The downsampling by a factor of 4 can introduce aliasing (because you upsampled only by a factor 2 in the first stage). If this is the case, it cannot be undone by the following upsampling operation. So in general this system will not produce at its output the original input signal $x[n]$.

up sample and down sample
I'm writing Integration Tests using nightwatch.js in a Node.js application. For a particular test case, I want nightwatch to connect via a proxy. What would be the right way to do this? I can't find anything from its official documentation, or from its Google Group.

The Selenium documentation suggests setting it on the webdriver instance as described here. I'm not sure how to do this via nightwatch.
