diff --git a/tests/test_equalizer.py b/tests/test_equalizer.py
index ce50a32..52b5838 100644
--- a/tests/test_equalizer.py
+++ b/tests/test_equalizer.py
@@ -1,8 +1,7 @@
-from amodem import train
-from amodem import dsp
+from amodem import train, dsp, config, send
 from numpy.linalg import norm
 import numpy as np
-
+import itertools
 
 def test_fir():
     a = [1, 0.8, -0.1, 0, 0]
@@ -25,3 +24,43 @@ def test_iir():
     h_expected = np.array([alpha ** i for i in range(len(h_))])
     assert norm(h_ - h_expected) < 1e-12
     assert (norm(tx - tx_) / norm(tx)) < 1e-12
+
+
+import random
+
+_constellation = [1, 1j, -1, -1j]
+
+def train_symbols(length, seed=0):
+    r = random.Random(seed)
+    choose = lambda: [r.choice(_constellation) for j in range(config.Nfreq)]
+    return np.array([choose() for i in range(length)])
+
+def modulator(length):
+    symbols = train_symbols(length)
+    carriers = send.sym.carrier
+    result = []
+    for s in symbols:
+        result.append(np.dot(s, carriers) / len(carriers))
+    result = np.concatenate(result).real
+    assert np.max(np.abs(result)) <= 1
+    return result
+
+def demodulator(signal):
+    signal = itertools.chain(signal, itertools.repeat(0))
+    return dsp.Demux(signal, config.frequencies)
+
+def test_training():
+    L = 1000
+    t1 = train_symbols(L)
+    t2 = train_symbols(L)
+    assert (t1 == t2).all()
+
+def test_modem():
+    L = 1000
+    x = modulator(L)
+    s = demodulator(x)
+    s = list(itertools.islice(s, L))
+    sent = train_symbols(L)
+    received = np.array(s) * len(send.sym.carrier)
+    err = sent - received
+    assert norm(err) < 1e-12