Digital Signal Processing in Experimental Research Volume Title: Fast Transform Methods in Digital Signal Processing

Discrete Fourier Transform and its Derivatives

Author(s): Leonid Yaroslavsky

Pp: 7-31 (25)

DOI: 10.2174/978160805230111101010007

* (Excluding Mailing and Handling)

Abstract

In this chapter, we provide basics of integral Fourier Transform and present discrete transforms originated from this very basic signal transform. We consider different versions of the Discrete Fourier Transform (DFT) that can be obtained in different conditions of signal sampling and introduce, as its important special case, Discrete Cosine Transform that proved to serve as an ideal substitution to DFT in all its applications.

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      • 13. app/Models/UserAccess/UserAccess.php:1266
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      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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      Backtrace
      • 13. app/Models/UserAccess/UserAccess.php:1266
      • 14. app/Http/Controllers/ChapterController.php:1549
      • 15. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
      • 16. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
      • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
    • select b.banner_link, b.banner_name, b.banner_script, b.banner_remarks, b.banner_file_name, b.banner_placement, bd.content_type, bd.content_id from `tbl_banner` as `b` inner join `tbl_banner_detail` as `bd` on `bd`.`banner_id` = `b`.`banner_id` inner join `users` as `u` on `u`.`id` = `b`.`updated_by` where `b`.`banner_ebook` = 1 and `bd`.`content_type` = 'B' and `bd`.`content_id` = 890 and `b`.`banner_from_date` <= 1740516382 and `b`.`banner_to_date` >= 1740516382 and `b`.`banner_status` = 'A' order by `b`.`banner_id` desc
      1.1msalphaeurekaselec_live_10_06_2022Banner.php#95
      Bindings
      • 0: 1
      • 1: B
      • 2: 890
      • 3: 1740516382
      • 4: 1740516382
      • 5: A
      Backtrace
      • 13. app/Models/Banner.php:95
      • 14. app/Http/helpers.php:404
      • 17. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 18. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    • select count(*) as aggregate from `uc_cart_products` where cart_id='73022e1d88bae8d1375daa8c2cbb134d'
      210μsalphaeurekaselec_live_10_06_2022Cart.php#271
      Backtrace
      • 15. app/Models/Cart.php:271
      • 16. view::layouts._header:260
      • 18. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:124
      • 19. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
      • 20. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:73
    App\Models\Chapter
    1Chapter.php#?
    App\Models\Keywords
    1Keywords.php#?
    App\Models\Ebook
    1Ebook.php#?
        _token
        AO5VltOpplVK5CVs10NnaaHTuV44r8E0BJaJZwIQ
        uc_cart_id
        73022e1d88bae8d1375daa8c2cbb134d
        _previous
        array:1 [ "url" => "http://alpha.eurekaselect.com/chapter/1392" ]
        _flash
        array:2 [ "old" => [] "new" => [] ]
        PHPDEBUGBAR_STACK_DATA
        []
        path_info
        /chapter/1392
        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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        ClearShow all
        Date ↕MethodURLData
        #12025-02-25 20:46:22GET/chapter/1392112193