diff --git a/Filter.cc b/Filter.cc
index 3920a49..930a410 100644
--- a/Filter.cc
+++ b/Filter.cc
@@ -109,22 +109,27 @@ void LowPassFilterFirIQ::process(const IQSampleVector& samples_in,
     if (n == 0)
         return;
 
+    // NOTE: We use m_coeff the wrong way around because it is slightly
+    // faster to scan forward through the array. The result is still correct
+    // because the coefficients are symmetric.
+
     // The first few samples need data from m_state.
     unsigned int i = 0;
     for (; i < n && i < order; i++) {
-        IQSample y(0);
-        for (unsigned int j = 0; j <= i; j++)
-            y += samples_in[i-j] * m_coeff[j];
-        for (unsigned int j = i + 1; j <= order; j++)
-            y += m_state[order + i - j] * m_coeff[j];
+        IQSample y = 0;
+        for (unsigned int j = 0; j < order - i; j++)
+            y += m_state[i+j] * m_coeff[j];
+        for (unsigned int j = order - i; j <= order; j++)
+            y += samples_in[i-order+j] * m_coeff[j];
         samples_out[i] = y;
     }
 
     // Remaining samples only need data from samples_in.
     for (; i < n; i++) {
-        IQSample y(0);
+        IQSample y = 0;
+        IQSampleVector::const_iterator inp = samples_in.begin() + i - order;
         for (unsigned int j = 0; j <= order; j++)
-            y += samples_in[i-j] * m_coeff[j];
+            y += inp[j] * m_coeff[j];
         samples_out[i] = y;
     }
 
@@ -182,17 +187,17 @@ void DownsampleFilter::process(const SampleVector& samples_in,
         unsigned int i = 0;
         for (; p < n && p < order; p += pstep, i++) {
             Sample y = 0;
-            for (unsigned int j = 0; j <= p; j++)
+            for (unsigned int j = 1; j <= p; j++)
                 y += samples_in[p-j] * m_coeff[j];
             for (unsigned int j = p + 1; j <= order; j++)
-                y += m_state[order + p - j] * m_coeff[j];
+                y += m_state[order+p-j] * m_coeff[j];
             samples_out[i] = y;
         }
 
         // Remaining samples only need data from samples_in.
         for (; p < n; p += pstep, i++) {
             Sample y = 0;
-            for (unsigned int j = 0; j <= order; j++)
+            for (unsigned int j = 1; j <= order; j++)
                 y += samples_in[p-j] * m_coeff[j];
             samples_out[i] = y;
         }