# decimation and interpolation in dsp pdf

The interpolation filter has many zeros in its input signal, as illustrated by the direct interpolation filter structure on the left in Figure 2. • Resampling with Rational Factor: Interpolation by L and decimation by M can be com-bined to change the eﬀective sampling rate of a signal by the rational factor L M. This process is called “resampling” or “sample-rate conversion”. Finally a number of multiplierless 5th and 10th order elliptic filter designs are presented which are applicable to efficient polyphase interpolation and decimation. endstream endobj 381 0 obj <>/Encoding<>>>>> endobj 58 0 obj <> endobj 59 0 obj <> endobj 301 0 obj <> endobj 267 0 obj <> endobj 234 0 obj <> endobj 201 0 obj <> endobj 143 0 obj <> endobj 60 0 obj <> endobj 61 0 obj <> endobj 43 0 obj <>/ProcSet[/PDF/ImageC/ImageB/ImageI]>>/Type/Page>> endobj 46 0 obj <>/ProcSet[/PDF/ImageC/ImageB/ImageI]>>/Type/Page>> endobj 49 0 obj <>/ProcSet[/PDF/ImageC/ImageB/ImageI]>>/Type/Page>> endobj 52 0 obj <>/ProcSet[/PDF/ImageC/ImageB/ImageI]>>/Type/Page>> endobj 55 0 obj <>/ProcSet[/PDF/ImageC/ImageB/ImageI]>>/Type/Page>> endobj 56 0 obj <>stream If we upsample by factor L to get v[m], the desired portion of V(ejω) is the spectrum in −π L, Then the techniques of decimation and interpolation enable this operation, providing the ratio T1/T2 is a rational number i.e. Interpolation and decimation . Download as PDF. Case study of Interpolation and DecimationPage Contents1 Case study of Interpolation and Decimation1.0.1 THEORY1.0.2 Sampling:1.0.3 Downsampling (Decimation):1.0.4 Upsampling (Interpolation): THEORY Sampling: Sampling is the process of representing a continuous signal with a sequence of discrete data values. h�bbd```b``��! The CIC Decimation block performs a sample rate decrease (decimation) on an input signal by an integer factor. 15. ��OB4����Ԙ�OZM�4�[��Z�'K�Z ս��Z�K���k��o�g�{*��Y�"��]8����]ukI�ӓu��a}���r�i$�J���I������꿯���+�{���:I?T���k��/����/[�_O}/KkK��������k���������^���UuV�W���]%�v�������U�;)]Ҵ��Z�vP����'K�z��u���q~kk���+��A+���=5� ��K��-���'K��WɲP4��A�V�?^ 2. uuid:4be995db-6968-a44e-8d94-56cd6b0650c2 1.1 Decimation and Interpolation 1.2 Digital Filter Banks Basic Multi-rate Operations: Decimation and Interpolation Building blocks for traditional single-rate digital signal processing: multiplier (with a constant), adder, delay, multiplier (of 2 signals) New building blocks in multi-rate signal processing: M-fold decimator L-fold expander Readings: Vaidyanathan Book x4.1; tutorial Sec. Good questions! The block supports real and complex fixed-point inputs. endstream endobj 128 0 obj <> endobj 129 0 obj <> endobj 130 0 obj <>stream 0�G��Td��-Q�Z��Z� 0�G������ 0�F@aj� 0�G�Tr��]�S�{��������-_��-Q����@aj���ҿ��w��m�ˢ������,�.6����@aj�������2T|���������`f,��A��)�}Q�^ d��1��,�#�2ʡQ�? Each TMS320C80 DSP parallel processor (PP) contains four major units operating in parallel. 9.2 Decimation Decimation can be regarded as the discrete-time counterpart of sampling. Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals. between the sampling playback rates so that you don't have to keep reloading code to the DSP! Let us assume that the signal x(n) with spectrum X( ) is to be down sampled by an integer factor D. The spectrum X( ) is assumed to be �uy�Q4nJ�T� j�W��#� �U˚ Choosing a filter implementation that is appropriate for the targeted application helps ensure proper operation at minimum cost with respect to the designMultirateFIR(L,M) designs an FIR filter for interpolation by an integer factor L and decimation by an integer factor M. designMultirateFIR returns filter coefficients. 141 0 obj <>/Filter/FlateDecode/ID[<96B5F680F483E53ADCD832CB0859C2A2>]/Index[127 25]/Info 126 0 R/Length 84/Prev 629771/Root 128 0 R/Size 152/Type/XRef/W[1 3 1]>>stream %PDF-1.6 %���� Explain the decimation and interpolation process with an example. Abstract: The concepts of digital signal processing are playing an increasingly important role in the area of multirate signal processing, i.e. The sampling rate Fs refers to the input signal. Multirate DSP Using Decimation and Interpolation 2.1. In this case, we must use a process called decimation to reduce the sampling rate of the signal. ���T�����8$�!Ӻ�a'K���=/20�U�W����$� ��J݊`��U������b�wt�_��M���t���1��U� ��]�� �|�`��ީ_��g�S2P��/��!��C�?��ү�����>�z����y�E�����餙� q�^�'5��~s��[�{U�P��%����v�~:֕m���}�����klWD�j��2�>EG�q_̆�0�kD�z���$�K���0���}�������\�,�^}]��/]_���w��_'�n4�}�:�t���gu�~�K��`���� .��M���(�t3���!ܥS� �z2&���H��?��$U���!�< ?��@���Ț���8)u�u�� eÑ���u�q�mׯ�����Ր&9�?o�91�DG�U�LٴG��q�Qs#�p��$"%@(#�!���0���j�5}�$6 �qE2Hک����A! ;���84 Should I multiply the output signal for each stage by a constant value? Resample uniform or nonuniform data to a new fixed rate. – Higher sampling rate preserves ﬁdelity. Solution: Decimation and Interpolation are two techniques used to alter the sampling rate of a sequence. �>����;E�I�l���|�e�7��)����}��S���5:���WwW��bY'v:��fs����c��Q�rg��~g���!یKwpC9��N���ē�͔t��Bۿ�v�ucs @���,��̔��]�Jѓϕz�I�$��e�F7����y_��j ���{-b��*�0��-{]�R���zT��G_dH9v�E\�ڸ� The filter sample rate is 2x > the input series. The group delay variation can be minimised by adding all-pass equaliser sections. tors, decimation and interpolation filters, and digital filter banks, are reviewed, along with the interconnection prop- erties of the building blocks. Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals. Myself, I've experimented with cubic interpolation in audio applications and it sounded better than linear … Decimation, interpolation, downsampling, upsampling, antialiasing filter. 1.1.1 Floating point Floating point is a method to represent real numbers. DSP operations can use either floating-point or fixed-point formats. ߟ�DDDH[)9C��9��zYP����{�9zl?���^`2@�},�����ȻV���~��>G��d(�du����,KB@�P_i� �]P7��6�Vu��V��b""���������ԈlR�H�*�q^��8����$�����S�s����nx(2�!�����R p�������#�d��{ DDDDD2�dc:�&{!���$0�t� x**\�^�*�2�(C� d�l6! As with decimation, in practice an acceptable transition width needs to be incorporated into the design of the lowpass filter used for interpolation along with passband ripple and a finite stopband attenuation. In section Ill, some applica- tions of multirate DSP are indicated, in digital audio sys- tems, in subband coding, and in voice privacy systems. 2.4.7 How do I test a FIR decimator? ��) Ќ�T� �����*e2�1�,Z&DA"f�X �Q���Z�EYl,z��9��0�V��ר�%�2&�Z#��BFe%����ڦ�}c� ]Ð*��,�x���9�$�l,~Q�x5�����:����6�V�W9�n���.��'P_��j���}���5�������������%��P2� ���_\�����B2�;ɷ �E>�k��龀���mL�8`A3�w�i�����"���@���"���V��-ґ�� �E����+`L&VK X���1�G�������5ܒ��M���/ u�5� �QDv��B��. 14. Audio application such as to plot a time and frequency display of microphone plus a cosine using DSP. Decimation (DDC) and Interpolation (DUC) Concepts TIPL 4701 Presented by Jim Seton Prepared by Jim Seton 1. L/M. It can be applied for the derivation of new sampling theorems and the recovering bandlim-ited signal from nonuniformly sampled versions. 16. – Higher sampling rate preserves ﬁdelity. Filter Decimation Summarized (1) x n h n M w n y m k w n h k x n k y m w mM k k y m h k x mM k h mM k x k Assume a causal FIR filter of length M: From: R.E. 14. system are decreasing (decimation) and increasing (interpolation) the sampling-rate of a signal. 13. The combination of an analog or digital delta‐sigma modulator with its companion digital decimation or interpolation functions constitutes a full delta‐sigma analog‐to‐digital converters (ADC) or digital to analog converters (DAC) system. 3.26 for L = 3 with the assumption of ideal decimation and interpolation filters. Chapter 2, p. 31-39. %PDF-1.5 %���� Example of Decimation and Interpolation Sample the signal x()t = 5sin 2000() t cos 20,000() t at 80 kHz to form a discrete-time signal x[]n, take every fourth sample of x[]n to form x s[]n and decimate x s[]n to form x d[]n. Then upsample x d[]n by a factor of four to form x i[]n and compare it to x[]n. �K����� t�Ɏ /���M����%���}$�+�����ױ�N�������p��X��!��-&�����e@nGK���gf��i$�� x(r��(���䇹ڨ9|�Ј��Ige��_7��h��I]�im-�B""C9��A��9F�qǷ��D 3t%��""���_Zl"C�j���'.dAۨa_��B������,{{� '�V��O_+�"�\I\A��a��#� �8�wt�����Cv�aڶGdta�ˆi����w�x5��� x+B���+@x��� x49B��A�R Let us assume that the signal x(n) with spectrum X( ) is to be down sampled by an integer factor D. The spectrum X( ) is assumed to be That is, some frequencies above the cutoff frequency are not attenuated by the value of Ast. ��,2L��L�`�*)wDr��է��| 0;H2N�$��~��4�,��H���1�@� � " Thus (10.3.9) Since v(k) = 0 except at multiples of l, where v(kl) = x(k), (10.3.9) becomes (10.3.10) The scale factor C is selected so that the output y(m) = x(m/l) for m = 0, +21.. endstream endobj startxref ��̫_2-�v#�?��W#�|����e��E�oR�C[b�e�_I�(�f�>����}���v:_غYڅ�������z_�ic�����kgcw���EU��u������k��_I����{^�M��}-t��V�������������'�^�]zW��gb�o��}[�����O�����69������խ��z��k��y��I����W������{��z���uֽ=�k��L��+;�S�>�� �����V�����z��}7��Uls��������0�o_FUt��;���'�0 &������/���Z /�'ҿ�}RX�� ��*_����sFAu��-���uM�W�����A��ӂRL��ޗB������A ���+�]}�� A���z�_�W�����o�������?��Y�+m�ے�_�� t���ޭ���K��uqu�u������>��������-d�������k��5�u�PgH����Z�o�����K��Y'�� ޭ���[zH;�ΡӺ�u~��uK; Consider an input signal x[n] that is ω0-bandlimited in the DTFT domain. uuid:e6871ea1-e89d-f045-b544-dd56d540b131 �? Whereas in sampling we start with a 4 . … We begin in Section I1 with the mathematical (and signal processing) framework of %%EOF ���7��}�����������w���J��k��n�2���r�i6�O���ݪ�*ĖA;%Z������D�0�s[��A"��Y�֟ÖG��һt�w�kK���UW��Mߐ��Aq� oI�^�aY application/pdf However, this occurs only in the transition band of the filter. hUYO�@�+��ҽ��"� �#�iAZ��$Kp�đc$��;���QZ������ ��$�J ���"B"�Id�j�� ��1=%�[F�������H{_�Ј�jBF�R�_]z_h*�K��%z�*����K��� /����ڷ�?p������k��m� �drհ�U��m��ih;l ��wЊI� B���q�$�{��y�k�� Dt�������]�%}oo^� C do��6H� ��p�&�?����i~����C�/��4;�(�ޤ�q��uB����K� �>+�%��%;�����a-�����m����eB��Z 6�����b��d&����I�`�ڿ��`+x�U���¥}'�U�#�W���M�i+��G�Aa����M=mo�[twE�X}�W��놺�{j8�_�V��O����[��V�k*�j�a]w�����M=�t�K������ե�Zߨ�������������`����!��B[zߤ���/��wS�U�t��a%x�酶�vsz��7��կ���%�WjwR��ZK�6�?T��N����k�ݩ�u����/��תm����~�;��v����S�'��&���}����j������/T����%K�z��[�����j�5����ޝ������8ˢ>G���W���TGDp!����.�Ut���%�H������@��Y#� ���+�)�� ^��I����� ���e�k(�6�������Z�Rs��Z4[�Q߆�JrC����l���.��eYC�cEa\Hr�V�����,���J��^=��CK��Ј� o�=�m�=��|R�����$ o�W�d6�Ϋk�ѐZ0���;w�ؒ�#�����DG˂=�$�G��o�K)h�G }��D� _��3�#�tl%�X����o��n�@wP��k x0��� C�/�Z��:B�I��aT2Ps!A�b������M����a|/�K �i}���N��J�~[���W��I!+K����w�l�Uun�m?�kNK��n���o����vZ������:ۥﺥz�&�g���D�Y6��z������{Q�cK�������t�l?Q�M��=a�߭[6����i8o��j��z�������k�m��}ҷ��ݪUޭ��������t��Wv�n�� ���v����C��K���wI��v��KI����}��Nҗ}���6��[��_ޓut����;����7_�'_���賧4��_�m&�'Y�K����{m/�Ն�Z �S�C7�ց~��/n���un��T�q?��f��.V#�տ��V���z2������k��ס��[��붖�Q|����:��I�? Cf., e.g., least-squares approximation. 127 0 obj <> endobj called decimation to reduce the sampling rate of the signal. The reason for this LPF, however, is quite different for each case. Set alert. In practice, sampling is performed by applying a continuous signal … h�T��n�0E�|�,[uac(I%�T�M}����1�H�X�,������Ν;���G;,����;\���8O��� 3�e��֣t�Bs���G�OP���y�+ܝN��{��`�A)��WP��s?8�]�CӀ�>c�t�rD`��&�V� ������F/���M. If we want to interpolate by a factor of 4, we would ideally design a lowpass filter running at 192 Hz with a cutoff at 24 Hz. must incorporate the filtering operations for both interpolation and decimation, and hence it should ideally possess the frequency response characteristic filter. Department of Digital Signal Processing Master of Science in Electronics Multirate Systems Homework 1 Decimation and interpolation Dr. Gordana Jovanovic Dolecek Ojeda Loredo Fernando June/15/2015 Sta. Crochiere and L.R. ���VFѴG";#�l2��.�I@�n� ���̗�p�L� ��ނ -�K�U�C��� �p\�`�fr��_�N����DN�J6�J��d����f���\C��v�U��~֕�I" �%�A������&����M5C&?$��*�֗����D:��%ۤ���"�����ڪ�A4�%�-��@��!�Tսz�t ��Ȩ>��IuH}�]���K�$�a�%A/���ݫ_Kh �B^�";��Az��VׯK���;"��K }��l�~��J(���kh&���V-Q�� Multirate DSP Using Decimation and Interpolation 2.1. Introduction The decimator is a device that reduces the sampling rate by an integer factor of M, whereas the … ����BQ:"8!|������e���� �9�!D���. endstream endobj 133 0 obj <>stream • Decimation – Reduce the sampling rate of a discrete-time signal. ֈ("�k�(m'��8�ݮ��� �| �tW+";>Dq�H��b;y�. Apps. 15. ���-Q���O�3� ��3_o�@� To start consider changing the rate of a signal by a factor of 2. h��T;o�@��Wl�s�o�]A�K).�r�� The transfer function of a decimation filter can be used in an interpolation filter, and block diagrams can be turned around to transform a decimation filter into an interpolation filter, and vice versa. Increasing the number of samples per unit time, sometimes called upsampling, amounts to interpolation. tors, decimation and interpolation filters, and digital filter banks, are reviewed, along with the interconnection prop- erties of the building blocks. > [1/2 1 1/2] is a typical filter to interpolate between samples and is the > same as straight line averaging at a midpoint. To plot a time and frequency display of microphone plus a cosine using DSP. Read a .wav file and match with their respective spectrograms. Although the example uses decimation-by-2 stages, our approach applies to any integer decimation factor. 16. St0Bi8��������hn��Î����|�!�o�߯m'�t���`f�T�y�(_���Wyy$E�'����|�跋����o��W��|�iS�fvO/�z��^t�V�7yY�z�E��i�? Rather than cascading an anti-imaging ﬁlter for interpolation with an anti-aliasing ﬁlter for decimation, we imple- ment one ﬁlter with the minim Frequently, there is the need in DSP to change the sampling rate of existing data. Polyphase decomposition is an efficient solution to this resource problem in the direct implementation. Ma. ... general tree structure and its frequency resolution are displayed in Fig. • Decimation – Reduce the sampling rate of a discrete-time signal. (6marks) (DEC’09-JAN’10) (Dec.12, 6m). 0 The advanced blockset allows you to quickly design an algorithm, such as a high performance resampling filter, without regard for the hardware implementation details. I Decimation, I Interpolation, I Non-integer sample rate conversion, I Multistage sample rate conversion. i.e. “Interpolation”, in the DSP sense, is the process of upsampling followed by filtering. Therefore, for the input and output of the model concerned, the sampling rate is NOT changed, but it is changed within the model. Digital Signal Processing - September 2010. (The filtering removes the undesired spectral images.) h�b```f``rd`2��@(�^�0�,�j`�*0)XaR�������Ϯ�$d�����K�/p�s1�90,Z�d�̙+gN[ $f. I have designed a decimation and interpolation filter, the amplitude after each decimation decreases. In digital signal processing, downsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. polyphase lters I and Applications. Solution: Decimation and Interpolation are two techniques used to alter the sampling rate of a sequence. Decimation Decimation of a signal x(n) by a factor D means that its sampling rate is reduced by a factor D. This process is called downsampling. bC@P�n�>x>�Љ-�B[�M�:��Aw"uDpV��V�)�@�qE�A�D!�s�g�E�'!\�8�q�6I�d$���w���H�����.Vo�B#5�pl#�@3R���a����� ���Gg��7�D����`�ADG�3��p_i��a�������}H\/+ ,��|-��� ��_xd �e��?�usXZ�NA�sJaYP?d8�$�"&i.���pR�� � �-�]릪�Mۍ��w�cD�7S�,��7^�U8�z��b�8�a Purdue University: ECE438 - Digital Signal Processing with Applications 4 rate is lower than the sampling rate of the available data. Then, we describe properties pertaining to the multirate systems, namely their valid inverse operations and the noble identities. 2007-11-30T07:41:46Z In an analogous manner to decimation, when used for interpolation, Nyquist filters allow some degree of imaging. In practice, sampling is performed by applying a continuous signal … Resample uniform or nonuniform data to a new fixed rate. endstream endobj 132 0 obj <>stream {ۺ�^|ȶ�(�d5G!���vH��!�� �D4ܡ��L�DBE��/�r�b(���P About this page. The main use of interpolation is to create a high definition video image from a low definition image. Furthermore, wikipedia interpolation: "Upsampling requires a lowpass filter after increasing the data rate, and downsampling requires a lowpass filter before decimation. ־(��&��7x�8�t�k��4zeO5�j�u�6���/*r��|�O�վIJ�zN*��/wM2e��/%��2]!a���&�HpH�̰���GY���R�]�Ն EnD���[�K�C���Ƀ��U���>�����g��VҮ����G�����.8~ů ! E�=�WnQl���W��u�8$����d<�������4҇�+_��.�S/��J+�!Rʌ3+d� Sampling-rate conversion can be accomplished by L-fold expansion, followed by low-pass filtering and then M-fold decimation, as depicted in Figure 9.7. 2. The radix-4 DIF algorithm increases the execution speed of the FFT. E��jֲ�8DDDr�mV$�N�-��\Ma�����j�tꁮ���`K�J���n֟��� �������_���O���������#wI7��_Ao���mj��_���?�� �~M�W�+\:��������ʿ^� ��������&֖����K��{�����rtM�m�}?I���k��� �r�8��������֛����������uU"����5��[�N�/o�� ��$E�����7�� ��6��i}���臷��S�?�q�����鷯��N�?~:��d����I��>���Pʆ���c�"T�['�,'��_��*(�����k�%���ԁ��5v���%.��AUa�����}��lZ�~�)!�_�����uu���z���*�����־D�ɶ-*]����|jo��Q�k�Z�K������C>�������"�"� S�Y�]}�ׯ��C�h_����;��7�}+�}{��?Iֿ��j�I��Uv\^�~�Ww��B������AX?In��_�7�_X���a� �[ ~D;�4Z����Z^���>���2^�w��\s�[�A�^@����a3�6T��F~Ƥ����*��6&y��+���?����<4��tD�w��L����`���OZrd�-~�%��0ߵ�� ��p���av�^��7W����`P���p2S]����e@i�K&280�����������eq�T xn�R�"AV���8�+�^�N)�,8�k в֫"l@����#�����5���C�X����j�ۋ�È����jz �y 2�H���`}ia�u ��t5���@�B�(F�}mVC,� W=�"C`��!�9C��9��>�a�����Y��*�ւ���1Bt:�Y�2�G2���f)8����Ԥ3(P�~�H U���Z���! interpolation" method (interpolate to get the coeffeicents, then use them to interpolate the data) in their audio sample rate converter products. Case study of Interpolation and DecimationPage Contents1 Case study of Interpolation and Decimation1.0.1 THEORY1.0.2 Sampling:1.0.3 Downsampling (Decimation):1.0.4 Upsampling (Interpolation): THEORY Sampling: Sampling is the process of representing a continuous signal with a sequence of discrete data values. decimation and interpolation in the multirate digital signal processing systems. q 595.20 0 0 841.92 0.00 4.08 cm 1 g /Obj183 Do Q endstream endobj 57 0 obj <>/Height 3508/Type/XObject>>stream About this page. In this system, the decimation factor is always is equal to the interpolation fac-tor. o Constructing a curve that is as close as possible but does not include all the given points is referred to as approximation. DSP and Digital Filters (2016-9045) Polyphase Filters: 12 – 1 / 10. Decreasing the number of samples per unit time, sometimes called downsampling, is decimation … Started by seb January 13, 2004. Decimation and Interpolation Decimation Filtering • Consider ﬁltering followed by downsampling by N. We throw away N −1 out of N samples: intuition tells us there should be some way to reduce computations by a factor of N. • Thought Exercise: Blocking and Averaging Consider ﬁltering by 1/N times length-N rectangular window, then ���b�������C�\$T�$�h��ћL#ʧ6o�F��l�ҭ�\X�v�2��n������},_Lj3M�v��F�:�@R$���z�+�\�/dx��fxN��5���a� ��O�#�_��M����a0�f�z���^�36_�yw�_y�M�-k�r�l�j�?�c��1] �mk>6.^يn+���j_���:ߚ#�KfF2{/4-��.���%�G)�����+5_�܍K�cMR��魌G&Q�����,�ci4�b�ҥ��]���Æ��A��_XG�(�&����Ȭ�/��z/��/?���oa�@���[ 2007-11-20T15:00:19Z IEEE, … C���H�,am�,sCB�a ����� T���(d��P�2�@�1*:A2�@��:�� �ԹL�P l@��� * a�5� ��4`xs8+p>agpe�^�Q�� ������Yi6�vXU(��(���#x]: |FW� �ׂo Forums More Forums comp.dsp . Heavy Lowpass ﬁltering 12: Polyphase Filters •Heavy Lowpass ﬁltering •Maximum Decimation Frequency •Polyphase decomposition •Downsampled Polyphase Filter •Polyphase Upsampler •Complete Filter •Upsampler Implementation •Downsampler Implementation •Summary DSP and Digital Filters (2016-9045) … Chronological; Newest First; Reply by Jon Harris January 15, 2004 2004-01-15. Lizhe Tan, Jean Jiang, in Digital Signal Processing (Third Edition), 2019. �hV1K�5�s! 1.1 Decimation and Interpolation 1.2 Digital Filter Banks Basic Multi-rate Operations: Decimation and Interpolation Building blocks for traditional single-rate digital signal processing: multiplier (with a constant), adder, delay, multiplier (of 2 signals) New building blocks in multi-rate signal processing: M-fold decimator L-fold expander It will be published Monday, April 28. Yes it is possible to do something in between linear and a much higher-order FIR filter. Both downsampling and decimation can be synonymous with compression, or they can describe an entire process of bandwidth reduction and sample-rate reduction. decimation in frequency (DIF) fast Fourier transform (FFT) algorithm using the Texas Instruments (TITM) TMS320C80 digital signal processor (DSP). Explain the decimation and interpolation process with an example. This article is available in PDF format for easy printing. h�T�Mo� ���>n�Bh�JQK5)�}h�v��t��Hz�`�j�����l��ݾ�� Document from Glenys • Interpolation – Increase the sampling rate of a discrete-time signal. 1.1 Decimation and Interpolation 1.2 Digital Filter Banks Basic Multi-rate Operations: Decimation and Interpolation Building blocks for traditional single-rate digital signal processing: multiplier (with a constant), adder, delay, multiplier (of 2 signals) New building blocks in multi-rate signal processing: M-fold decimator L-fold expander ��#��i��� �Dp�зn����=1�T(+K����T��?��_K D/������WIt���\%���H��dN���f�^�_�}$��Ap��.�G�?�0Z_]0C��l5Z_ i/��J�;��t�-���|/�z�[B9W��5���P���Z��ici8��D���r For decimation, the LPF serves to eliminate high frequency components in the spectrum. This chapter investigates basics of multirate digital signal processing, illustrates how to change a sampling rate for speech and audio signals, and describes the polyphase implementation for the decimation filter and interpolation filter. In this paper we present a tutorial overview of multirate digital signal processing as applied to systems for decimation and interpolation. Mathematical interpolation vs. interpolation in DSP vs. decimation • In mathematics, interpolation stands for constructing a smooth curve that travels through all given points. Figure 1 illustrates a polyphase decimation filter at … Figure 1. 2 Decimation/Interpolation Filters In a fixed-precision environment like the C54x DSP, the correct choice for the type and structure of the decimation/interpolation filters is crucial. Working of interpolation or decimation . Halfband FIR filters are implemented in dsp.FIRHalfbandInterpolator and dsp.FIRHalfbandDecimator. 151 0 obj <>stream Halfband filters are an efficient way of doing this. 1 1. Perform decimation and linear or higher-order interpolation without introducing aliasing. ... First, we study the basic operations of decimation and interpolation, and show how arbitrary rational sampling-rate changes can be implemented with them. If these components were not filtered out, they would alias when the reduction in sample rate is performed. Their IIR counterparts, dsp.IIRHalfbandInterpolator and dsp.IIRHalfbandDecimatorcan be an even more efficient way of interpolating/decimating by 2. These coefficients are to be used with dsp.FIRDecimator (L=1), dsp.FIRInterpolator (M=1), and dsp.FIRRateConverter (general case). This is the basic point of view we have taken in this paper. • Digital Filter Design for Interpolation and Decimation: First we treat ﬁlter design for in-terpolation. Mathematical interpolation vs. interpolation in DSP vs. decimation • In mathematics, interpolation stands for constructing a smooth curve that travels through all given points. (6marks) (DEC’09-JAN’10) (Dec.12, 6m). Theories and applications of polyphase decomposition for the decimation and interpolation in the FT and FRFT domain have To Implement Interpolation Process of any given sequence. To Implement I/D sampling rate converters. [�b endstream endobj 131 0 obj <>stream The major DSP vendors provide examples of FIR decimators in their data books and application notes; check their web sites. A so-designed lowpass filter is lin-ear phase, but periodically time-varying. �K�$�1R�C��Yb�N�{�����k^�|��Ʃ��T% – Low sampling rate reduces storage and computation requirements. To Implement Decimation Process of any given sequence. Implementation of Interpolation Process. Multirate systems are sometimes used for sampling-rate conversion, which involves both decimation and interpolation. What shall I do to get the initial signal's amplitude. HD video from non HD sources on a modern TV. ��W%�5�����~�1o1�ta_�0X[ɽ6Z*���|�8 tZf�uiI��G��*N~v@�x�� ����������n�M��3Iɷ�0fd�4wP2sI���9n���n��[+d ��C9� �9Gp��Q|����q�H�U�9�(L̞"�4��"$��d�Ćm��05餼��Y3 Decimating, or downsampling, a signal x(n) by a factor of D is the process of creating a From a digital signal processing point of view, both the pro- cesses of interpolation and decimation can be well formulated in terms of linear filtering operations. Therefore y(n) is simply x(Dn). (However, you can do interpolation prior to decimation to achieve an overall rational factor, for example, “4/5”; see Part 4: Resampling.) INTRODUCTION TO DIGITAL SIGNAL PROCESSING Question No. Decimating, or downsampling, a signal x(n) by a factor of D is the process of creating a new signal y(n) by taking only every Dth sample of x(n). In multirate Digital Signal Processing (DSP), interpolation is required wh enever it is necessary to increase the sampling r ate of a digital signal. 12. This parallel operation allows Decimation by 8. There are many more to topics and techniques in multirate digital signal processing including: I Implementation techniques, e.g. Multiple stages for decimation (or interpolation) can reduce the number of lter coe cients in the lter speci cations. The Altera DSP Builder advanced blockset is a high-level synthesis tool that is integrated with the Mathworks Simulink tool. 13. Implementation of I/D sampling rate converters. 2007-11-30T07:41:46Z Tonantzintla, Puebla 2. {i}?��Ҧ�� Set alert. The signal can be decimated more than once, using a gradual change in sampling frequency. 12. Cf., e.g., least-squares approximation. Therefore, both operations can be accomplished by a single filter with the lower of the two cutoff frequencies. Decimation, interpolation, downsampling, upsampling, antialiasing filter. In section Ill, some applica- tions of multirate DSP are indicated, in digital audio sys- tems, in subband coding, and in voice privacy systems. o���c���4�M�/K�� g20�莈�Ddph/�ь� &��@b��M��wB������"�"������d6 "�DD8�����_��b"""|������TV�G)��D��Yq@o |�rZiR�z��Z�� �ʳq^w+B �� �~�>� �#�8�4��?�Uگ�it"""�AqА�O�B�!�� In the case of interpolation, the filter retains most of the spec… 11.2 Polyphase Filter Structure and Implementation. Rabiner, "Multirate Digital Signal Processing," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1983. Both the interpolation and decimation filters incorporate a low-pass filtering function. Cascaded Integrator-Comb (CIC) filters are a class of linear phase FIR filters comprised of a comb part and an integrator part. Decimation Decimation of a signal x(n) by a factor D means that its sampling rate is reduced by a factor D. This process is called downsampling. (However, you can do interpolation prior to decimation to achieve an overall rational factor, for example, “4/5”; see Part 4: Resampling.) �!�d¥��^GGtP�U�����&�a��v��cs�6y�����DA3�V �Ӑ��7L�j�����pD��e�p���\��t3�/�[���c�w�k�x0��7��.'�./7�s�i�k��9a_�����=M�u�w�����ܪ! K���o�$W_� �ჴA .����_�A���=��� 訍 �a�O���I����0�u�{� Decimation & Aliasing. Learn more about image processing, interpolation, decimation MATLAB X'�{�ۇ��������{�]z�ԛ���o]+C� 5�&�@�ި?2���� ��Iv��,t��T����ɾ�C���=�-�{�����'�2�ޓC��� �e9�*^�$�߈�-�^�cK��M���m���̡5�/��VŵK�������a�*M����%�]��=$��j5��Z�t��R��oT�_[zUt�^+��^����n���0�w^���I:ޅ�t���_�Rn&��v����I�q�*�}�) The floating point unit in the Cortex®-M4 is only single precision, as it includes an 8-bit exponent field and a 23-bit fraction, for a total of 32 bits (see Figure 1). �Z��Z�rTrW��-Q�Z��Z��-Q���������?���?���? It also looks at multistage decimation and polyphase filters. �����0Qr�(�$�$9�B&�<5Ϋ4��3�W膰�x��Q�""5��'bC>�p�+���$wP(.f�.!=RLU%��dpI��Hf�S�ć(��9��r4�=>����BB8E�x�#�р���ZI2(�A@�(��k�%d. Let’s look at an example to see how to calculate the frequency response. ��Ϻ�����|�ሧ�B)��z�*�zRX0��eũ��u]����w�C��y�~��@��� Implementation of Decimation Process. HP 9100C Digital Sender Xilinx DSP slices is presented. This chapter shifts the emphasis to the design of the companion digital interpolation and decimation filters. o Constructing a curve that is as close as possible but does not include all the given points is referred to as approximation. • Interpolation – Increase the sampling rate of a discrete-time signal. signal processing algorithms that involve more than one sampling rate. decimation interpolation Resampling by rational fractions Multirate identities Polyphase representations Maximally decimated ﬁlter banks aliasing amplitude and phase distortion perfect reconstruction conditions Digital Signal Processing – p.2/25 – Low sampling rate reduces storage and computation requirements. Thanks Habib Decimation filters should not have attenuation. Record several seconds of a waveform into SRAM at 32 KHz and this time remove Decimation and Interpolation 1. The steps for 2x interpolation are as follows: 1.Insert a 0 between each sample (zero stuffing / up sampling) 2.Filter the resulting images from the up sample process 3.Repeat another 2x interpolation to get 4x, and again for 8x Cascading multiple 2x stages to increase interpolation is best due to efficient half-band filters. Download as PDF. 2.1.5 Which signals can be downsampled? 65 0 obj <> endobj 352 0 obj <> endobj 353 0 obj <>/page.1<>/page.2<>/page.3<>/page.4<>/page.5<>/page.6<>/page.7<>/page.8<>/page.9<>/page.10<>/page.11<>/page.12<>/page.13<>/page.14<>/page.15<>/page.16<>/page.17<>/page.18<>/page.19<>/page.20<>/page.21<>/page.22<>/page.23<>/page.24<>/page.25<>>> endobj 62 0 obj <>stream Signal Analyzer: Visualize and compare multiple signals and spectra: Functions. Perform decimation and linear or higher-order interpolation without introducing aliasing. DSP Decimation filters for Σ∆ADCs • Digital decimation filters –Aliasing in the analog domain ... –Linear phase implications –Multi-stage decimation Ref: R. E. Crochiereand L. R. Rabiner, “Interpolation and Decimation of Digital Signals –A Tutorial Review”, Proc.

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