diff --git a/test/torchaudio_unittest/functional/functional_cpu_test.py b/test/torchaudio_unittest/functional/functional_cpu_test.py
index 9f4b4f1a64..b9c5a6f64e 100644
--- a/test/torchaudio_unittest/functional/functional_cpu_test.py
+++ b/test/torchaudio_unittest/functional/functional_cpu_test.py
@@ -14,29 +14,19 @@
     skipIfNoSox,
 )
 
-from .functional_impl import Lfilter, Spectrogram, FunctionalComplex
+from .functional_impl import Functional, FunctionalComplex
 
 
-class TestLFilterFloat32(Lfilter, common_utils.PytorchTestCase):
+class TestFunctionalFloat32(Functional, common_utils.PytorchTestCase):
     dtype = torch.float32
     device = torch.device('cpu')
 
     @unittest.expectedFailure
-    def test_9th_order_filter_stability(self):
-        super().test_9th_order_filter_stability()
+    def test_lfilter_9th_order_filter_stability(self):
+        super().test_lfilter_9th_order_filter_stability()
 
 
-class TestLFilterFloat64(Lfilter, common_utils.PytorchTestCase):
-    dtype = torch.float64
-    device = torch.device('cpu')
-
-
-class TestSpectrogramFloat32(Spectrogram, common_utils.PytorchTestCase):
-    dtype = torch.float32
-    device = torch.device('cpu')
-
-
-class TestSpectrogramFloat64(Spectrogram, common_utils.PytorchTestCase):
+class TestFunctionalFloat64(Functional, common_utils.PytorchTestCase):
     dtype = torch.float64
     device = torch.device('cpu')
 
diff --git a/test/torchaudio_unittest/functional/functional_cuda_test.py b/test/torchaudio_unittest/functional/functional_cuda_test.py
index 62d9eff3eb..ebf8cd8326 100644
--- a/test/torchaudio_unittest/functional/functional_cuda_test.py
+++ b/test/torchaudio_unittest/functional/functional_cuda_test.py
@@ -2,33 +2,21 @@
 import unittest
 
 from torchaudio_unittest import common_utils
-from .functional_impl import Lfilter, Spectrogram, FunctionalComplex
+from .functional_impl import Functional, FunctionalComplex
 
 
 @common_utils.skipIfNoCuda
-class TestLFilterFloat32(Lfilter, common_utils.PytorchTestCase):
+class TestFunctionalloat32(Functional, common_utils.PytorchTestCase):
     dtype = torch.float32
     device = torch.device('cuda')
 
     @unittest.expectedFailure
-    def test_9th_order_filter_stability(self):
-        super().test_9th_order_filter_stability()
+    def test_lfilter_9th_order_filter_stability(self):
+        super().test_lfilter_9th_order_filter_stability()
 
 
 @common_utils.skipIfNoCuda
-class TestLFilterFloat64(Lfilter, common_utils.PytorchTestCase):
-    dtype = torch.float64
-    device = torch.device('cuda')
-
-
-@common_utils.skipIfNoCuda
-class TestSpectrogramFloat32(Spectrogram, common_utils.PytorchTestCase):
-    dtype = torch.float32
-    device = torch.device('cuda')
-
-
-@common_utils.skipIfNoCuda
-class TestSpectrogramFloat64(Spectrogram, common_utils.PytorchTestCase):
+class TestLFilterFloat64(Functional, common_utils.PytorchTestCase):
     dtype = torch.float64
     device = torch.device('cuda')
 
diff --git a/test/torchaudio_unittest/functional/functional_impl.py b/test/torchaudio_unittest/functional/functional_impl.py
index c4f863fe45..8b890e9563 100644
--- a/test/torchaudio_unittest/functional/functional_impl.py
+++ b/test/torchaudio_unittest/functional/functional_impl.py
@@ -9,8 +9,8 @@
 from torchaudio_unittest.common_utils import nested_params
 
 
-class Lfilter(common_utils.TestBaseMixin):
-    def test_simple(self):
+class Functional(common_utils.TestBaseMixin):
+    def test_lfilter_simple(self):
         """
         Create a very basic signal,
         Then make a simple 4th order delay
@@ -25,7 +25,7 @@ def test_simple(self):
 
         self.assertEqual(output_waveform[:, 3:], waveform[:, 0:-3], atol=1e-5, rtol=1e-5)
 
-    def test_clamp(self):
+    def test_lfilter_clamp(self):
         input_signal = torch.ones(1, 44100 * 1, dtype=self.dtype, device=self.device)
         b_coeffs = torch.tensor([1, 0], dtype=self.dtype, device=self.device)
         a_coeffs = torch.tensor([1, -0.95], dtype=self.dtype, device=self.device)
@@ -40,7 +40,7 @@ def test_clamp(self):
         ((2, 3, 44100),),
         ((1, 2, 3, 44100),)
     ])
-    def test_shape(self, shape):
+    def test_lfilter_shape(self, shape):
         torch.random.manual_seed(42)
         waveform = torch.rand(*shape, dtype=self.dtype, device=self.device)
         b_coeffs = torch.tensor([0, 0, 0, 1], dtype=self.dtype, device=self.device)
@@ -48,7 +48,7 @@ def test_shape(self, shape):
         output_waveform = F.lfilter(waveform, a_coeffs, b_coeffs)
         assert shape == waveform.size() == output_waveform.size()
 
-    def test_9th_order_filter_stability(self):
+    def test_lfilter_9th_order_filter_stability(self):
         """
         Validate the precision of lfilter against reference scipy implementation when using high order filter.
         The reference implementation use cascaded second-order filters so is more numerically accurate.
@@ -70,10 +70,8 @@ def test_9th_order_filter_stability(self):
         yhat = F.lfilter(x, a, b, False)
         self.assertEqual(yhat, y, atol=1e-4, rtol=1e-5)
 
-
-class Spectrogram(common_utils.TestBaseMixin):
     @parameterized.expand([(0., ), (1., ), (2., ), (3., )])
-    def test_grad_at_zero(self, power):
+    def test_spectogram_grad_at_zero(self, power):
         """The gradient of power spectrogram should not be nan but zero near x=0
 
         https://github.com/pytorch/audio/issues/993