title: How to use Gaussian random numbers as input to a low pass filter
body: <p>I need to generate a Gaussian random numbers with zero mean and variance 2. Then use it as input to a low pass filter with cutt-off frequency of 1000Hz.</p>
  
  <p>I have generated the random number as:</p>
  
  <p><code>k = randn(1000,1) * sqrt(2);</code></p>
  
  <p>But I do not know how to proceed to use a low pass filter to filter it.</p>
  
  <p>And, how can I calculate the autocorrelation and power spectrum at input and output of the filter?</p>