title: How to recognize Low/High/Band pass filters after FFT?
body: <p>I'm having two zero padded signals in Matlab</p>
  
  <pre><code>h_1[n] = {...,0,0,1,2,1,0,0,...} 
  h_2[n] = {...,0,1,0,2,0,1,0,...}
  </code></pre>
  
  <p>and below you can see their <strong>FFT</strong> plots:</p>
  
  <pre><code>% N1 and N2 are just the lengths of h1 and h2.
  H1 = fft(h1, N1); 
  H2 = fft(h2, N2);
  
  % ...
  
  figure;
  from = -floor(length(H1)/2);
  to   = floor(length(H1)/2);
  stem(from:to, abs(H1));
  </code></pre>
  
  <p><img src="https://i.stack.imgur.com/EOmHq.png" alt="enter image description here"></p>
  
  <p><img src="https://i.stack.imgur.com/ktXPa.png" alt="enter image description here"></p>
  
  <p>My question is how one can decide whether those are low-,high- or band-pass filters.</p>
  
  <p>I know <strong>FFT</strong> decomposes my functions of time, here <code>h_1[n]</code> and <code>h_2[n]</code>, into the frequencies of which they are made up: <code>H_1[k]</code> and <code>H_2[k]</code> if I got that right but so far those plots tell me almost nothing.</p>
  
  <p>So how does one interpret those plots? I don't know why we had to add more zeros to <code>h_2[n]</code>, could this be to have a higher sampling rate?</p>
  
  <p>Thank you for any explanation!</p>