Synthesis of electrical networks

H. Baher

Chapter 9 Synthesis of Digital Filters - all with Video Answers

Educators

Chapter Questions

Problem 1

Check the stability of the following transfer unctions, then realize each function in direct canonic form
$$
H(z)=\frac{z^{-1}\left(1+z^{-1}\right)}{1-0.5 z^{-1}+0.25 z^{-2}}
$$
$$
H(z)=\frac{z^{-1}\left(1-z^{-1}\right)^3}{1+1.75 z^{-1}+0.5 z^{-2}+0.25 z^{-3}+0.25 z^{-4}}
$$

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Problem 2

Find the non-recursive direct realization of the FIR transfer function
$$
H(z)=1+z^{-1}+z^{-2}+3 z^{-3}+5 z^{-4}+2 z^{-5}
$$

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Problem 3

Realize the following IIR transfer function once in cascade form, and a second time in parallel form
$$
H(z)=\frac{z^{-1}\left(1+z^{-1}\right)}{\left(1+0.75 z^{-1}\right)\left(1-0.5 z^{-1}+0.25 z^{-2}\right)}
$$

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03:05

Problem 4

Obtain the wave digital realization of the following transfer functions
$$
S_{21}(\lambda)=\frac{\left(1-\lambda^2\right)^{3 / 2}}{6+11 \lambda+6 \lambda^2+\lambda^3}
$$
$$
S_{21}(\lambda)=\frac{1}{\lambda^2+5 \lambda+6}
$$
both with $1 \Omega$ terminating resistors.

Amit Srivastava

Numerade Educator

Problem 5

By first transforming the transfer functions in Problem 9.4 into the $z^{-1}$-domain, realize each function in direct and casc de forms.

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Problem 6

Obtain the wave digital equivalent of the doubly terminated cascade of UEs shown in Fig. P9.6. Calculate the transfer fur tion of the filter and sketch its magnitude versus frequency for a sampling frequency of $20 \mathrm{kHz}$.

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Problem 7

Using the low-pass all-stub ladder filter shown in Fig. P9.7 as a reference filter, obtain a wave digital filter possessing the same transfer function, and having the true ladder topology. Sketch the magnitude of the filter transfer function against $\omega / \omega_{\mathrm{N}}$, where $\omega_{\mathrm{N}}$ is the radian sampling frequency.

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