Chapter 12, Approximation Methods for Digital Filters Video Solutions, Synthesis of electrical networks

Problem 1

Design a low-pass Chebyshev digital filter with the following specifications:
Passband: $0-0.5 \mathrm{kHz}, 0.1 \mathrm{~dB}$ ripple
Stopband edge: $0.7 \mathrm{kHz}$, attenuation $\geq 40 \mathrm{~dB}$
Sampling frequency: $2 \mathrm{kHz}$

The realization is required in cascade form, and as a wave digital structure.

Check back soon!

Problem 2

Consider the transfer function of a third order elliptic lumped filter
$$
S_{21}(p)=\frac{0.314\left(p^2+2.806\right)}{(p+0.767)\left(p^2+0.453 p+1.149\right)}
$$
which gives a passband ripple of $0.5 \mathrm{~dB}$, a minimum stopband attenuation of $21 \mathrm{~dB}$, for $\omega_5 / \omega_0=1.5$.

Use the given prototype function to design a digital filter with passband edge at $500 \mathrm{~Hz}$ and a sampling frequency of $3 \mathrm{kHz}$.

Check back soon!

Problem 3

The following standard set of specifications are to be met by the transmit band-pass filter employed in a codec (coder-decoder) for PCM telephony,
Passband: $300-3200 \mathrm{~Hz}, 0.25 \mathrm{~dB}$ ripple
Stopband edge frequencies: $100 \mathrm{~Hz}$ and $4600 \mathrm{~Hz}$ with $32 \mathrm{~dB}$ minimum attenuation.

Design a Chebyshev digital filter which meets the above specifications. Use a lumped prototype function.

Check back soon!

Problem 4

Design a low-pass Chebyshev wave digital filter as a cascade of wave UEs to meet the following specifications:
Passband: $0-3.4 \mathrm{kHz}, 0.25 \mathrm{~dB}$ ripple
Stopband edge: $4.6 \mathrm{kHz}$, attenuation $\geq 30 \mathrm{~dB}$
Sampling frequency: $32 \mathrm{kHz}$
$50 \Omega$ equal termination.

Check back soon!

Problem 5

Consider the transfer function in (12.26) to (12.27) which possesses simultaneous maximally flat amplitude and group-delay at the origin $(\lambda=0)$. Show that the fifth degree function with $\alpha=10$ meets the following set of specifications:
Passband: $0-2.25 \mathrm{kHz}$, attenuation $\leq 1 \mathrm{~dB}$, delay variation $\leq 30 \mu \mathrm{s}$
Stopband: $3.6 \mathrm{kHz}-5 \mathrm{kHz}$, attenuation $\geq 15 \mathrm{~dB}$.

Realize the transfer function in cascade form.

Check back soon!