diff --git a/lib/matplotlib/mlab.py b/lib/matplotlib/mlab.py
@@ -212,16 +212,8 @@ def detrend_linear(y):
 
 
 def _stride_windows(x, n, noverlap=0):
-    x = np.asarray(x)
-
     _api.check_isinstance(Integral, n=n, noverlap=noverlap)
-    if not (1 <= n <= x.size and n < noverlap):
-        raise ValueError(f'n ({n}) and noverlap ({noverlap}) must be positive integers '
-                         f'with n < noverlap and n <= x.size ({x.size})')
-
-    if n == 1 and noverlap == 0:
-        return x[np.newaxis]
-
+    x = np.asarray(x)
     step = n - noverlap
     shape = (n, (x.shape[-1]-noverlap)//step)
     strides = (x.strides[0], step*x.strides[0])
@@ -257,7 +249,7 @@ def _spectral_helper(x, y=None, NFFT=None, Fs=None, detrend_func=None,
     if NFFT is None:
         NFFT = 256
 
-    if noverlap >= NFFT:
+    if not (0 <= noverlap < NFFT):
         raise ValueError('noverlap must be less than NFFT')
 
     if mode is None or mode == 'default':

diff --git a/lib/matplotlib/tests/test_mlab.py b/lib/matplotlib/tests/test_mlab.py
@@ -1,3 +1,5 @@
+import sys
+
 from numpy.testing import (assert_allclose, assert_almost_equal,
                            assert_array_equal, assert_array_almost_equal_nulp)
 import numpy as np
@@ -429,7 +431,16 @@ def test_spectral_helper_psd(self, mode, case):
         assert spec.shape[0] == freqs.shape[0]
         assert spec.shape[1] == getattr(self, f"t_{case}").shape[0]
 
-    def test_csd(self):
+    @pytest.mark.parametrize('bitsize', [
+        pytest.param(None, id='default'),
+        pytest.param(32,
+                     marks=pytest.mark.skipif(sys.maxsize <= 2**32,
+                                              reason='System is already 32-bit'),
+                     id='32-bit')
+    ])
+    def test_csd(self, bitsize, monkeypatch):
+        if bitsize is not None:
+            monkeypatch.setattr(sys, 'maxsize', 2**bitsize)
         freqs = self.freqs_density
         spec, fsp = mlab.csd(x=self.y, y=self.y+1,
                              NFFT=self.NFFT_density,