diff --git a/analysis.ipynb b/analysis.ipynb
index 29dd725..bad0f33 100644
--- a/analysis.ipynb
+++ b/analysis.ipynb
@@ -1,5 +1,84 @@
 {
  "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/Users/xiayunsun/code/venvs/py367/lib/python3.6/site-packages/gym/envs/registration.py:14: PkgResourcesDeprecationWarning: Parameters to load are deprecated.  Call .resolve and .require separately.\n",
+      "  result = entry_point.load(False)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "(210, 160, 3)\n",
+      "0.78125\n",
+      "(210, 160)\n",
+      "(128, 128)\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 2 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# visualise DQN preprocess\n",
+    "import gym\n",
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline\n",
+    "import numpy as np\n",
+    "import scipy.ndimage\n",
+    "\n",
+    "env = gym.make('BreakoutNoFrameskip-v4')\n",
+    "env.reset()\n",
+    "# accumulate 5 frames\n",
+    "frames = []\n",
+    "for i in range(5):\n",
+    "    frame, reward, is_done, info = env.step(env.action_space.sample())\n",
+    "    frames.append(frame)\n",
+    "print(frames[0].shape)\n",
+    "\n",
+    "plt.figure(1)\n",
+    "plt.subplot(121)\n",
+    "plt.imshow(frames[0])\n",
+    "plt.subplot(122)\n",
+    "\n",
+    "frame = np.maximum(frames[0], frames[1])\n",
+    "frame = np.divide(frame, 256)\n",
+    "print(np.amax(frame))\n",
+    "# greyscale\n",
+    "frame = np.dot(frame[...,:3], [0.299, 0.587, 0.114])\n",
+    "print(frame.shape)\n",
+    "# rescale\n",
+    "frame = scipy.ndimage.interpolation.zoom(frame, zoom = np.divide(128, frame.shape))\n",
+    "print(frame.shape)\n",
+    "\n",
+    "plt.imshow(frame, cmap = plt.get_cmap('gray'))\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
   {
    "cell_type": "code",
    "execution_count": 12,
@@ -47,13 +126,6 @@
     "ax.legend(loc=4)\n",
     "plt.show()"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
diff --git a/common/preprocess.py b/common/preprocess.py
new file mode 100644
index 0000000..4bbe9fc
--- /dev/null
+++ b/common/preprocess.py
@@ -0,0 +1,34 @@
+import numpy as np
+import scipy.ndimage
+
+
+def dqn_preprocess(frames, frames_to_stack=4, cropped_size=128.):
+    '''
+    preprocess following dqn nature paper
+    1. remove flickering: max(pixel) over previous frame
+    2. Convert RGB to greyscale
+    3. rescale to 84x84
+    4. do 1-4 for 4 frames and stack them
+    :param frames: last 5 frames of shape (210, 160, 3), we need 5 to perform the remove flickering step
+    :return: (84,84,4)
+    '''
+    RGB = 256
+    assert len(frames) == frames_to_stack + 1
+
+    processed_frames = []
+    for i in range(1, frames_to_stack + 1):
+        current_frame = frames[i]
+        prev_frame = frames[i - 1]
+        # step 1
+        frame = np.maximum(current_frame, prev_frame)
+        # step 2
+        # first normalise
+        assert np.amax(frame) <= RGB
+        frame = np.divide(frame, RGB)
+        frame = np.dot(frame[..., :3], [0.299, 0.587, 0.114])  # (210, 160)
+        # step 3
+        frame = scipy.ndimage.interpolation.zoom(frame, zoom=np.divide(cropped_size, frame.shape))
+
+        processed_frames.append(frame)
+
+    return np.dstack(processed_frames)
diff --git a/tests/test_proprocess.py b/tests/test_proprocess.py
new file mode 100644
index 0000000..4a419e9
--- /dev/null
+++ b/tests/test_proprocess.py
@@ -0,0 +1,17 @@
+import unittest
+
+import gym
+
+from common.preprocess import dqn_preprocess
+
+
+class TestPreprocess(unittest.TestCase):
+    def test_dqn_preprocess(self):
+        env = gym.make('BreakoutNoFrameskip-v0')
+        env.reset()
+        frames = []
+        for i in range(5):
+            observation, _, _, _ = env.step(env.action_space.sample())
+            frames.append(observation)
+        result = dqn_preprocess(frames)
+        assert result.shape == (128, 128, 4)