Example

Create a digital lowpass filter with SPTool. The sampling frequency is 22050 Hz, the passband edge is at 1800 Hz (F_p), the stopband edge at 2400 Hz (F_s), the passband ripple 1 dB (R_p), the minimum stopband attenuation 40 dB (R_s).
Start with a filter of Butterworth IIR. Try next other IIR designs like elliptic one. Then, choose an equiripple FIR. What is the order of different algorithms? What are typical orders of IIR and FIR filters? How are the attenuations? What is the phase response and group delay of each filter?

Solution

1.

Open SPTool and the Filter Designer. Open Filter Viewer for observations.

2.

Choose Butterworth IIR from the popup-menu Algorithm. Set the sampling frequency and type specifications into the edit boxes in the left. Press enter in the keyboard after each value. After giving all values, press Apply button. The order of the filter should be 18, actual (measured) ripple 0.6471 dB and the 3dB point at 1887 Hz.

3.

Choose Elliptic IIR from the popup-menu Algorithm. Check that specifications stayed the same. Now the order should be 5. See the figures 3 (Designer) and 4 (Viewer).

4.

Choose Equiripple FIR from the popup-menu Algorithm. Now the order is as high as 52. The specifications are actually not met. Notice from the Filter Viewer that the phase is linear which implies that group delay is constant (52/2=26 time units), see the figures 5 and 6.

  

Figure 3: Filter Designer GUI for elliptic IIR. Notice the filter order in the right.

  

Figure 4: The corresponding Viewer for elliptic IIR of figure 3. There are four plots, magnitude and phase response of a filter, group delay (derivate of phase) and zero-pole-diagram.

  

Figure 5: The same design problem now with an equiripple FIR design.

  

Figure 6: The corresponding Viewer. See the higher order and linear-phase (constant group delay) of FIR.