How to make an activity background transparent and blur the background

how to blur the background?

You can use RenderScript available in support library

public class BlurBuilder {
    private static final float BITMAP_SCALE = 0.4f;
    private static final float BLUR_RADIUS = 7.5f;

    public static Bitmap blur(Context context, Bitmap image) {
        int width = Math.round(image.getWidth() * BITMAP_SCALE);
        int height = Math.round(image.getHeight() * BITMAP_SCALE);

        Bitmap inputBitmap = Bitmap.createScaledBitmap(image, width, height, false);
        Bitmap outputBitmap = Bitmap.createBitmap(inputBitmap);

        RenderScript rs = RenderScript.create(context);
        ScriptIntrinsicBlur theIntrinsic = ScriptIntrinsicBlur.create(rs, Element.U8_4(rs));
        Allocation tmpIn = Allocation.createFromBitmap(rs, inputBitmap);
        Allocation tmpOut = Allocation.createFromBitmap(rs, outputBitmap);
        theIntrinsic.setRadius(BLUR_RADIUS);
        theIntrinsic.setInput(tmpIn);
        theIntrinsic.forEach(tmpOut);
        tmpOut.copyTo(outputBitmap);

        return outputBitmap;
    }
}

see this link for more details

Or you can use Blurry

Does anyone has an idea where is the code in android to do that?

For taking screenshot of your app screen see this link

I used this to give a blur effect to my edit text background, you can modify it according to your preference, play around with opacity:

<?xml version="1.0" encoding="utf-8"?><!--  res/drawable/rounded_edittext.xml -->
<shape xmlns:android="http://schemas.android.com/apk/res/android"
    android:shape="rectangle">
    <gradient
        android:centerColor="#33FFFFFF"
        android:endColor="#33FFFFFF"
        android:gradientRadius="270"
        android:startColor="#33FFFFFF"
        android:type="radial" />
    <corners
        android:bottomLeftRadius="25dp"
        android:bottomRightRadius="25dp"
        android:topLeftRadius="25dp"
        android:topRightRadius="25dp" />
</shape>

alternatively, you might be interested in this or this

As one more alternative you can use a small blur bitmap and repeat it:

    <xml version="1.0" encoding="utf-8"?>
    <LinearLayout
    android:id="@+id/MainLayout"
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent"
    android:orientation="vertical"
    android:background="@drawable/backrepeat"
    >

Then prepare:

    <bitmap xmlns:android="http://schemas.android.com/apk/res/android"
        android:src="@drawable/back" 
        android:tileMode="repeat" />