Update readme.md

Author: swharden

projects/18-01-11_microphone_spectrograph/readme.md

@@ -1,2 +1,38 @@
 # Realtime Spectrograph
-write-up in progress...
+
+* **YouTube Demonstration: https://youtu.be/MS1Qgo710Vo**
+* This examples uses [naudio](https://github.com/naudio/NAudio) library to access the sound card
+* Unlike previous examples in this repository, the FFT is calculated using nAudio (not Accord)
+
+![](spectrograph.gif)
+
+## Example: FFT with NAudio
+```c#
+using NAudio.Wave; // for sound card access
+using NAudio.Dsp; // for FastFourierTransform
+```
+
+```c#
+// prepare the complex data which will be FFT'd
+Complex[] fft_buffer = new Complex[fft_size];
+for (int i=0; i < fft_size; i++)
+{
+    fft_buffer[i].X = (float)(unanalyzed_values[i] * FastFourierTransform.HammingWindow(i, fft_size));
+    fft_buffer[i].Y = 0;
+}
+
+// perform the FFT
+FastFourierTransform.FFT(true, (int)Math.Log(fft_size, 2.0), fft_buffer);
+
+// a list with FFT values
+List<double> new_data = new List<double>();
+for (int i = 0; i < spec_data[spec_data.Count - 1].Count; i++)
+{
+    // should this be sqrt(X^2+Y^2)?
+    double val;
+    val = (double)fft_buffer[i].X + (double)fft_buffer[i].Y;
+    val = Math.Abs(val);
+    if (checkBox1.Checked) val = Math.Log(val);
+    new_data.Add(val);
+}
+```