Loop Filter Identification

For loop-filter design, we wish to minimize the error in

• partial decay time (set by amplitude response)
• partial overtone tuning (set by phase response)

Simple and effective method (MUS421 style):

• Estimate pitch (elaborated next page)
• Set Hamming FFT-window length to four periods
• Compute the short-time Fourier transform (STFT)
• Detect peaks in each spectral frame
• Connect peaks through time (amplitude envelopes)
• Amplitude envelopes must decay exponentially
• On a dB scale, exponential decay is a straight line
• Slope of straight line determines decay time-constant
• Can use 1st-order polyfit in Matlab or Octave
• For beating decay, connect amplitude envelope peaks
• Decay rates determine ideal amplitude response
• Partial tuning determines ideal phase response