1.

For the filter below, determine the values of L and C so that

1. The magnitude response is maximally flat at ? = 0.

2. The group delay response is maximally flat at ? = 0.

Figure P.3-1

For each case H( j ?) is to be 3 dB down at ? = 1.

2.

The transfer function of an all-pass filter (Fig. 3-12 a) is

What is the ratio ?/ ? for maximally flat delay at ? = 0?

3.

Determine a ₁ and a ₂ so that f( x) = a ₁x + a ₂x ² approximates the function g( x) = in the least-squares sense over the interval 0 ? x ? 2 ( w ( x) = 1).

4.

For the Butterworth response, what is the order n necessary to obtain A _s decibels at ? ₃, when the response is 3 dB down at at ? = 1?

5.

Consider a Chebyshev filter ( n = 5) normalized for unity ripple-bandwidth. The passband ripple is 0.35 dB.

1. What is the filter attenuation at ? = 2?

2. What is the 3-dB frequency?

6.

Consider the third-order Chebyshev filter (0.1-dB passband ripple). What is the attenuation at twice the 3-dB frequency?

7.

Use the recursion formula to determine the fifth-order Bessel filter transfer function normalized for unit delay and...