title: How do I display a spectrogram from a wav file in C++?
body: <p>I am doing a project in which I want to embed images into a .wav file so that when one sees the spectrogram using certain parameters, they will see the hidden image. My question is, in C++, how can I use the data in a wav file to display a spectrogram without using any signal processing libraries?</p>
  <p>An explanation of the math (especially the Hanning window) will also be of great help, I am fairly new to signal processing. Also, since this is a very broad question, detailed steps are preferable over actual code.</p>
  <hr />
  <h3>Example:</h3>
  <p><em>above: output spectrogram;
  below: input audio waveform (.wav file)</em></p>
  <p><a href="https://i.stack.imgur.com/RJnhA.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/RJnhA.png" alt="above: output spectrogram; below: input audio waveform" /></a></p>