qgis - Increasing extent of Raster?

I have a Raster, which covers only the southern part of the country, like this:

I wish to have a Raster, which covers the entire country (including the North part)? The northern part should have the nodata values.

How do I do this using GDAL or QGIS?

( I do not have ArcGIS, so I can't use the answer given here: Increasing raster extent by filling extent with no data using ArcGIS Desktop without Spatial Analyst?)

I tried using gdalwarp's -te parameter; It was successful in reducing the extent, but did not extend the extent to the Northern part.

Answer

My suggested workflow:

1. 
   

   Create a polygon of the extent you want to cover

   
   
   


2. 
   

   rasterize the polygon

   
   


3. 
   

   fill it with a nodata value using gdalcalc

   
   


4. 
   

   add the existing raster with gdalwarp without the -overwrite option.