Chapter 6, Problem 32

`}function getSectionHTML(section, chapter_number){ if (section.has_questions){ const current_section_id = ''; const active_str = current_section_id == section.id ? 'active' : ''; return `

${chapter_number}.${section.number} ${section.name}

` } return '';}function getProblemHTML(problem, appendix){ var active_str = problem.active == true ? 'active' : '' return `

`}function getProblemsHTML(problems, section_id){ var output = ''; var abc = " ABCDEFGHIJKLMNOPQRSTUWXYZ".split(""); var idx = 0; var last_problem = 0; for (let i = 0; i < problems.length; i++) { if (section_id == 0){ var times = Math.floor(idx/25)+1; var appendix = abc[idx%25+1].repeat(times) }else{ var appendix = ''; } output += getProblemHTML(problems[i], appendix) if (last_problem != problems[i].number){ idx = 1; }else{ idx = idx + 1; } last_problem = problems[i].number } return output;}function getChaptersHTML(chapters){ var output = ''; for (let i = 0; i < chapters.length; i++) { output += getChapterHTML(chapters[i]) } return output;}function getSectionsHTML(section, chapter_number){ var output = ''; for (let i = 0; i < section.length; i++) { output += getSectionHTML(section[i], chapter_number) } return output;}$(function(){ $.ajax({ url: `/api/v1/chapters/`, data:{ book_id : '26807' }, method: 'GET', success: function(res){ $("#book-chapters").html(getChaptersHTML(res)); $(".collapsable-chapter-arrow").on('click',function(e){ var section = $(this).siblings(".section-container"); var chapter_id = $(this).data('chapter-id') var chapter_number = $(this).data('chapter-number') if(section.is(":visible")){ $(this).removeClass('open'); section.hide('slow'); }else{ $(this).addClass('open'); section.show('slow') if (section.children('li').length == 0){ $.ajax({ url: `/api/v1/sections/`, data:{ chapter_id : chapter_id }, method: 'GET', success: function(res){ section.html(getSectionsHTML(res, chapter_number)) $(".collapsable-section-arrow").off('click').on('click',function(e){ var problems = $(this).siblings(".problem-container"); if(problems.is(":visible")){ $(this).removeClass('open'); problems.hide('slow'); }else{ var section_id = $(this).data('section-id'); var question_id = $(this).data('current-problem'); $(this).addClass('open'); problems.show('slow') if (problems.children('li').length == 0){ $.ajax({ url: `/api/v1/section/problems/`, data:{ section_id : section_id, question_id: question_id }, method: 'GET', success: function(res){ problems.html(getProblemsHTML(res, section_id)) }, error: function(err){ console.log(err); } }); } } }); if(first_section_load){ $(".collapsable-arrow.open").siblings(".section-container").find(`.collapsable-section-arrow[data-section-id=${current_section}]`).click(); first_section_load = false; } }, error: function(err){ console.log(err); } }); } } }); if(current_chapter && first_chapter_load){ $(`.collapsable-chapter-arrow[data-chapter-id=${current_chapter}]`).click(); first_chapter_load = false; } }, error: function(err){ console.log(err); } }); });

### Question

Answered step-by-step

Using the MATLAB functions ellipap, impulse and step:

(a) Determine the transfer function in polynomial form, and also factored to indicate the poles and zeros, of an elliptic filter with $\omega_p=1$, $A_p=1.2 \mathrm{~dB}, A_s=70 \mathrm{~dB}$, and $N=6$.

(b) Determine the impulse response and the step response for the filter of part (a).

(c) By multiplying the pole vector and the zero vector found in part (a) by $2 \pi 1000$ determine the transfer function of an elliptic filter with $f_p=1000 \mathrm{~Hz}, A_p=1.2 \mathrm{~dB}, A_s=70 \mathrm{~dB}$, and $N=6$.

(d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in $d B$ and a linear horizontal scale from 0 to $5000 \mathrm{~Hz}$. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap rather than plotting the principle phase.

(e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by $1 /(2 \pi 1000)$, and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of $2 \pi 1000$

(f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d).

(g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): $t_{g d}(n) \cong-[\phi(n)-\phi(n-1)] / S_s$, where $\phi(n)$ is the phase in radians at step $n$, and $S_s$ is the step size in $\mathrm{rad} / \mathrm{s}$.

### Video Answer

Get the answer to your homework problem.

Try Numerade free for 7 days

Input your name and email to request the answer

Numerade Educator

### Request a Custom Video Solution

We will assign your question to a Numerade educator to answer.

#### Answer Delivery Time

**You are asking**at 3:30PM Today

Using the MATLAB functions ellipap, impulse and step:(a) Determine the transfer function in polynomial form, and also factored to indicate the poles and zeros, of an elliptic filter with $\omega_p=1$, $A_p=1.2 \mathrm{~dB}, A_s=70 \mathrm{~dB}$, and $N=6$.(b) Determine the impulse response and the step response for the filter of part (a).(c) By multiplying the pole vector and the zero vector found in part (a) by $2 \pi 1000$ determine the transfer function of an elliptic filter with $f_p=1000 \mathrm{~Hz}, A_p=1.2 \mathrm{~dB}, A_s=70 \mathrm{~dB}$, and $N=6$.(d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in $d B$ and a linear horizontal scale from 0 to $5000 \mathrm{~Hz}$. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap rather than plotting the principle phase.(e) By appropriately scaling the impulse response and the step response of part (b), determine and plot the impulse response and the step response of the filter of part (c). That is, the time axis for the step response needs to scaled by $1 /(2 \pi 1000)$, and the unit impulse response needs the same time-axis scaling and requires an amplitude scaling of $2 \pi 1000$(f) Determine and plot the phase delay of the filter of part (c). Note that this is easily obtained from the phase response of part (d).(g) Determine and plot the group delay of the filter of part (c). Note that this also is easily obtained from the phase response of part (d): $t_{g d}(n) \cong-[\phi(n)-\phi(n-1)] / S_s$, where $\phi(n)$ is the phase in radians at step $n$, and $S_s$ is the step size in $\mathrm{rad} / \mathrm{s}$.

We’ll notify you at this email when your answer is ready.

## More Than Just

#### We take learning seriously. So we developed a line of study tools to help students learn their way.

#### Ace Chat

Your personal AI tutor, companion, and study partner. Available 24/7.

#### Ask Our Educators

Ask unlimited questions and get video answers from our expert STEM educators.

#### Notes & Exams

Millions of real past notes, study guides, and exams matched directly to your classes.

### Video Answers to Similar Questions

Best Matched Videos Solved By Our Expert Educators

### More Solved Questions in Your Textbook

Not your book?

#### Design and Analysis of Analog Filters: A Signal Processing Perspective

Chapter 6

** Chapter 1

** Chapter 2

** Chapter 3

** Chapter 4

** Chapter 5

** Chapter 6

** Chapter 7

** Chapter 8

** Chapter 9

** Chapter 10

** Chapter 11

Sections

Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34

### NO COMMENTS YET

Just now.