                                       np.array([f(x) for x in self.interpx]),
+                                       decimal=7)
+
+    def test_fit_basis_chebyshev2basis(self):
+        """Fit a Chebyshev2 basis."""
+
+        f = lambda x: x
+        interpy = self.fit_basis_helper(gtsam.FitBasisChebyshev2Basis,
+                                        gtsam.Chebyshev2Basis)
+        # test a basis by checking that the fit result matches the function at x-values interpx.
+        np.testing.assert_almost_equal(interpy,
+                                       np.array([f(x) for x in self.interpx]),
+                                       decimal=7)
+
+    def test_fit_basis_chebyshev2(self):
+        """Fit a Chebyshev2 pseudospectral basis."""
+
+        f = lambda x: x
+        interpy = self.fit_basis_helper(gtsam.FitBasisChebyshev2,
+                                        gtsam.Chebyshev2)
+        # test a basis by checking that the fit result matches the function at x-values interpx.
+        np.testing.assert_almost_equal(interpy,
+                                       np.array([f(x) for x in self.interpx]),
+                                       decimal=7)
+
+
+if __name__ == "__main__":
+    unittest.main()