diff --git a/doc/release/1.12.0-notes.rst b/doc/release/1.12.0-notes.rst
index 98dd3b31697e..07871c10ceef 100644
--- a/doc/release/1.12.0-notes.rst
+++ b/doc/release/1.12.0-notes.rst
@@ -132,6 +132,11 @@ New nanfunctions ``nancumsum`` and ``nancumprod`` added
 Nanfunctions ``nancumsum`` and ``nancumprod`` have been added to
 compute ``cumsum`` and ``cumprod`` by ignoring nans.
 
+``np.interp`` can now interpolate complex values
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+``np.lib.interp(x, xp, fp)`` now allows the interpolated array ``fp``
+to be complex and will interpolate at ``complex128`` precision.
+
 Improvements
 ============
 
diff --git a/numpy/core/src/multiarray/compiled_base.c b/numpy/core/src/multiarray/compiled_base.c
index 136d0859ea0b..213d74f44031 100644
--- a/numpy/core/src/multiarray/compiled_base.c
+++ b/numpy/core/src/multiarray/compiled_base.c
@@ -664,6 +664,182 @@ arr_interp(PyObject *NPY_UNUSED(self), PyObject *args, PyObject *kwdict)
     return NULL;
 }
 
+/* As for arr_interp but for complex fp values */
+NPY_NO_EXPORT PyObject *
+arr_interp_complex(PyObject *NPY_UNUSED(self), PyObject *args, PyObject *kwdict)
+{
+
+    PyObject *fp, *xp, *x;
+    PyObject *left = NULL, *right = NULL;
+    PyArrayObject *afp = NULL, *axp = NULL, *ax = NULL, *af = NULL;
+    npy_intp i, lenx, lenxp;
+
+    const npy_double *dx, *dz;
+    const npy_cdouble *dy; 
+    npy_cdouble lval, rval; 
+    npy_cdouble *dres, *slopes = NULL;
+
+    static char *kwlist[] = {"x", "xp", "fp", "left", "right", NULL};
+
+    NPY_BEGIN_THREADS_DEF;
+
+    if (!PyArg_ParseTupleAndKeywords(args, kwdict, "OOO|OO", kwlist,
+                                     &x, &xp, &fp, &left, &right)) {
+        return NULL;
+    }
+
+    afp = (PyArrayObject *)PyArray_ContiguousFromAny(fp, NPY_CDOUBLE, 1, 1);
+
+    if (afp == NULL) {
+        return NULL;
+    }
+
+    axp = (PyArrayObject *)PyArray_ContiguousFromAny(xp, NPY_DOUBLE, 1, 1);
+    if (axp == NULL) {
+        goto fail;
+    }
+    ax = (PyArrayObject *)PyArray_ContiguousFromAny(x, NPY_DOUBLE, 1, 0);
+    if (ax == NULL) {
+        goto fail;
+    }
+    lenxp = PyArray_SIZE(axp);
+    if (lenxp == 0) {
+        PyErr_SetString(PyExc_ValueError,
+                "array of sample points is empty");
+        goto fail;
+    }
+    if (PyArray_SIZE(afp) != lenxp) {
+        PyErr_SetString(PyExc_ValueError,
+                "fp and xp are not of the same length.");
+        goto fail;
+    }
+
+    lenx = PyArray_SIZE(ax);
+    dx = (const npy_double *)PyArray_DATA(axp);
+    dz = (const npy_double *)PyArray_DATA(ax);
+
+    af = (PyArrayObject *)PyArray_SimpleNew(PyArray_NDIM(ax),
+                                            PyArray_DIMS(ax), NPY_CDOUBLE);
+    if (af == NULL) {
+        goto fail;
+    }
+        
+    dy = (const npy_cdouble *)PyArray_DATA(afp);
+    dres = (npy_cdouble *)PyArray_DATA(af);
+    /* Get left and right fill values. */
+    if ((left == NULL) || (left == Py_None)) {
+        lval = dy[0];
+    }
+    else {
+        lval.real = PyComplex_RealAsDouble(left);
+        if ((lval.real == -1) && PyErr_Occurred()) {
+            goto fail;
+        }
+        lval.imag = PyComplex_ImagAsDouble(left);
+        if ((lval.imag == -1) && PyErr_Occurred()) {
+            goto fail;
+        }
+    }
+        
+    if ((right == NULL) || (right == Py_None)) {
+        rval = dy[lenxp - 1];
+    }
+    else {
+        rval.real = PyComplex_RealAsDouble(right);
+        if ((rval.real == -1) && PyErr_Occurred()) {
+            goto fail;
+        }
+        rval.imag = PyComplex_ImagAsDouble(right);
+        if ((rval.imag == -1) && PyErr_Occurred()) {
+            goto fail;
+        }
+    }
+        
+    /* binary_search_with_guess needs at least a 3 item long array */
+    if (lenxp == 1) {
+        const npy_double xp_val = dx[0];
+        const npy_cdouble fp_val = dy[0];
+            
+        NPY_BEGIN_THREADS_THRESHOLDED(lenx);
+        for (i = 0; i < lenx; ++i) {
+            const npy_double x_val = dz[i];
+            dres[i] = (x_val < xp_val) ? lval :
+              ((x_val > xp_val) ? rval : fp_val);
+        }
+        NPY_END_THREADS;
+    }
+    else {
+        npy_intp j = 0;
+        
+        /* only pre-calculate slopes if there are relatively few of them. */
+        if (lenxp <= lenx) {
+            slopes = PyArray_malloc((lenxp - 1) * sizeof(npy_cdouble));
+            if (slopes == NULL) {
+                goto fail;
+            }
+        }
+            
+        NPY_BEGIN_THREADS;
+        
+        if (slopes != NULL) {
+            for (i = 0; i < lenxp - 1; ++i) {
+                const double inv_dx = 1.0 / (dx[i+1] - dx[i]);
+                slopes[i].real = (dy[i+1].real - dy[i].real) * inv_dx;
+                slopes[i].imag = (dy[i+1].imag - dy[i].imag) * inv_dx;
+            }
+        }
+        
+        for (i = 0; i < lenx; ++i) {
+            const npy_double x_val = dz[i];
+            
+            if (npy_isnan(x_val)) {
+                dres[i].real = x_val;
+                dres[i].imag = 0.0;
+                continue;
+            }
+            
+            j = binary_search_with_guess(x_val, dx, lenxp, j);
+            if (j == -1) {
+                dres[i] = lval;
+            }
+            else if (j == lenxp) {
+                dres[i] = rval;
+            }
+            else if (j == lenxp - 1) {
+                dres[i] = dy[j];
+            }
+            else {
+                if (slopes!=NULL) {
+                    dres[i].real = slopes[j].real*(x_val - dx[j]) + dy[j].real;
+                    dres[i].imag = slopes[j].imag*(x_val - dx[j]) + dy[j].imag;
+                }
+                else {
+                    const npy_double inv_dx = 1.0 / (dx[j+1] - dx[j]);
+                    dres[i].real = (dy[j+1].real - dy[j].real)*(x_val - dx[j])*
+			inv_dx + dy[j].real;
+                    dres[i].imag = (dy[j+1].imag - dy[j].imag)*(x_val - dx[j])*
+			inv_dx + dy[j].imag;
+                }
+            }
+        }
+        
+        NPY_END_THREADS;
+    } 
+    PyArray_free(slopes);
+    
+    Py_DECREF(afp);
+    Py_DECREF(axp);
+    Py_DECREF(ax);
+    return (PyObject *)af;
+
+fail:
+    Py_XDECREF(afp);
+    Py_XDECREF(axp);
+    Py_XDECREF(ax);
+    Py_XDECREF(af);
+    return NULL;
+}
+
 /*
  * Converts a Python sequence into 'count' PyArrayObjects
  *
diff --git a/numpy/core/src/multiarray/compiled_base.h b/numpy/core/src/multiarray/compiled_base.h
index 19e3778adfc3..51508531c5a3 100644
--- a/numpy/core/src/multiarray/compiled_base.h
+++ b/numpy/core/src/multiarray/compiled_base.h
@@ -11,6 +11,8 @@ arr_digitize(PyObject *, PyObject *, PyObject *kwds);
 NPY_NO_EXPORT PyObject *
 arr_interp(PyObject *, PyObject *, PyObject *);
 NPY_NO_EXPORT PyObject *
+arr_interp_complex(PyObject *, PyObject *, PyObject *);
+NPY_NO_EXPORT PyObject *
 arr_ravel_multi_index(PyObject *, PyObject *, PyObject *);
 NPY_NO_EXPORT PyObject *
 arr_unravel_index(PyObject *, PyObject *, PyObject *);
diff --git a/numpy/core/src/multiarray/multiarraymodule.c b/numpy/core/src/multiarray/multiarraymodule.c
index e2731068b5ef..62b5628566e9 100644
--- a/numpy/core/src/multiarray/multiarraymodule.c
+++ b/numpy/core/src/multiarray/multiarraymodule.c
@@ -4233,6 +4233,8 @@ static struct PyMethodDef array_module_methods[] = {
         METH_VARARGS | METH_KEYWORDS, NULL},
     {"interp", (PyCFunction)arr_interp,
         METH_VARARGS | METH_KEYWORDS, NULL},
+    {"interp_complex", (PyCFunction)arr_interp_complex,
+        METH_VARARGS | METH_KEYWORDS, NULL},
     {"ravel_multi_index", (PyCFunction)arr_ravel_multi_index,
         METH_VARARGS | METH_KEYWORDS, NULL},
     {"unravel_index", (PyCFunction)arr_unravel_index,
diff --git a/numpy/lib/function_base.py b/numpy/lib/function_base.py
index 8f15fc547b74..3533a59fcafd 100644
--- a/numpy/lib/function_base.py
+++ b/numpy/lib/function_base.py
@@ -23,8 +23,10 @@
 from numpy.core.numerictypes import typecodes, number
 from numpy.lib.twodim_base import diag
 from .utils import deprecate
-from numpy.core.multiarray import _insert, add_docstring
-from numpy.core.multiarray import digitize, bincount, interp as compiled_interp
+from numpy.core.multiarray import (
+    _insert, add_docstring, digitize, bincount, 
+    interp as compiled_interp, interp_complex as compiled_interp_complex
+    )
 from numpy.core.umath import _add_newdoc_ufunc as add_newdoc_ufunc
 from numpy.compat import long
 from numpy.compat.py3k import basestring
@@ -1663,13 +1665,13 @@ def interp(x, xp, fp, left=None, right=None, period=None):
         `period` is not specified. Otherwise, `xp` is internally sorted after
         normalizing the periodic boundaries with ``xp = xp % period``.
 
-    fp : 1-D sequence of floats
+    fp : 1-D sequence of float or complex
         The y-coordinates of the data points, same length as `xp`.
 
-    left : float, optional
+    left : optional float or complex corresponding to fp
         Value to return for `x < xp[0]`, default is `fp[0]`.
 
-    right : float, optional
+    right : optional float or complex corresponding to fp
         Value to return for `x > xp[-1]`, default is `fp[-1]`.
 
     period : None or float, optional
@@ -1681,7 +1683,7 @@ def interp(x, xp, fp, left=None, right=None, period=None):
 
     Returns
     -------
-    y : float or ndarray
+    y : float or complex (corresponding to fp) or ndarray 
         The interpolated values, same shape as `x`.
 
     Raises
@@ -1732,14 +1734,31 @@ def interp(x, xp, fp, left=None, right=None, period=None):
     >>> np.interp(x, xp, fp, period=360)
     array([7.5, 5., 8.75, 6.25, 3., 3.25, 3.5, 3.75])
 
+    Complex interpolation
+    >>> x = [1.5, 4.0]
+    >>> xp = [2,3,5]
+    >>> fp = [1.0j, 0, 2+3j]
+    >>> np.interp(x, xp, fp)
+    array([ 0.+1.j ,  1.+1.5j])
+
     """
+
+    fp = np.asarray(fp)
+
+    if np.iscomplexobj(fp):
+        interp_func = compiled_interp_complex
+        input_dtype = np.complex128
+    else:
+        interp_func = compiled_interp
+        input_dtype = np.float64
+
     if period is None:
         if isinstance(x, (float, int, number)):
-            return compiled_interp([x], xp, fp, left, right).item()
+            return interp_func([x], xp, fp, left, right).item()
         elif isinstance(x, np.ndarray) and x.ndim == 0:
-            return compiled_interp([x], xp, fp, left, right).item()
+            return interp_func([x], xp, fp, left, right).item()
         else:
-            return compiled_interp(x, xp, fp, left, right)
+            return interp_func(x, xp, fp, left, right)
     else:
         if period == 0:
             raise ValueError("period must be a non-zero value")
@@ -1752,7 +1771,8 @@ def interp(x, xp, fp, left=None, right=None, period=None):
             x = [x]
         x = np.asarray(x, dtype=np.float64)
         xp = np.asarray(xp, dtype=np.float64)
-        fp = np.asarray(fp, dtype=np.float64)
+        fp = np.asarray(fp, dtype=input_dtype)
+
         if xp.ndim != 1 or fp.ndim != 1:
             raise ValueError("Data points must be 1-D sequences")
         if xp.shape[0] != fp.shape[0]:
@@ -1765,12 +1785,12 @@ def interp(x, xp, fp, left=None, right=None, period=None):
         fp = fp[asort_xp]
         xp = np.concatenate((xp[-1:]-period, xp, xp[0:1]+period))
         fp = np.concatenate((fp[-1:], fp, fp[0:1]))
+
         if return_array:
-            return compiled_interp(x, xp, fp, left, right)
+            return interp_func(x, xp, fp, left, right)
         else:
-            return compiled_interp(x, xp, fp, left, right).item()
-
-
+            return interp_func(x, xp, fp, left, right).item()
+                
 def angle(z, deg=0):
     """
     Return the angle of the complex argument.
diff --git a/numpy/lib/tests/test_function_base.py b/numpy/lib/tests/test_function_base.py
index 0442792947fa..0f71393ad148 100644
--- a/numpy/lib/tests/test_function_base.py
+++ b/numpy/lib/tests/test_function_base.py
@@ -2235,6 +2235,28 @@ def test_scalar_interpolation_point(self):
         assert_almost_equal(np.interp(x0, x, y), x0)
         x0 = np.nan
         assert_almost_equal(np.interp(x0, x, y), x0)
+        
+    def test_complex_interp(self):
+        # test complex interpolation
+        x = np.linspace(0, 1, 5)
+        y = np.linspace(0, 1, 5) + (1 + np.linspace(0, 1, 5))*1.0j
+        x0 = 0.3
+        y0 = x0 + (1+x0)*1.0j
+        assert_almost_equal(np.interp(x0, x, y), y0)
+        # test complex left and right
+        x0 = -1
+        left = 2 + 3.0j
+        assert_almost_equal(np.interp(x0, x, y, left=left), left)
+        x0 = 2.0
+        right = 2 + 3.0j
+        assert_almost_equal(np.interp(x0, x, y, right=right), right)
+        # test complex periodic
+        x = [-180, -170, -185, 185, -10, -5, 0, 365]
+        xp = [190, -190, 350, -350]
+        fp = [5+1.0j, 10+2j, 3+3j, 4+4j]
+        y = [7.5+1.5j, 5.+1.0j, 8.75+1.75j, 6.25+1.25j, 3.+3j, 3.25+3.25j, 
+             3.5+3.5j, 3.75+3.75j]
+        assert_almost_equal(np.interp(x, xp, fp, period=360), y)
 
     def test_zero_dimensional_interpolation_point(self):
         x = np.linspace(0, 1, 5)