Question
11.
Design a first-order digital lowpass Chebyshev filter with a cutoff frequency of 1.5 kHz and a passband ripple of 1 dB at a sampling frequency of 8,000 Hz.
a. Determine the transfer function and difference equation.
b. Use MATLAB to plot the magnitude and phase frequency responses.

12.
Design a second-order digital lowpass Chebyshev filter with a cutoff frequency of 1.5 kHz and a passband ripple of 0.5 dB at a sampling frequency of 8,000 Hz. Use MATLAB to plot the magnitude and phase frequency responses.

13.
Design a third-order digital highpass Chebyshev filter with a cutoff frequency of 2 kHz and a passband ripple of 1 dB at a sampling frequency of 8,000 Hz.
a. Determine the transfer function and difference equation.
b. Use MATLAB to plot the magnitude and phase frequency responses.

14.
Design a second-order digital bandpass Chebyshev filter with the following specifications: Center frequency of 1.5 kHz
Bandwidth of 200 Hz
0.5 dB passband ripple
Sampling frequency of 8,000 Hz
a. Determine the transfer function and difference equation.
b. Use MATLAB to plot the magnitude and phase frequency responses.

15.
Design a second-order bandstop digital Chebyshev filter with the following specifications:
Center frequency of 2.5 kHz
Bandwidth of 200 Hz
1 dB stopband ripple
Sampling frequency of 8,000 Hz.
a. Determine the transfer function and difference equation.
b. Use MATLAB to plot the magnitude and phase frequency responses
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      • Illuminate\Database\Events\StatementPrepared (932μs)
      • Illuminate\Database\Events\QueryExecuted (1.08ms)
      • eloquent.retrieved: App\Models\SubjectCat (87μs)
      • Illuminate\Cache\Events\KeyWritten (313μs)
      • Illuminate\Cache\Events\CacheHit (1.29ms)
      • Illuminate\Cache\Events\CacheHit (241μs)
      • Illuminate\Cache\Events\CacheHit (153μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (124μs)
      • Illuminate\Cache\Events\CacheHit (384μs)
      • Illuminate\Cache\Events\CacheHit (171μs)
      • Illuminate\Cache\Events\CacheHit (146μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (128μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (119μs)
      • Illuminate\Cache\Events\CacheHit (101μs)
      • Illuminate\Cache\Events\CacheHit (115μs)
      • Illuminate\Cache\Events\CacheHit (100μs)
      • Illuminate\Cache\Events\CacheHit (116μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • creating: site.layouts.app (382μs)
      • composing: site.layouts.app (17μs)
      • creating: components.canonical (417μs)
      • composing: components.canonical (71μs)
      • creating: components.open-graph (149μs)
      • composing: components.open-graph (50μs)
      • creating: site.headers.header (232μs)
      • composing: site.headers.header (52μs)
      • Illuminate\Cache\Events\CacheHit (1.43ms)
      • creating: components.footer (77μs)
      • composing: components.footer (75μs)
      • Illuminate\Cache\Events\CacheHit (678μs)
      • Illuminate\Cache\Events\CacheMissed (251μs)
      • Illuminate\Database\Events\StatementPrepared (777μs)
      • Illuminate\Database\Events\QueryExecuted (1.12ms)
      • eloquent.retrieved: App\Models\SubjectCat (100μs)
      • Illuminate\Cache\Events\KeyWritten (448μs)
      • Illuminate\Cache\Events\CacheHit (524μs)
      • Illuminate\Cache\Events\CacheHit (159μs)
      • Illuminate\Cache\Events\CacheHit (141μs)
      • Illuminate\Cache\Events\CacheHit (138μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (363μs)
      • Illuminate\Cache\Events\CacheHit (342μs)
      • Illuminate\Cache\Events\CacheHit (223μs)
      • Illuminate\Cache\Events\CacheHit (203μs)
      • Illuminate\Cache\Events\CacheHit (191μs)
      • Illuminate\Cache\Events\CacheHit (209μs)
      • Illuminate\Cache\Events\CacheHit (184μs)
      • creating: components.forms.contact-us (311μs)
      • composing: components.forms.contact-us (200μs)
      • creating: components.forms.get-started (229μs)
      • composing: components.forms.get-started (142μs)
      • creating: components.forms.free-tool-download (162μs)
      • composing: components.forms.free-tool-download (80μs)
      • creating: components.forms.claim-free-worksheet (165μs)
      • composing: components.forms.claim-free-worksheet (74μs)
      • creating: components.forms.tutor-subscription-waitlist (140μs)
      • composing: components.forms.tutor-subscription-waitlist (83μs)
      • creating: components.forms.tutor-subscription-join (127μs)
      • composing: components.forms.tutor-subscription-join (58μs)
      • creating: components.forms.tutor-support (124μs)
      • composing: components.forms.tutor-support (71μs)
      • 311 x Illuminate\Cache\Events\CacheHit (14.85%)
        67.18ms
        20 x Illuminate\Database\Events\StatementPrepared (8.37%)
        37.87ms
        20 x Illuminate\Database\Events\QueryExecuted (5.52%)
        24.98ms
        11 x Illuminate\Cache\Events\CacheMissed (1.95%)
        8.83ms
        11 x Illuminate\Cache\Events\KeyWritten (1.11%)
        5.02ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.01%)
        4.58ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.31%)
        1.41ms
        1 x Illuminate\Routing\Events\Routing (0.31%)
        1.39ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.25%)
        1.15ms
        1 x Illuminate\Routing\Events\RouteMatched (0.13%)
        568μs
        6 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.12%)
        554μs
        1 x creating: homework.show (0.1%)
        471μs
        1 x creating: components.canonical (0.09%)
        417μs
        2 x eloquent.retrieved: App\Models\Subject (0.09%)
        415μs
        1 x creating: site.layouts.app (0.08%)
        382μs
        1 x eloquent.booting: App\Models\SubjectCat (0.08%)
        374μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.07%)
        322μs
        1 x creating: components.forms.contact-us (0.07%)
        311μs
        1 x creating: components.breadcrumbs (0.06%)
        291μs
        1 x composing: homework.show (0.06%)
        282μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.06%)
        267μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        241μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.05%)
        233μs
        1 x creating: site.headers.header (0.05%)
        232μs
        1 x creating: components.forms.get-started (0.05%)
        229μs
        1 x composing: components.forms.contact-us (0.04%)
        200μs
        1 x creating: components.forms.claim-free-worksheet (0.04%)
        165μs
        1 x creating: components.forms.free-tool-download (0.04%)
        162μs
        1 x creating: components.open-graph (0.03%)
        149μs
        1 x composing: components.forms.get-started (0.03%)
        142μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        140μs
        1 x creating: components.forms.tutor-subscription-join (0.03%)
        127μs
        1 x creating: components.forms.tutor-support (0.03%)
        124μs
        1 x composing: components.breadcrumbs (0.02%)
        104μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.02%)
        83μs
        1 x composing: components.forms.free-tool-download (0.02%)
        80μs
        1 x creating: components.footer (0.02%)
        77μs
        1 x composing: components.footer (0.02%)
        75μs
        1 x composing: components.forms.claim-free-worksheet (0.02%)
        74μs
        1 x composing: components.canonical (0.02%)
        71μs
        1 x composing: components.forms.tutor-support (0.02%)
        71μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        70μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        62μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        58μs
        1 x composing: site.headers.header (0.01%)
        52μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        51μs
        1 x composing: components.open-graph (0.01%)
        50μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        48μs
        1 x composing: site.layouts.app (0%)
        17μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated47.5ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '45752' limit 1
        20.24mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 45752
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (355)
        1.33mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (45752)
        1.77mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.16mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 10
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 45752 and `subject` = 355 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        2.67mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 45752
        • 1: 355
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (355)
        2.91mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 45752 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.24mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 45752
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 45752 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        1.17mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 45752
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 45752 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.24mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 45752
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.11mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 10
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.13mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.33mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.07mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.18mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.34mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.54mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.2mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.37mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.24mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.26mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      6HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          RzCeGZbK1SzYUmBs5uC1dTQwlTUt51zOQtvZc2BS
          utm_source
          direct
          redirectUrl
          /college-homework-library/Engineering/Communication-Engineering/45752
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          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Engineering/Com...
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          PHPDEBUGBAR_STACK_DATA
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          path_info
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          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
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          request_cookies
          []
          
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