> 0000003117 00000 n >> 0000005682 00000 n /TR2 /Default endobj "F$H:R��!z��F�Qd?r9�\A&�G���rQ��h������E��]�a�4z�Bg�����E#H �*B=��0H�I��p�p�0MxJ$�D1��D, V���ĭ����KĻ�Y�dE�"E��I2���E�B�G��t�4MzN�����r!YK� ���?%_&�#���(��0J:EAi��Q�(�()ӔWT6U@���P+���!�~��m���D�e�Դ�!��h�Ӧh/��']B/����ҏӿ�?a0n�hF!��X���8����܌k�c&5S�����6�l��Ia�2c�K�M�A�!�E�#��ƒ�d�V��(�k��e���l ����}�}�C�q�9 /S /S << N'��)�].�u�J�r� /SA false 433 26 /ca 1 /N 3 endobj 0000028040 00000 n /op false ORTHOGONAL SETSWe are primarily interested in infinite sets of orthogonal >> 435 0 obj<>stream Thus the vector concepts like the inner product and orthogonality of vectors can be extended to func-tions. x�b```b``5d`e`�X��π �@1V�p!� ��`CF����.�F�G�k%�I\��� �!z�WC(��Aj߻8��L�-.�tx_TX��4e��͠)k5�L�֪z1� �ER|�5�s~��2r).x�u�����} /Border [0 0 0] 0000005815 00000 n 0000005444 00000 n /BS /Type /ExtGState /Filter /FlateDecode /AIS false /Type /Annot 2y�.-;!���K�Z� ���^�i�"L��0���-�� @8(��r�;q��7�L��y��&�Q��q�4�j���|�9�� 8 0 obj 0000013729 00000 n /D [7 0 R /Fit] trailer 433 0 obj<> endobj endobj 5 0 obj /A 6 0 R /Type /ExtGState stream �V��)g�B�0�i�W��8#�8wթ��8_�٥ʨQ����Q�j@�&�A)/��g�>'K�� �t�;\�� ӥ$պF�ZUn����(4T�%)뫔�0C&�����Z��i���8��bx��E���B�;�����P���ӓ̹�A�om?�W= 9 0 obj Orthogonal functions A function can be considered to be a generalization of a vector. %PDF-1.4 /SA false 0000005044 00000 n We have Zπ −π sin(3x) cos(3x)dx = 0 since sin(3x) cos(3x) is odd and the interval [−π,π] is symmetric about 0. 0 /BG2 /Default /Length 2571 ��w�G� xR^���[�oƜch�g�`>b���$���*~� �:����E���b��~���,m,�-��ݖ,�Y��¬�*�6X�[ݱF�=�3�뭷Y��~dó ���t���i�z�f�6�~`{�v���.�Ng����#{�}�}��������j������c1X6���fm���;'_9 �r�:�8�q�:��˜�O:ϸ8������u��Jq���nv=���M����m����R 4 � 0000002115 00000 n Analogy between functions of time and vectors 2. /TK true /CA 1 /TR2 /Default 0000027645 00000 n H���yTSw�oɞ����c [���5la�QIBH�ADED���2�mtFOE�.�c��}���0��8�׎�8G�Ng�����9�w���߽��� �'����0 �֠�J��b� << Orthogonal Functions and Fourier Series. /Rect [71.804695 711.493469 332.707489 729.758057] 6 0 obj /UCR2 /Default •Example: f(x) = sin(3x), g(x) = cos(3x). >> /SM 0.02 For then ⁡ ⁡ = ⁡ ((−)) − ⁡ ((+)), and the integral of the product of the two sine functions vanishes. Periodic signals can be represented as a sum of sinusoidal functions. endobj 0000006272 00000 n /HT /Default �ꇆ��n���Q�t�}MA�0�al������S�x ��k�&�^���>�0|>_�'��,�G! W�$Tdr�&m;�X�x�C�R'��$�:���H(�*. %%EOF Orthogonal Functions and Fourier Series March 17, 2008 Today’s Topics 1. 0000000833 00000 n /Subtype /Link 0000002517 00000 n 0000001970 00000 n 0000006768 00000 n << %PDF-1.4 %���� /W 0 0000003040 00000 n A familiar example is Fourier series, where the function is a periodic function on the interval ( L=2;L=2). /H /N << In this section we will define periodic functions, orthogonal functions and mutually orthogonal functions. %���� /OPM 0 0000014844 00000 n We will also work a couple of examples showing intervals on which cos( n pi x / L) and sin( n pi x / L) are mutually orthogonal. /OP false /BM /Normal xref 0000003153 00000 n 0000013532 00000 n 0000006528 00000 n 0000000016 00000 n Orthogonal Functions -Orthogonal Functions -DDefinitionefinition ... another Example ... f (x) =x2, 0 > >> 0000007475 00000 n For example, the sine functions sin nx and sin mx are orthogonal on the interval ∈ (−,) when ≠ and n and m are positive integers. Fourier series Take Away Periodic complex exponentials have properties analogous to vectors in n dimensional spaces. n�3ܣ�k�Gݯz=��[=��=�B�0FX'�+������t���G�,�}���/���Hh8�m�W�2p[����AiA��N�#8$X�?�A�KHI�{!7�. << "/> > 0000003117 00000 n >> 0000005682 00000 n /TR2 /Default endobj "F$H:R��!z��F�Qd?r9�\A&�G���rQ��h������E��]�a�4z�Bg�����E#H �*B=��0H�I��p�p�0MxJ$�D1��D, V���ĭ����KĻ�Y�dE�"E��I2���E�B�G��t�4MzN�����r!YK� ���?%_&�#���(��0J:EAi��Q�(�()ӔWT6U@���P+���!�~��m���D�e�Դ�!��h�Ӧh/��']B/����ҏӿ�?a0n�hF!��X���8����܌k�c&5S�����6�l��Ia�2c�K�M�A�!�E�#��ƒ�d�V��(�k��e���l ����}�}�C�q�9 /S /S << N'��)�].�u�J�r� /SA false 433 26 /ca 1 /N 3 endobj 0000028040 00000 n /op false ORTHOGONAL SETSWe are primarily interested in infinite sets of orthogonal >> 435 0 obj<>stream Thus the vector concepts like the inner product and orthogonality of vectors can be extended to func-tions. x�b```b``5d`e`�X��π �@1V�p!� ��`CF����.�F�G�k%�I\��� �!z�WC(��Aj߻8��L�-.�tx_TX��4e��͠)k5�L�֪z1� �ER|�5�s~��2r).x�u�����} /Border [0 0 0] 0000005815 00000 n 0000005444 00000 n /BS /Type /ExtGState /Filter /FlateDecode /AIS false /Type /Annot 2y�.-;!���K�Z� ���^�i�"L��0���-�� @8(��r�;q��7�L��y��&�Q��q�4�j���|�9�� 8 0 obj 0000013729 00000 n /D [7 0 R /Fit] trailer 433 0 obj<> endobj endobj 5 0 obj /A 6 0 R /Type /ExtGState stream �V��)g�B�0�i�W��8#�8wթ��8_�٥ʨQ����Q�j@�&�A)/��g�>'K�� �t�;\�� ӥ$պF�ZUn����(4T�%)뫔�0C&�����Z��i���8��bx��E���B�;�����P���ӓ̹�A�om?�W= 9 0 obj Orthogonal functions A function can be considered to be a generalization of a vector. %PDF-1.4 /SA false 0000005044 00000 n We have Zπ −π sin(3x) cos(3x)dx = 0 since sin(3x) cos(3x) is odd and the interval [−π,π] is symmetric about 0. 0 /BG2 /Default /Length 2571 ��w�G� xR^���[�oƜch�g�`>b���$���*~� �:����E���b��~���,m,�-��ݖ,�Y��¬�*�6X�[ݱF�=�3�뭷Y��~dó ���t���i�z�f�6�~`{�v���.�Ng����#{�}�}��������j������c1X6���fm���;'_9 �r�:�8�q�:��˜�O:ϸ8������u��Jq���nv=���M����m����R 4 � 0000002115 00000 n Analogy between functions of time and vectors 2. /TK true /CA 1 /TR2 /Default 0000027645 00000 n H���yTSw�oɞ����c [���5la�QIBH�ADED���2�mtFOE�.�c��}���0��8�׎�8G�Ng�����9�w���߽��� �'����0 �֠�J��b� << Orthogonal Functions and Fourier Series. /Rect [71.804695 711.493469 332.707489 729.758057] 6 0 obj /UCR2 /Default •Example: f(x) = sin(3x), g(x) = cos(3x). >> /SM 0.02 For then ⁡ ⁡ = ⁡ ((−)) − ⁡ ((+)), and the integral of the product of the two sine functions vanishes. Periodic signals can be represented as a sum of sinusoidal functions. endobj 0000006272 00000 n /HT /Default �ꇆ��n���Q�t�}MA�0�al������S�x ��k�&�^���>�0|>_�'��,�G! W�$Tdr�&m;�X�x�C�R'��$�:���H(�*. %%EOF Orthogonal Functions and Fourier Series March 17, 2008 Today’s Topics 1. 0000000833 00000 n /Subtype /Link 0000002517 00000 n 0000001970 00000 n 0000006768 00000 n << %PDF-1.4 %���� /W 0 0000003040 00000 n A familiar example is Fourier series, where the function is a periodic function on the interval ( L=2;L=2). /H /N << In this section we will define periodic functions, orthogonal functions and mutually orthogonal functions. %���� /OPM 0 0000014844 00000 n We will also work a couple of examples showing intervals on which cos( n pi x / L) and sin( n pi x / L) are mutually orthogonal. /OP false /BM /Normal xref 0000003153 00000 n 0000013532 00000 n 0000006528 00000 n 0000000016 00000 n Orthogonal Functions -Orthogonal Functions -DDefinitionefinition ... another Example ... f (x) =x2, 0 > >> 0000007475 00000 n For example, the sine functions sin nx and sin mx are orthogonal on the interval ∈ (−,) when ≠ and n and m are positive integers. Fourier series Take Away Periodic complex exponentials have properties analogous to vectors in n dimensional spaces. n�3ܣ�k�Gݯz=��[=��=�B�0FX'�+������t���G�,�}���/���Hh8�m�W�2p[����AiA��N�#8$X�?�A�KHI�{!7�. << "> > 0000003117 00000 n >> 0000005682 00000 n /TR2 /Default endobj "F$H:R��!z��F�Qd?r9�\A&�G���rQ��h������E��]�a�4z�Bg�����E#H �*B=��0H�I��p�p�0MxJ$�D1��D, V���ĭ����KĻ�Y�dE�"E��I2���E�B�G��t�4MzN�����r!YK� ���?%_&�#���(��0J:EAi��Q�(�()ӔWT6U@���P+���!�~��m���D�e�Դ�!��h�Ӧh/��']B/����ҏӿ�?a0n�hF!��X���8����܌k�c&5S�����6�l��Ia�2c�K�M�A�!�E�#��ƒ�d�V��(�k��e���l ����}�}�C�q�9 /S /S << N'��)�].�u�J�r� /SA false 433 26 /ca 1 /N 3 endobj 0000028040 00000 n /op false ORTHOGONAL SETSWe are primarily interested in infinite sets of orthogonal >> 435 0 obj<>stream Thus the vector concepts like the inner product and orthogonality of vectors can be extended to func-tions. x�b```b``5d`e`�X��π �@1V�p!� ��`CF����.�F�G�k%�I\��� �!z�WC(��Aj߻8��L�-.�tx_TX��4e��͠)k5�L�֪z1� �ER|�5�s~��2r).x�u�����} /Border [0 0 0] 0000005815 00000 n 0000005444 00000 n /BS /Type /ExtGState /Filter /FlateDecode /AIS false /Type /Annot 2y�.-;!���K�Z� ���^�i�"L��0���-�� @8(��r�;q��7�L��y��&�Q��q�4�j���|�9�� 8 0 obj 0000013729 00000 n /D [7 0 R /Fit] trailer 433 0 obj<> endobj endobj 5 0 obj /A 6 0 R /Type /ExtGState stream �V��)g�B�0�i�W��8#�8wթ��8_�٥ʨQ����Q�j@�&�A)/��g�>'K�� �t�;\�� ӥ$պF�ZUn����(4T�%)뫔�0C&�����Z��i���8��bx��E���B�;�����P���ӓ̹�A�om?�W= 9 0 obj Orthogonal functions A function can be considered to be a generalization of a vector. %PDF-1.4 /SA false 0000005044 00000 n We have Zπ −π sin(3x) cos(3x)dx = 0 since sin(3x) cos(3x) is odd and the interval [−π,π] is symmetric about 0. 0 /BG2 /Default /Length 2571 ��w�G� xR^���[�oƜch�g�`>b���$���*~� �:����E���b��~���,m,�-��ݖ,�Y��¬�*�6X�[ݱF�=�3�뭷Y��~dó ���t���i�z�f�6�~`{�v���.�Ng����#{�}�}��������j������c1X6���fm���;'_9 �r�:�8�q�:��˜�O:ϸ8������u��Jq���nv=���M����m����R 4 � 0000002115 00000 n Analogy between functions of time and vectors 2. /TK true /CA 1 /TR2 /Default 0000027645 00000 n H���yTSw�oɞ����c [���5la�QIBH�ADED���2�mtFOE�.�c��}���0��8�׎�8G�Ng�����9�w���߽��� �'����0 �֠�J��b� << Orthogonal Functions and Fourier Series. /Rect [71.804695 711.493469 332.707489 729.758057] 6 0 obj /UCR2 /Default •Example: f(x) = sin(3x), g(x) = cos(3x). >> /SM 0.02 For then ⁡ ⁡ = ⁡ ((−)) − ⁡ ((+)), and the integral of the product of the two sine functions vanishes. Periodic signals can be represented as a sum of sinusoidal functions. endobj 0000006272 00000 n /HT /Default �ꇆ��n���Q�t�}MA�0�al������S�x ��k�&�^���>�0|>_�'��,�G! W�$Tdr�&m;�X�x�C�R'��$�:���H(�*. %%EOF Orthogonal Functions and Fourier Series March 17, 2008 Today’s Topics 1. 0000000833 00000 n /Subtype /Link 0000002517 00000 n 0000001970 00000 n 0000006768 00000 n << %PDF-1.4 %���� /W 0 0000003040 00000 n A familiar example is Fourier series, where the function is a periodic function on the interval ( L=2;L=2). /H /N << In this section we will define periodic functions, orthogonal functions and mutually orthogonal functions. %���� /OPM 0 0000014844 00000 n We will also work a couple of examples showing intervals on which cos( n pi x / L) and sin( n pi x / L) are mutually orthogonal. /OP false /BM /Normal xref 0000003153 00000 n 0000013532 00000 n 0000006528 00000 n 0000000016 00000 n Orthogonal Functions -Orthogonal Functions -DDefinitionefinition ... another Example ... f (x) =x2, 0 > >> 0000007475 00000 n For example, the sine functions sin nx and sin mx are orthogonal on the interval ∈ (−,) when ≠ and n and m are positive integers. Fourier series Take Away Periodic complex exponentials have properties analogous to vectors in n dimensional spaces. n�3ܣ�k�Gݯz=��[=��=�B�0FX'�+������t���G�,�}���/���Hh8�m�W�2p[����AiA��N�#8$X�?�A�KHI�{!7�. << ">

salford city fc fixtures

Orthogonal Functions contd. >> 0000001474 00000 n /S /GoTo University of Texas at Austin CS384G - Computer Graphics Spring 2010 Don Fussell Vector Spaces Set of vectors Closed under the following operations Vector addition: v 1 + v 2 = v 3 Scalar multiplication: s v 1 = v 2 Linear combinations: Scalars come from some field F e.g. 0000001659 00000 n /Type /Border 0000027414 00000 n 4 0 obj [5 0 R] �x������- �����[��� 0����}��y)7ta�����>j���T�7���@���tܛ�`q�2��ʀ��&���6�Z�L�Ą?�_��yxg)˔z���çL�U���*�u�Sk�Se�O4?׸�c����.� � �� R� ߁��-��2�5������ ��S�>ӣV����d�`r��n~��Y�&�+`��;�A4�� ���A9� =�-�t��l�`;��~p���� �Gp| ��[`L��`� "A�YA�+��Cb(��R�,� *�T�2B-� endobj << 0000003375 00000 n For example, the functions f 1(x) x2 and f 2(x) x3 are orthogonal on the interval [ 1, 1], since Unlike in vector analysis, in which the word orthogonal is a synonym for perpendic- ular, in this present context the term orthogonal and condition (1) have no geometric significance. 0000007054 00000 n /SMask /None <]>> 0000003117 00000 n >> 0000005682 00000 n /TR2 /Default endobj "F$H:R��!z��F�Qd?r9�\A&�G���rQ��h������E��]�a�4z�Bg�����E#H �*B=��0H�I��p�p�0MxJ$�D1��D, V���ĭ����KĻ�Y�dE�"E��I2���E�B�G��t�4MzN�����r!YK� ���?%_&�#���(��0J:EAi��Q�(�()ӔWT6U@���P+���!�~��m���D�e�Դ�!��h�Ӧh/��']B/����ҏӿ�?a0n�hF!��X���8����܌k�c&5S�����6�l��Ia�2c�K�M�A�!�E�#��ƒ�d�V��(�k��e���l ����}�}�C�q�9 /S /S << N'��)�].�u�J�r� /SA false 433 26 /ca 1 /N 3 endobj 0000028040 00000 n /op false ORTHOGONAL SETSWe are primarily interested in infinite sets of orthogonal >> 435 0 obj<>stream Thus the vector concepts like the inner product and orthogonality of vectors can be extended to func-tions. x�b```b``5d`e`�X��π �@1V�p!� ��`CF����.�F�G�k%�I\��� �!z�WC(��Aj߻8��L�-.�tx_TX��4e��͠)k5�L�֪z1� �ER|�5�s~��2r).x�u�����} /Border [0 0 0] 0000005815 00000 n 0000005444 00000 n /BS /Type /ExtGState /Filter /FlateDecode /AIS false /Type /Annot 2y�.-;!���K�Z� ���^�i�"L��0���-�� @8(��r�;q��7�L��y��&�Q��q�4�j���|�9�� 8 0 obj 0000013729 00000 n /D [7 0 R /Fit] trailer 433 0 obj<> endobj endobj 5 0 obj /A 6 0 R /Type /ExtGState stream �V��)g�B�0�i�W��8#�8wթ��8_�٥ʨQ����Q�j@�&�A)/��g�>'K�� �t�;\�� ӥ$պF�ZUn����(4T�%)뫔�0C&�����Z��i���8��bx��E���B�;�����P���ӓ̹�A�om?�W= 9 0 obj Orthogonal functions A function can be considered to be a generalization of a vector. %PDF-1.4 /SA false 0000005044 00000 n We have Zπ −π sin(3x) cos(3x)dx = 0 since sin(3x) cos(3x) is odd and the interval [−π,π] is symmetric about 0. 0 /BG2 /Default /Length 2571 ��w�G� xR^���[�oƜch�g�`>b���$���*~� �:����E���b��~���,m,�-��ݖ,�Y��¬�*�6X�[ݱF�=�3�뭷Y��~dó ���t���i�z�f�6�~`{�v���.�Ng����#{�}�}��������j������c1X6���fm���;'_9 �r�:�8�q�:��˜�O:ϸ8������u��Jq���nv=���M����m����R 4 � 0000002115 00000 n Analogy between functions of time and vectors 2. /TK true /CA 1 /TR2 /Default 0000027645 00000 n H���yTSw�oɞ����c [���5la�QIBH�ADED���2�mtFOE�.�c��}���0��8�׎�8G�Ng�����9�w���߽��� �'����0 �֠�J��b� << Orthogonal Functions and Fourier Series. /Rect [71.804695 711.493469 332.707489 729.758057] 6 0 obj /UCR2 /Default •Example: f(x) = sin(3x), g(x) = cos(3x). >> /SM 0.02 For then ⁡ ⁡ = ⁡ ((−)) − ⁡ ((+)), and the integral of the product of the two sine functions vanishes. Periodic signals can be represented as a sum of sinusoidal functions. endobj 0000006272 00000 n /HT /Default �ꇆ��n���Q�t�}MA�0�al������S�x ��k�&�^���>�0|>_�'��,�G! W�$Tdr�&m;�X�x�C�R'��$�:���H(�*. %%EOF Orthogonal Functions and Fourier Series March 17, 2008 Today’s Topics 1. 0000000833 00000 n /Subtype /Link 0000002517 00000 n 0000001970 00000 n 0000006768 00000 n << %PDF-1.4 %���� /W 0 0000003040 00000 n A familiar example is Fourier series, where the function is a periodic function on the interval ( L=2;L=2). /H /N << In this section we will define periodic functions, orthogonal functions and mutually orthogonal functions. %���� /OPM 0 0000014844 00000 n We will also work a couple of examples showing intervals on which cos( n pi x / L) and sin( n pi x / L) are mutually orthogonal. /OP false /BM /Normal xref 0000003153 00000 n 0000013532 00000 n 0000006528 00000 n 0000000016 00000 n Orthogonal Functions -Orthogonal Functions -DDefinitionefinition ... another Example ... f (x) =x2, 0 > >> 0000007475 00000 n For example, the sine functions sin nx and sin mx are orthogonal on the interval ∈ (−,) when ≠ and n and m are positive integers. Fourier series Take Away Periodic complex exponentials have properties analogous to vectors in n dimensional spaces. n�3ܣ�k�Gݯz=��[=��=�B�0FX'�+������t���G�,�}���/���Hh8�m�W�2p[����AiA��N�#8$X�?�A�KHI�{!7�. <<

Badminton Court Size In Meter, My Christmas Love Soundtrack, Mc Eiht New Album, Screaming Yourself Awake, Best Tristar Movies, William Makepeace Thackeray Biography,

Featured Bookie
Solarbet
New Casinos
3.5 rating
Indulge in a four way Welcome bonus in KingBilly online casino!
3.5 rating
Claim your $800 Welcome Bonus today!
3.3 rating
Start playing and get 200% Welcome Bonus!
ThinkBookie
© Copyright 2020 ThinkBookie.com