**Question 2**

Equation 8.10.2 in DSP First (MacLellan, Shafer, Yoder, Prentice Hall, 1998)

Approximates B, the width of the half-power, 3 dB passband, dependent on the absolute value of (1-r), the distance of the poles from the unit circle. For a real filter such as ours, where the poles are located within the unit circle, the equation becomes:

Where B is the bandwidth of the filter, and a is the magnitude of the poles, or their distance from the origin. For a bandwidth of 500 Hz (when the sampling frequency fS is 500 Hz) a=0.82198