diff --git a/docs/source/networks.rst b/docs/source/networks.rst
index 420da311d2..6a05d72b66 100644
--- a/docs/source/networks.rst
+++ b/docs/source/networks.rst
@@ -203,6 +203,11 @@ Layers
 .. autoclass:: BilateralFilter
     :members:
 
+`SavitzkyGolayFilter`
+~~~~~~~~~~~~~~~~~~~~~
+.. autoclass:: SavitzkyGolayFilter
+    :members:
+
 `HilbertTransform`
 ~~~~~~~~~~~~~~~~~~
 .. autoclass:: HilbertTransform
diff --git a/docs/source/transforms.rst b/docs/source/transforms.rst
index c769771f4a..90d960a6b9 100644
--- a/docs/source/transforms.rst
+++ b/docs/source/transforms.rst
@@ -186,6 +186,12 @@ Intensity
     :members:
     :special-members: __call__
 
+`SavitzkyGolaySmooth`
+"""""""""""""""""""""
+.. autoclass:: SavitzkyGolaySmooth
+    :members:
+    :special-members: __call__
+
 `GaussianSmooth`
 """"""""""""""""
 .. autoclass:: GaussianSmooth
diff --git a/monai/networks/layers/__init__.py b/monai/networks/layers/__init__.py
index dabec727ac..49c18eb5bf 100644
--- a/monai/networks/layers/__init__.py
+++ b/monai/networks/layers/__init__.py
@@ -19,6 +19,7 @@
     GaussianFilter,
     HilbertTransform,
     Reshape,
+    SavitzkyGolayFilter,
     SkipConnection,
     separable_filtering,
 )
diff --git a/monai/networks/layers/simplelayers.py b/monai/networks/layers/simplelayers.py
index a6524669b1..285b0d629f 100644
--- a/monai/networks/layers/simplelayers.py
+++ b/monai/networks/layers/simplelayers.py
@@ -39,6 +39,7 @@
     "LLTM",
     "Reshape",
     "separable_filtering",
+    "SavitzkyGolayFilter",
     "HilbertTransform",
     "ChannelPad",
 ]
@@ -163,7 +164,9 @@ def forward(self, x: torch.Tensor) -> torch.Tensor:
         return x.reshape(shape)
 
 
-def separable_filtering(x: torch.Tensor, kernels: Union[Sequence[torch.Tensor], torch.Tensor]) -> torch.Tensor:
+def separable_filtering(
+    x: torch.Tensor, kernels: Union[Sequence[torch.Tensor], torch.Tensor], mode: str = "zeros"
+) -> torch.Tensor:
     """
     Apply 1-D convolutions along each spatial dimension of `x`.
 
@@ -171,10 +174,14 @@ def separable_filtering(x: torch.Tensor, kernels: Union[Sequence[torch.Tensor],
         x: the input image. must have shape (batch, channels, H[, W, ...]).
         kernels: kernel along each spatial dimension.
             could be a single kernel (duplicated for all dimension), or `spatial_dims` number of kernels.
+        mode (string, optional): padding mode passed to convolution class. ``'zeros'``, ``'reflect'``, ``'replicate'``
+            or ``'circular'``. Default: ``'zeros'``. Modes other than ``'zeros'`` require PyTorch version >= 1.5.1. See
+            torch.nn.Conv1d() for more information.
 
     Raises:
         TypeError: When ``x`` is not a ``torch.Tensor``.
     """
+
     if not torch.is_tensor(x):
         raise TypeError(f"x must be a torch.Tensor but is {type(x).__name__}.")
 
@@ -184,7 +191,7 @@ def separable_filtering(x: torch.Tensor, kernels: Union[Sequence[torch.Tensor],
         for s in ensure_tuple_rep(kernels, spatial_dims)
     ]
     _paddings = [cast(int, (same_padding(k.shape[0]))) for k in _kernels]
-    n_chns = x.shape[1]
+    n_chs = x.shape[1]
 
     def _conv(input_: torch.Tensor, d: int) -> torch.Tensor:
         if d < 0:
@@ -192,15 +199,95 @@ def _conv(input_: torch.Tensor, d: int) -> torch.Tensor:
         s = [1] * len(input_.shape)
         s[d + 2] = -1
         _kernel = kernels[d].reshape(s)
-        _kernel = _kernel.repeat([n_chns, 1] + [1] * spatial_dims)
+        # if filter kernel is unity, don't convolve
+        if _kernel.numel() == 1 and _kernel[0] == 1:
+            return _conv(input_, d - 1)
+        _kernel = _kernel.repeat([n_chs, 1] + [1] * spatial_dims)
         _padding = [0] * spatial_dims
         _padding[d] = _paddings[d]
         conv_type = [F.conv1d, F.conv2d, F.conv3d][spatial_dims - 1]
-        return conv_type(input=_conv(input_, d - 1), weight=_kernel, padding=_padding, groups=n_chns)
+        # translate padding for input to torch.nn.functional.pad
+        _reversed_padding_repeated_twice = [p for p in reversed(_padding) for _ in range(2)]
+        pad_mode = "constant" if mode == "zeros" else mode
+        return conv_type(
+            input=_conv(F.pad(input_, _reversed_padding_repeated_twice, mode=pad_mode), d - 1),
+            weight=_kernel,
+            groups=n_chs,
+        )
 
     return _conv(x, spatial_dims - 1)
 
 
+class SavitzkyGolayFilter(nn.Module):
+    """
+    Convolve a Tensor along a particular axis with a Savitzky-Golay kernel.
+
+    Args:
+        window_length: Length of the filter window, must be a positive odd integer.
+        order: Order of the polynomial to fit to each window, must be less than ``window_length``.
+        axis (optional): Axis along which to apply the filter kernel. Default 2 (first spatial dimension).
+        mode (string, optional): padding mode passed to convolution class. ``'zeros'``, ``'reflect'``, ``'replicate'`` or
+        ``'circular'``. Default: ``'zeros'``. See torch.nn.Conv1d() for more information.
+    """
+
+    def __init__(self, window_length: int, order: int, axis: int = 2, mode: str = "zeros"):
+
+        super().__init__()
+        if order >= window_length:
+            raise ValueError("order must be less than window_length.")
+
+        self.axis = axis
+        self.mode = mode
+        self.coeffs = self._make_coeffs(window_length, order)
+
+    def forward(self, x: torch.Tensor) -> torch.Tensor:
+        """
+        Args:
+            x: Tensor or array-like to filter. Must be real, in shape ``[Batch, chns, spatial1, spatial2, ...]`` and
+                have a device type of ``'cpu'``.
+        Returns:
+            torch.Tensor: ``x`` filtered by Savitzky-Golay kernel with window length ``self.window_length`` using
+            polynomials of order ``self.order``, along axis specified in ``self.axis``.
+        """
+
+        # Make input a real tensor on the CPU
+        x = torch.as_tensor(x, device=x.device if torch.is_tensor(x) else None)
+        if torch.is_complex(x):
+            raise ValueError("x must be real.")
+        else:
+            x = x.to(dtype=torch.float)
+
+        if (self.axis < 0) or (self.axis > len(x.shape) - 1):
+            raise ValueError("Invalid axis for shape of x.")
+
+        # Create list of filter kernels (1 per spatial dimension). The kernel for self.axis will be the savgol coeffs,
+        # while the other kernels will be set to [1].
+        n_spatial_dims = len(x.shape) - 2
+        spatial_processing_axis = self.axis - 2
+        new_dims_before = spatial_processing_axis
+        new_dims_after = n_spatial_dims - spatial_processing_axis - 1
+        kernel_list = [self.coeffs.to(device=x.device, dtype=x.dtype)]
+        for _ in range(new_dims_before):
+            kernel_list.insert(0, torch.ones(1, device=x.device, dtype=x.dtype))
+        for _ in range(new_dims_after):
+            kernel_list.append(torch.ones(1, device=x.device, dtype=x.dtype))
+
+        return separable_filtering(x, kernel_list, mode=self.mode)
+
+    @staticmethod
+    def _make_coeffs(window_length, order):
+
+        half_length, rem = divmod(window_length, 2)
+        if rem == 0:
+            raise ValueError("window_length must be odd.")
+
+        idx = torch.arange(window_length - half_length - 1, -half_length - 1, -1, dtype=torch.float, device="cpu")
+        a = idx ** torch.arange(order + 1, dtype=torch.float, device="cpu").reshape(-1, 1)
+        y = torch.zeros(order + 1, dtype=torch.float, device="cpu")
+        y[0] = 1.0
+        return torch.lstsq(y, a).solution.squeeze()
+
+
 class HilbertTransform(nn.Module):
     """
     Determine the analytical signal of a Tensor along a particular axis.
diff --git a/monai/transforms/__init__.py b/monai/transforms/__init__.py
index 8f46abf522..9eaedd6b15 100644
--- a/monai/transforms/__init__.py
+++ b/monai/transforms/__init__.py
@@ -78,6 +78,7 @@
     RandHistogramShift,
     RandScaleIntensity,
     RandShiftIntensity,
+    SavitzkyGolaySmooth,
     ScaleIntensity,
     ScaleIntensityRange,
     ScaleIntensityRangePercentiles,
diff --git a/monai/transforms/intensity/array.py b/monai/transforms/intensity/array.py
index 2d3cca64e6..205b719246 100644
--- a/monai/transforms/intensity/array.py
+++ b/monai/transforms/intensity/array.py
@@ -20,7 +20,7 @@
 import numpy as np
 import torch
 
-from monai.networks.layers import GaussianFilter, HilbertTransform
+from monai.networks.layers import GaussianFilter, HilbertTransform, SavitzkyGolayFilter
 from monai.transforms.compose import Randomizable, Transform
 from monai.transforms.utils import rescale_array
 from monai.utils import PT_BEFORE_1_7, InvalidPyTorchVersionError, dtype_torch_to_numpy, ensure_tuple_size
@@ -39,6 +39,7 @@
     "ScaleIntensityRangePercentiles",
     "MaskIntensity",
     "DetectEnvelope",
+    "SavitzkyGolaySmooth",
     "GaussianSmooth",
     "RandGaussianSmooth",
     "GaussianSharpen",
@@ -544,6 +545,44 @@ def __call__(self, img: np.ndarray, mask_data: Optional[np.ndarray] = None) -> n
         return img * mask_data_
 
 
+class SavitzkyGolaySmooth(Transform):
+    """
+    Smooth the input data along the given axis using a Savitzky-Golay filter.
+
+    Args:
+        window_length: Length of the filter window, must be a positive odd integer.
+        order: Order of the polynomial to fit to each window, must be less than ``window_length``.
+        axis: Optional axis along which to apply the filter kernel. Default 1 (first spatial dimension).
+        mode: Optional padding mode, passed to convolution class. ``'zeros'``, ``'reflect'``, ``'replicate'``
+            or ``'circular'``. Default: ``'zeros'``. See ``torch.nn.Conv1d()`` for more information.
+    """
+
+    def __init__(self, window_length: int, order: int, axis: int = 1, mode: str = "zeros"):
+
+        if axis < 0:
+            raise ValueError("axis must be zero or positive.")
+
+        self.window_length = window_length
+        self.order = order
+        self.axis = axis
+        self.mode = mode
+
+    def __call__(self, img: np.ndarray) -> np.ndarray:
+        """
+        Args:
+            img: numpy.ndarray containing input data. Must be real and in shape [channels, spatial1, spatial2, ...].
+
+        Returns:
+            np.ndarray containing smoothed result.
+
+        """
+        # add one to transform axis because a batch axis will be added at dimension 0
+        savgol_filter = SavitzkyGolayFilter(self.window_length, self.order, self.axis + 1, self.mode)
+        # convert to Tensor and add Batch axis expected by HilbertTransform
+        input_data = torch.as_tensor(np.ascontiguousarray(img)).unsqueeze(0)
+        return savgol_filter(input_data).squeeze(0).numpy()
+
+
 class DetectEnvelope(Transform):
     """
     Find the envelope of the input data along the requested axis using a Hilbert transform.
diff --git a/tests/test_savitzky_golay_filter.py b/tests/test_savitzky_golay_filter.py
new file mode 100644
index 0000000000..d76c42c15f
--- /dev/null
+++ b/tests/test_savitzky_golay_filter.py
@@ -0,0 +1,152 @@
+# Copyright 2020 MONAI Consortium
+# 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
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import unittest
+
+import numpy as np
+import torch
+from parameterized import parameterized
+
+from monai.networks.layers import SavitzkyGolayFilter
+from tests.utils import skip_if_no_cuda
+
+# Zero-padding trivial tests
+
+TEST_CASE_SINGLE_VALUE = [
+    {"window_length": 3, "order": 1},
+    torch.Tensor([1.0]).unsqueeze(0).unsqueeze(0),  # Input data: Single value
+    torch.Tensor([1 / 3]).unsqueeze(0).unsqueeze(0),  # Expected output: With a window length of 3 and polyorder 1
+    # output should be equal to mean of 0, 1 and 0 = 1/3 (because input will be zero-padded and a linear fit performed)
+    1e-15,  # absolute tolerance
+]
+
+TEST_CASE_1D = [
+    {"window_length": 3, "order": 1},
+    torch.Tensor([1.0, 1.0, 1.0]).unsqueeze(0).unsqueeze(0),  # Input data
+    torch.Tensor([2 / 3, 1.0, 2 / 3])
+    .unsqueeze(0)
+    .unsqueeze(0),  # Expected output: zero padded, so linear interpolation
+    # over length-3 windows will result in output of [2/3, 1, 2/3].
+    1e-15,  # absolute tolerance
+]
+
+TEST_CASE_2D_AXIS_2 = [
+    {"window_length": 3, "order": 1},  # along default axis (2, first spatial dim)
+    torch.ones((3, 2)).unsqueeze(0).unsqueeze(0),
+    torch.Tensor([[2 / 3, 2 / 3], [1.0, 1.0], [2 / 3, 2 / 3]]).unsqueeze(0).unsqueeze(0),
+    1e-15,  # absolute tolerance
+]
+
+TEST_CASE_2D_AXIS_3 = [
+    {"window_length": 3, "order": 1, "axis": 3},  # along axis 3 (second spatial dim)
+    torch.ones((2, 3)).unsqueeze(0).unsqueeze(0),
+    torch.Tensor([[2 / 3, 1.0, 2 / 3], [2 / 3, 1.0, 2 / 3]]).unsqueeze(0).unsqueeze(0),
+    1e-15,  # absolute tolerance
+]
+
+# Replicated-padding trivial tests
+
+TEST_CASE_SINGLE_VALUE_REP = [
+    {"window_length": 3, "order": 1, "mode": "replicate"},
+    torch.Tensor([1.0]).unsqueeze(0).unsqueeze(0),  # Input data: Single value
+    torch.Tensor([1.0]).unsqueeze(0).unsqueeze(0),  # Expected output: With a window length of 3 and polyorder 1
+    # output will be equal to mean of [1, 1, 1] = 1 (input will be nearest-neighbour-padded and a linear fit performed)
+    1e-15,  # absolute tolerance
+]
+
+TEST_CASE_1D_REP = [
+    {"window_length": 3, "order": 1, "mode": "replicate"},
+    torch.Tensor([1.0, 1.0, 1.0]).unsqueeze(0).unsqueeze(0),  # Input data
+    torch.Tensor([1.0, 1.0, 1.0]).unsqueeze(0).unsqueeze(0),  # Expected output: zero padded, so linear interpolation
+    # over length-3 windows will result in output of [2/3, 1, 2/3].
+    1e-15,  # absolute tolerance
+]
+
+TEST_CASE_2D_AXIS_2_REP = [
+    {"window_length": 3, "order": 1, "mode": "replicate"},  # along default axis (2, first spatial dim)
+    torch.ones((3, 2)).unsqueeze(0).unsqueeze(0),
+    torch.Tensor([[1.0, 1.0], [1.0, 1.0], [1.0, 1.0]]).unsqueeze(0).unsqueeze(0),
+    1e-15,  # absolute tolerance
+]
+
+TEST_CASE_2D_AXIS_3_REP = [
+    {"window_length": 3, "order": 1, "axis": 3, "mode": "replicate"},  # along axis 3 (second spatial dim)
+    torch.ones((2, 3)).unsqueeze(0).unsqueeze(0),
+    torch.Tensor([[1.0, 1.0, 1.0], [1.0, 1.0, 1.0]]).unsqueeze(0).unsqueeze(0),
+    1e-15,  # absolute tolerance
+]
+
+# Sine smoothing
+
+TEST_CASE_SINE_SMOOTH = [
+    {"window_length": 3, "order": 1},
+    # Sine wave with period equal to savgol window length (windowed to reduce edge effects).
+    torch.as_tensor(np.sin(2 * np.pi * 1 / 3 * np.arange(100)) * np.hanning(100)).unsqueeze(0).unsqueeze(0),
+    # Should be smoothed out to zeros
+    torch.zeros(100).unsqueeze(0).unsqueeze(0),
+    # tolerance chosen by examining output of SciPy.signal.savgol_filter when provided the above input
+    2e-2,  # absolute tolerance
+]
+
+
+class TestSavitzkyGolayCPU(unittest.TestCase):
+    @parameterized.expand(
+        [
+            TEST_CASE_SINGLE_VALUE,
+            TEST_CASE_1D,
+            TEST_CASE_2D_AXIS_2,
+            TEST_CASE_2D_AXIS_3,
+            TEST_CASE_SINE_SMOOTH,
+        ]
+    )
+    def test_value(self, arguments, image, expected_data, atol):
+        result = SavitzkyGolayFilter(**arguments)(image)
+        np.testing.assert_allclose(result, expected_data, atol=atol)
+
+
+class TestSavitzkyGolayCPUREP(unittest.TestCase):
+    @parameterized.expand(
+        [TEST_CASE_SINGLE_VALUE_REP, TEST_CASE_1D_REP, TEST_CASE_2D_AXIS_2_REP, TEST_CASE_2D_AXIS_3_REP]
+    )
+    def test_value(self, arguments, image, expected_data, atol):
+        result = SavitzkyGolayFilter(**arguments)(image)
+        np.testing.assert_allclose(result, expected_data, atol=atol)
+
+
+@skip_if_no_cuda
+class TestSavitzkyGolayGPU(unittest.TestCase):
+    @parameterized.expand(
+        [
+            TEST_CASE_SINGLE_VALUE,
+            TEST_CASE_1D,
+            TEST_CASE_2D_AXIS_2,
+            TEST_CASE_2D_AXIS_3,
+            TEST_CASE_SINE_SMOOTH,
+        ]
+    )
+    def test_value(self, arguments, image, expected_data, atol):
+        result = SavitzkyGolayFilter(**arguments)(image.to(device="cuda"))
+        np.testing.assert_allclose(result.cpu(), expected_data, atol=atol)
+
+
+@skip_if_no_cuda
+class TestSavitzkyGolayGPUREP(unittest.TestCase):
+    @parameterized.expand(
+        [
+            TEST_CASE_SINGLE_VALUE_REP,
+            TEST_CASE_1D_REP,
+            TEST_CASE_2D_AXIS_2_REP,
+            TEST_CASE_2D_AXIS_3_REP,
+        ]
+    )
+    def test_value(self, arguments, image, expected_data, atol):
+        result = SavitzkyGolayFilter(**arguments)(image.to(device="cuda"))
+        np.testing.assert_allclose(result.cpu(), expected_data, atol=atol)
diff --git a/tests/test_savitzky_golay_smooth.py b/tests/test_savitzky_golay_smooth.py
new file mode 100644
index 0000000000..2be0da1360
--- /dev/null
+++ b/tests/test_savitzky_golay_smooth.py
@@ -0,0 +1,70 @@
+# Copyright 2020 MONAI Consortium
+# 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
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import unittest
+
+import numpy as np
+from parameterized import parameterized
+
+from monai.transforms import SavitzkyGolaySmooth
+
+# Zero-padding trivial tests
+
+TEST_CASE_SINGLE_VALUE = [
+    {"window_length": 3, "order": 1},
+    np.expand_dims(np.array([1.0]), 0),  # Input data: Single value
+    np.expand_dims(np.array([1 / 3]), 0),  # Expected output: With a window length of 3 and polyorder 1
+    # output should be equal to mean of 0, 1 and 0 = 1/3 (because input will be zero-padded and a linear fit performed)
+    1e-15,  # absolute tolerance
+]
+
+TEST_CASE_2D_AXIS_2 = [
+    {"window_length": 3, "order": 1, "axis": 2},  # along axis 2 (second spatial dim)
+    np.expand_dims(np.ones((2, 3)), 0),
+    np.expand_dims(np.array([[2 / 3, 1.0, 2 / 3], [2 / 3, 1.0, 2 / 3]]), 0),
+    1e-15,  # absolute tolerance
+]
+
+# Replicated-padding trivial tests
+
+TEST_CASE_SINGLE_VALUE_REP = [
+    {"window_length": 3, "order": 1, "mode": "replicate"},
+    np.expand_dims(np.array([1.0]), 0),  # Input data: Single value
+    np.expand_dims(np.array([1.0]), 0),  # Expected output: With a window length of 3 and polyorder 1
+    # output will be equal to mean of [1, 1, 1] = 1 (input will be nearest-neighbour-padded and a linear fit performed)
+    1e-15,  # absolute tolerance
+]
+
+# Sine smoothing
+
+TEST_CASE_SINE_SMOOTH = [
+    {"window_length": 3, "order": 1},
+    # Sine wave with period equal to savgol window length (windowed to reduce edge effects).
+    np.expand_dims(np.sin(2 * np.pi * 1 / 3 * np.arange(100)) * np.hanning(100), 0),
+    # Should be smoothed out to zeros
+    np.expand_dims(np.zeros(100), 0),
+    # tolerance chosen by examining output of SciPy.signal.savgol_filter() when provided the above input
+    2e-2,  # absolute tolerance
+]
+
+
+class TestSavitzkyGolaySmooth(unittest.TestCase):
+    @parameterized.expand([TEST_CASE_SINGLE_VALUE, TEST_CASE_2D_AXIS_2, TEST_CASE_SINE_SMOOTH])
+    def test_value(self, arguments, image, expected_data, atol):
+        result = SavitzkyGolaySmooth(**arguments)(image)
+        np.testing.assert_allclose(result, expected_data, atol=atol)
+
+
+class TestSavitzkyGolaySmoothREP(unittest.TestCase):
+    @parameterized.expand([TEST_CASE_SINGLE_VALUE_REP])
+    def test_value(self, arguments, image, expected_data, atol):
+        result = SavitzkyGolaySmooth(**arguments)(image)
+        np.testing.assert_allclose(result, expected_data, atol=atol)