Filtering a demodulated signal
If your required bandwidth is (say) 1 MHz then based on what you know about the noise, how much noise power is contained in the range DC to 1 MHz compared to how much is contained between 1 MHz and 99999999999 MHz (or more)?


  What is the need in filtering the demodulated signal and why is this
  needed before we can recover the signal?


Because it helps improve the signal to noise ratio and, in turn, makes data recovery more plausible.