Linear, recursive difference equation example
Noisy, discrete-time waveform
![[Graphics:../Images/index_gr_12.gif]](../Images/index_gr_12.gif)
![[Graphics:../Images/index_gr_13.gif]](../Images/index_gr_13.gif)
![[Graphics:../Images/index_gr_14.gif]](../Images/index_gr_14.gif)
![[Graphics:../Images/index_gr_15.gif]](../Images/index_gr_15.gif)
Experiment #1
Difference equation definition
![[Graphics:../Images/index_gr_16.gif]](../Images/index_gr_16.gif)
Initial condition and constant α
![[Graphics:../Images/index_gr_17.gif]](../Images/index_gr_17.gif)
Time domain
![[Graphics:../Images/index_gr_18.gif]](../Images/index_gr_18.gif)
![[Graphics:../Images/index_gr_19.gif]](../Images/index_gr_19.gif)
Frequency domain
![[Graphics:../Images/index_gr_20.gif]](../Images/index_gr_20.gif)
![[Graphics:../Images/index_gr_21.gif]](../Images/index_gr_21.gif)
Filter frequency response
![[Graphics:../Images/index_gr_22.gif]](../Images/index_gr_22.gif)
![[Graphics:../Images/index_gr_23.gif]](../Images/index_gr_23.gif)
![[Graphics:../Images/index_gr_24.gif]](../Images/index_gr_24.gif)
![[Graphics:../Images/index_gr_25.gif]](../Images/index_gr_25.gif)
![[Graphics:../Images/index_gr_26.gif]](../Images/index_gr_26.gif)
Experiment #2
Difference equation definition
![[Graphics:../Images/index_gr_27.gif]](../Images/index_gr_27.gif)
Initial condition and constant α
![[Graphics:../Images/index_gr_28.gif]](../Images/index_gr_28.gif)
Time domain
![[Graphics:../Images/index_gr_29.gif]](../Images/index_gr_29.gif)
![[Graphics:../Images/index_gr_30.gif]](../Images/index_gr_30.gif)
Frequency domain
![[Graphics:../Images/index_gr_31.gif]](../Images/index_gr_31.gif)
![[Graphics:../Images/index_gr_32.gif]](../Images/index_gr_32.gif)
Filter frequency response
![[Graphics:../Images/index_gr_33.gif]](../Images/index_gr_33.gif)
![[Graphics:../Images/index_gr_34.gif]](../Images/index_gr_34.gif)
![[Graphics:../Images/index_gr_35.gif]](../Images/index_gr_35.gif)
![[Graphics:../Images/index_gr_36.gif]](../Images/index_gr_36.gif)
![[Graphics:../Images/index_gr_37.gif]](../Images/index_gr_37.gif)
Experiment #3
Difference equation definition
![[Graphics:../Images/index_gr_38.gif]](../Images/index_gr_38.gif)
Initial condition and constant α
![[Graphics:../Images/index_gr_39.gif]](../Images/index_gr_39.gif)
Time domain
![[Graphics:../Images/index_gr_40.gif]](../Images/index_gr_40.gif)
![[Graphics:../Images/index_gr_41.gif]](../Images/index_gr_41.gif)
Frequency domain
![[Graphics:../Images/index_gr_42.gif]](../Images/index_gr_42.gif)
![[Graphics:../Images/index_gr_43.gif]](../Images/index_gr_43.gif)
Filter frequency response
![[Graphics:../Images/index_gr_44.gif]](../Images/index_gr_44.gif)
![[Graphics:../Images/index_gr_45.gif]](../Images/index_gr_45.gif)
![[Graphics:../Images/index_gr_46.gif]](../Images/index_gr_46.gif)
![[Graphics:../Images/index_gr_47.gif]](../Images/index_gr_47.gif)
![[Graphics:../Images/index_gr_48.gif]](../Images/index_gr_48.gif)
Converted by Mathematica
January 28, 2003