Filter bank Analysis 

We can now assemble a set of band pass filters to analyse speech. These need to be covering - that is every frequency is covered by one filter so no information is lost.

An example of one filter is figure 10:

  
Figure 10: A band pass filter

The output is a waveform, but as the phase is not so important we need the magnitude or the energy - how?

• Rectify and smooth - convenient for hardware implementations
• Square and smooth - gives a better estimation of the power
• Hilbert transforms - generate a signal that is 90 degrees out of phase, then square both signals and add:
  
  

  If the filter bank is implemented as an FIR filter, a simple transform of the coefficients yields the phase shifted signal (use sine coefficients on instead of cosine coefficients).

 
• Spectrograms
• Non-linear frequency scales