diff --git a/stumpy/sdp.py b/stumpy/sdp.py
index 551e8f2f2..bd1d8fea7 100644
--- a/stumpy/sdp.py
+++ b/stumpy/sdp.py
@@ -1,6 +1,8 @@
 import numpy as np
 from numba import njit
-from scipy.signal import convolve
+from scipy.fft import next_fast_len
+from scipy.fft._pocketfft.basic import c2r, r2c
+from scipy.signal import convolve, oaconvolve
 
 from . import config
 
@@ -23,11 +25,14 @@ def _njit_sliding_dot_product(Q, T):
     out : numpy.ndarray
         Sliding dot product between `Q` and `T`.
     """
-    m = Q.shape[0]
-    l = T.shape[0] - m + 1
+    m = len(Q)
+    l = len(T) - m + 1
     out = np.empty(l)
     for i in range(l):
-        out[i] = np.dot(Q, T[i : i + m])
+        result = 0.0
+        for j in range(m):
+            result += Q[j] * T[i + j]
+        out[i] = result
 
     return out
 
@@ -49,12 +54,59 @@ def _convolve_sliding_dot_product(Q, T):
     output : numpy.ndarray
         Sliding dot product between `Q` and `T`.
     """
-    n = T.shape[0]
-    m = Q.shape[0]
-    Qr = np.flipud(Q)  # Reverse/flip Q
-    QT = convolve(Qr, T)
+    return convolve(np.flipud(Q), T, mode="valid")
 
-    return QT.real[m - 1 : n]
+
+def _oaconvolve_sliding_dot_product(Q, T):
+    """
+    Use scipy's oaconvolve to calculate the sliding dot product.
+
+    Parameters
+    ----------
+    Q : numpy.ndarray
+        Query array or subsequence
+
+    T : numpy.ndarray
+        Time series or sequence
+
+    Returns
+    -------
+    output : numpy.ndarray
+        Sliding dot product between `Q` and `T`.
+    """
+    return oaconvolve(np.ascontiguousarray(Q[::-1]), T, mode="valid")
+
+
+def _pocketfft_sliding_dot_product(Q, T):
+    """
+    Use scipy.fft._pocketfft to compute
+    the sliding dot product.
+
+    Parameters
+    ----------
+    Q : numpy.ndarray
+        Query array or subsequence
+
+    T : numpy.ndarray
+        Time series or sequence
+
+    Returns
+    -------
+    output : numpy.ndarray
+        Sliding dot product between `Q` and `T`.
+    """
+    n = len(T)
+    m = len(Q)
+    next_fast_n = next_fast_len(n, real=True)
+
+    tmp = np.empty((2, next_fast_n))
+    tmp[0, :m] = Q[::-1]
+    tmp[0, m:] = 0.0
+    tmp[1, :n] = T
+    tmp[1, n:] = 0.0
+    fft_2d = r2c(True, tmp, axis=-1)
+
+    return c2r(False, np.multiply(fft_2d[0], fft_2d[1]), n=next_fast_n)[m - 1 : n]
 
 
 def _sliding_dot_product(Q, T):
diff --git a/tests/test_sdp.py b/tests/test_sdp.py
index 41e956274..b8d98eeb9 100644
--- a/tests/test_sdp.py
+++ b/tests/test_sdp.py
@@ -1,3 +1,7 @@
+import inspect
+import warnings
+from operator import eq, lt
+
 import naive
 import numpy as np
 import pytest
@@ -5,32 +9,146 @@
 
 from stumpy import sdp
 
-test_data = [
-    (np.array([-1, 1, 2], dtype=np.float64), np.array(range(5), dtype=np.float64)),
+# README
+# Real FFT algorithm performs more efficiently when the length
+# of the input array `arr` is composed of small prime factors.
+# The next_fast_len(arr, real=True) function from Scipy returns
+# the same length if len(arr) is composed of a subset of
+# prime numbers 2, 3, 5. Therefore, these radices are
+# considered as the most efficient for the real FFT algorithm.
+
+# To ensure that the tests cover different cases, the following cases
+# are considered:
+# 1. len(T) is even, and len(T) == next_fast_len(len(T), real=True)
+# 2. len(T) is odd, and len(T) == next_fast_len(len(T), real=True)
+# 3. len(T) is even, and len(T) < next_fast_len(len(T), real=True)
+# 4. len(T) is odd, and len(T) < next_fast_len(len(T), real=True)
+# And 5. a special case of 1, where len(T) is power of 2.
+
+# Therefore:
+# 1. len(T) is composed of 2 and a subset of {3, 5}
+# 2. len(T) is composed of a subset of {3, 5}
+# 3. len(T) is composed of a subset of {7, 11, 13, ...} and 2
+# 4. len(T) is composed of a subset of {7, 11, 13, ...}
+# 5. len(T) is power of 2
+
+# In some cases, the prime factors are raised to a power of
+# certain degree to increase the length of array to be around
+# 1000-2000. This allows us to test sliding_dot_product for
+# wider range of query lengths.
+
+# test cases 1-4
+test_inputs = [
+    # Input format:
+    # (
+    #     len(T),
+    #     remainder,  #  from `len(T) % 2`
+    #     comparator,  # for len(T) comparator next_fast_len(len(T), real=True)
+    # )
+    (
+        2 * (3**2) * (5**3),
+        0,
+        eq,
+    ),  # = 2250, Even `len(T)`, and `len(T) == next_fast_len(len(T), real=True)`
+    (
+        (3**2) * (5**3),
+        1,
+        eq,
+    ),  # = 1125, Odd `len(T)`, and `len(T) == next_fast_len(len(T), real=True)`.
+    (
+        2 * 7 * 11 * 13,
+        0,
+        lt,
+    ),  # = 2002, Even `len(T)`, and `len(T) < next_fast_len(len(T), real=True)`
     (
-        np.array([9, 8100, -60], dtype=np.float64),
-        np.array([584, -11, 23, 79, 1001], dtype=np.float64),
-    ),
-    (np.random.uniform(-1000, 1000, [8]), np.random.uniform(-1000, 1000, [64])),
+        7 * 11 * 13,
+        1,
+        lt,
+    ),  # = 1001, Odd `len(T)`, and `len(T) < next_fast_len(len(T), real=True)`
 ]
 
 
-@pytest.mark.parametrize("Q, T", test_data)
-def test_njit_sliding_dot_product(Q, T):
-    ref_mp = naive.rolling_window_dot_product(Q, T)
-    comp_mp = sdp._njit_sliding_dot_product(Q, T)
-    npt.assert_almost_equal(ref_mp, comp_mp)
+def get_sdp_function_names():
+    out = []
+    for func_name, func in inspect.getmembers(sdp, inspect.isfunction):
+        if func_name.endswith("sliding_dot_product"):
+            out.append(func_name)
+
+    return out
+
+
+@pytest.mark.parametrize("n_T, remainder, comparator", test_inputs)
+def test_sdp(n_T, remainder, comparator):
+    # test_sdp for cases 1-4
+
+    n_Q_prime = [
+        2,
+        3,
+        5,
+        7,
+        11,
+        13,
+        17,
+        19,
+        23,
+        29,
+        31,
+        37,
+        41,
+        43,
+        47,
+        53,
+        59,
+        61,
+        67,
+        71,
+        73,
+        79,
+        83,
+        89,
+        97,
+    ]
+    n_Q_power2 = [2, 4, 8, 16, 32, 64]
+    n_Q_values = n_Q_prime + n_Q_power2 + [n_T]
+    n_Q_values = sorted(n_Q for n_Q in set(n_Q_values) if n_Q <= n_T)
+
+    for n_Q in n_Q_values:
+        Q = np.random.rand(n_Q)
+        T = np.random.rand(n_T)
+        ref = naive.rolling_window_dot_product(Q, T)
+        for func_name in get_sdp_function_names():
+            func = getattr(sdp, func_name)
+            try:
+                comp = func(Q, T)
+                npt.assert_allclose(comp, ref)
+            except Exception as e:  # pragma: no cover
+                msg = f"Error in {func_name}, with n_Q={n_Q} and n_T={n_T}"
+                warnings.warn(msg)
+                raise e
+
+
+def test_sdp_power2():
+    # test for case 5. len(T) is power of 2
+    pmin = 3
+    pmax = 13
 
+    for func_name in get_sdp_function_names():
+        func = getattr(sdp, func_name)
+        try:
+            for q in range(pmin, pmax + 1):
+                n_Q = 2**q
+                for p in range(q, pmax + 1):
+                    n_T = 2**p
+                    Q = np.random.rand(n_Q)
+                    T = np.random.rand(n_T)
 
-@pytest.mark.parametrize("Q, T", test_data)
-def test_convolve_sliding_dot_product(Q, T):
-    ref_mp = naive.rolling_window_dot_product(Q, T)
-    comp_mp = sdp._convolve_sliding_dot_product(Q, T)
-    npt.assert_almost_equal(ref_mp, comp_mp)
+                    ref = naive.rolling_window_dot_product(Q, T)
+                    comp = func(Q, T)
+                    npt.assert_allclose(comp, ref)
 
+        except Exception as e:  # pragma: no cover
+            msg = f"Error in {func_name}, with q={q} and p={p}"
+            warnings.warn(msg)
+            raise e
 
-@pytest.mark.parametrize("Q, T", test_data)
-def test_sliding_dot_product(Q, T):
-    ref_mp = naive.rolling_window_dot_product(Q, T)
-    comp_mp = sdp._sliding_dot_product(Q, T)
-    npt.assert_almost_equal(ref_mp, comp_mp)
+    return