Music 320 lab 5
October 26, 2000

4. basic FIR filters

[bracketed comments refer to Matlab examples]

discussion: filtering in the time domain
   filtering as the universal "black box" operation on a signal

   FIR filters as the small subset of filtering with LTI properties
      linearity is particularly important in the frequency domain;
         modifying spectral content but not generating new frequencies
      causality is the "common sense" real world application
         but not always... signals stored on recording media can be 
	    filtered backwards (and it may be desirable to do so -- 
	    eliminating the phase shift created by a causal filter)

   virtues of FIR filters: 
      stability, design technique
   disadvantages:   
      increasing frequency precision requires increasing order
      FIR can be computationally expensive relative to "equivalent" IIR

   square wave demo:
      recall that a square wave can be considered as a sum of odd harmonics
      sharp edges are associated with high frequencies (the Gibbs phenomenon)
      [square wave in the time and frequency domain]

      one-zero FIR:
      y[n]=(a0*x[n])+(a1*x[n-1])
         set a0=1, a1=1
	 [y[n] in the time and frequency domain]
	 - smoothing associated with lowpass
	 - transient regions as filter engages and disengages
	 set a0=1, a1=-1
	 [y[n] in the time and frequency domain]

      running average filter
	 lowpass
	 [y[n] in the time and frequency domain]

      well-designed FIR:
         lowpass
	 [y[n] in the time and frequency domain]
	 highpass
	 [y[n] in the time and frequency domain]