decimation and interpolation in dsp pdf

December 2, 2020 in Uncategorized

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. Interpolation and decimation . between the sampling playback rates so that you don't have to keep reloading code to the DSP! Lizhe Tan, Jean Jiang, in Digital Signal Processing (Third Edition), 2019. Therefore, for the input and output of the model concerned, the sampling rate is NOT changed, but it is changed within the model. It can be applied for the derivation of new sampling theorems and the recovering bandlim-ited signal from nonuniformly sampled versions. – Higher sampling rate preserves fidelity. Multirate systems are sometimes used for sampling-rate conversion, which involves both decimation and interpolation. ���-Q���O�3� ��3_o�@� Explain the decimation and interpolation process with an example. ־(��&��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 ! {ۺ�^|ȶ�(�d5G!���vH��!�� �D4ܡ��L�DBE��/�r�b(���P �!�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! �>����;E�I�l���|߼�e�7��)����}��S���5:���WwW��bY'v:��fs����c��Q�rg��~g���!یKwpC9��N���ē�͔t��Bۿ�v�ucs @���,��̔��]�Jѓϕz�I�$��e�F7����y_��j ���{-b��*�0��-{]�R���zT��G_dH9v�E\�ڸ� Both downsampling and decimation can be synonymous with compression, or they can describe an entire process of bandwidth reduction and sample-rate reduction. • Decimation – Reduce the sampling rate of a discrete-time signal. Although the example uses decimation-by-2 stages, our approach applies to any integer decimation factor. Cf., e.g., least-squares approximation. Record several seconds of a waveform into SRAM at 32 KHz and this time remove endstream endobj 131 0 obj <>stream ���b�������C�\$T�$�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�@���[ That is, some frequencies above the cutoff frequency are not attenuated by the value of Ast. Decimation, interpolation, downsampling, upsampling, antialiasing filter. 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 "�DD8�����_��b"""|������TV�G)��D��Yq@o |�rZiR�z��Z�� �ʳq^w+B �� �~�>� �#�8�4��?�Uگ�it"""�AqА�O�B�!�� The advanced blockset allows you to quickly design an algorithm, such as a high performance resampling filter, without regard for the hardware implementation details. 2007-11-30T07:41:46Z HD video from non HD sources on a modern TV. ��̫_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��ޗB������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; Decreasing the number of samples per unit time, sometimes called downsampling, is decimation … g20�莈�Ddph/�ь� &��@b��M��wB������"�"������d6 – Higher sampling rate preserves fidelity. 127 0 obj <> endobj ����BQ:"8!|������e���� �9�!D���. However, this occurs only in the transition band of the filter. endstream endobj 132 0 obj <>stream INTRODUCTION TO DIGITAL SIGNAL PROCESSING Question No. Good questions! endstream endobj 128 0 obj <> endobj 129 0 obj <> endobj 130 0 obj <>stream h�bbd```b``��! Each TMS320C80 DSP parallel processor (PP) contains four major units operating in parallel. I have designed a decimation and interpolation filter, the amplitude after each decimation decreases. decimation in frequency (DIF) fast Fourier transform (FFT) algorithm using the Texas Instruments (TITM) TMS320C80 digital signal processor (DSP). 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. called decimation to reduce the sampling rate of the signal. %PDF-1.5 %���� 16. • Decimation – Reduce the sampling rate of a discrete-time signal. This chapter shifts the emphasis to the design of the companion digital interpolation and decimation filters. �K�$�1R�C��Yb�N�{�����k^�|��Ʃ��T% To plot a time and frequency display of microphone plus a cosine using DSP. tors, decimation and interpolation filters, and digital filter banks, are reviewed, along with the interconnection prop- erties of the building blocks. (6marks) (DEC’09-JAN’10) (Dec.12, 6m). 151 0 obj <>stream 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). Their IIR counterparts, dsp.IIRHalfbandInterpolator and dsp.IIRHalfbandDecimatorcan be an even more efficient way of interpolating/decimating by 2. In this system, the decimation factor is always is equal to the interpolation fac-tor. ��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��"$��d�Ćm��05餼��Y3 Resample uniform or nonuniform data to a new fixed rate. C���H�,am�,sCB�a ����� T���(d��P�2�@�1*:A2�@��:�� �ԹL�P l@��� * a�5� ��4`xs8+p>agpe�^�Q�� ������Yi6�vXU(��(���#x]: |FW� �ׂo Decimation (DDC) and Interpolation (DUC) Concepts TIPL 4701 Presented by Jim Seton Prepared by Jim Seton 1. 0�G��Td��-Q�Z��Z� 0�G������ 0�F@aj� 0�G�Tr��]�S�{�޿�������-_��-Q����@aj���ҿ��w��m�ˢ������,�.6����@aj�������2T|���������`f,��A��)�}Q�^ d��1��,�#�2ʡQ�? The transfer function of a decimation filter can be used in an interpolation filter, and block diagrams can be turned around to transform a decimation filter into an interpolation filter, and vice versa. Ma. bC@P�n�>x>�Љ-�B[�M�:��Aw"uDpV��V�)�@�qE�A�D!�s�g�E�'!\�8�q�6I�d$���w���H�����.Vo�B#5�pl#�@3R���a����� ���Gg��7�D����`�ADG�3��p_i��a�������}H\/+ ,��|-��� ��_xd �e��?�usXZ�NA�sJaYP?d8�$�"&i.���pR�� ��Ϻ�����|�ሧ�B)��z�*�zRX0��eũ��u]����w�C��y�~��@��� �����0Qr�(�$�$9�B&�<5Ϋ4��3�W膰�x��Q�""5��'bC>�p�+���$wP(.f�.!=RLU%��dpI��Hf�S�ć(��9��r4�=>����BB8E�x�#�р���ZI2(�A@�(��k�%d. Working of interpolation or decimation . o Constructing a curve that is as close as possible but does not include all the given points is referred to as approximation. 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. Halfband FIR filters are implemented in dsp.FIRHalfbandInterpolator and dsp.FIRHalfbandDecimator. Audio application such as to plot a time and frequency display of microphone plus a cosine using DSP. o Constructing a curve that is as close as possible but does not include all the given points is referred to as approximation. Then, we describe properties pertaining to the multirate systems, namely their valid inverse operations and the noble identities. application/pdf endstream endobj startxref Started by seb January 13, 2004. Both the interpolation and decimation filters incorporate a low-pass filtering function. 12. Halfband filters are an efficient way of doing this. Set alert. 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 must incorporate the filtering operations for both interpolation and decimation, and hence it should ideally possess the frequency response characteristic filter. Figure 1 illustrates a polyphase decimation filter at … 11.2 Polyphase Filter Structure and Implementation. The sampling rate Fs refers to the input signal. 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.. Implementation of Interpolation Process. Let’s look at an example to see how to calculate the frequency response. This article is available in PDF format for easy printing. 14. Implementation of Decimation Process. 15. � �-�]릪�Mۍ��w�cD�7S�,��7^�U8�z��b�8�a h�b```f``rd`2��@(�^�0�,�j`�*0)XaR�������Ϯ�$d�����K�/p�s1�90,Z�d�̙+gN[ $f. In practice, sampling is performed by applying a continuous signal … (6marks) (DEC’09-JAN’10) (Dec.12, 6m). • Digital Filter Design for Interpolation and Decimation: First we treat filter design for in-terpolation. �QDv��B��. The Altera DSP Builder advanced blockset is a high-level synthesis tool that is integrated with the Mathworks Simulink tool. There are many more to topics and techniques in multirate digital signal processing including: I Implementation techniques, e.g. Furthermore, wikipedia interpolation: "Upsampling requires a lowpass filter after increasing the data rate, and downsampling requires a lowpass filter before decimation. ���VFѴG";#�l2��.�I@�n� ���̗�p�L� Therefore, both operations can be accomplished by a single filter with the lower of the two cutoff frequencies. Perform decimation and linear or higher-order interpolation without introducing aliasing. 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. %PDF-1.6 %���� Polyphase decomposition is an efficient solution to this resource problem in the direct implementation. Explain the decimation and interpolation process with an example. 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. ���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 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. Yes it is possible to do something in between linear and a much higher-order FIR filter. ��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�$�a�%A/���ݫ_Kh �B^�";��Az��VׯK���;"��K }��l�~��J(���kh&���V-Q�� �hV1K�5�s! The signal can be decimated more than once, using a gradual change in sampling frequency. designMultirateFIR(L,M) designs an FIR filter for interpolation by an integer factor L and decimation by an integer factor M. designMultirateFIR returns filter coefficients. Let us assume that the signal x(n) with spectrum X( ) is to be down sampled by an integer factor D. The spectrum X( ) is assumed to be St0Bi8��������hn��Î����|�!�o�߯m'�t���`f�T�y�(_���Wyy$E�'����|�跋����o��W��|�iS�fvO/�z��^t�V�7yY�z�E��i�? In this paper we present a tutorial overview of multirate digital signal processing as applied to systems for decimation and interpolation. Decimation & Aliasing. Multiple stages for decimation (or interpolation) can reduce the number of lter coe cients in the lter speci cations. Crochiere and L.R. Tonantzintla, Puebla 2. The filter sample rate is 2x > the input series. … 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. �uy�Q4nJ�T� j�W��#� �U˚ {i}?��Ҧ�� 9.2 Decimation Decimation can be regarded as the discrete-time counterpart of sampling. HP 9100C Digital Sender 1.1.1 Floating point Floating point is a method to represent real numbers. In an analogous manner to decimation, when used for interpolation, Nyquist filters allow some degree of imaging. Therefore y(n) is simply x(Dn). 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. Document from Glenys Myself, I've experimented with cubic interpolation in audio applications and it sounded better than linear … The reason for this LPF, however, is quite different for each case. K���o�$W_� �ჴA .����_�A���=��� 訍 �a�O���I����0�u�{� Abstract: The concepts of digital signal processing are playing an increasingly important role in the area of multirate signal processing, i.e. ��1=%�[F�������H{_�Ј�jBF�R�_]z_h*�K��%z�*����K��� /����ڷ�?p������k��m� �drհ�U��m��ih;l ��wЊI� B���q�$�{��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˂=�$�G��o�K)h�G }��D� _��3�#�tl%�X����o��n�@wP��k x0��� C�/�Z��:B�I��aT2Ps!A�b������M����a|/�K �i}���N��J�~[���W��I!+K����w�l�Uun�m?�kNK��n���o����vZ������:ۥﺥz�&�g���D�Y6�޿�z������{Q�cK�������t�l?Q�M��=a�߭[6����i8o��j��z�������k�m��}ҷ��ݪUޭ��������t��Wv�n�� ���v����C��K���wI��v��KI����}��Nҗ}���6��[��_ޓut����;����7_�'_���賧4��_�m&�'Y�K����{m/�Ն�Z �S�C7�ց~��/n���un��T�q?��f��.V#�տ��V���z2������k��ס��[��붖�Q|����:��I�? �Z��Z�rTrW��-Q�Z��Z��-Q���������?���?���? Xilinx DSP slices is presented. Download as PDF. In the case of interpolation, the filter retains most of the spec… Then the techniques of decimation and interpolation enable this operation, providing the ratio T1/T2 is a rational number i.e. uuid:4be995db-6968-a44e-8d94-56cd6b0650c2 Frequently, there is the need in DSP to change the sampling rate of existing data. Decimation by 8. Chronological; Newest First; Reply by Jon Harris January 15, 2004 2004-01-15. E�=�WnQl���W��u�8$����d<�������4҇�+_��.�S/��J+�!Rʌ3+d� To Implement I/D sampling rate converters. o���c���4�M�/K�� 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. interpolation" method (interpolate to get the coeffeicents, then use them to interpolate the data) in their audio sample rate converter products. 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. Signal Analyzer: Visualize and compare multiple signals and spectra: Functions. Consider an input signal x[n] that is ω0-bandlimited in the DTFT domain. DSP and Digital Filters (2016-9045) Polyphase Filters: 12 – 1 / 10. Purdue University: ECE438 - Digital Signal Processing with Applications 4 rate is lower than the sampling rate of the available data. 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. 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 To Implement Interpolation Process of any given sequence. Decimating, or downsampling, a signal x(n) by a factor of D is the process of creating a It also looks at multistage decimation and polyphase filters. 12. polyphase lters I and Applications. If these components were not filtered out, they would alias when the reduction in sample rate is performed. – Low sampling rate reduces storage and computation requirements. Cf., e.g., least-squares approximation. Theories and applications of polyphase decomposition for the decimation and interpolation in the FT and FRFT domain have (The filtering removes the undesired spectral images.) To Implement Decimation Process of any given sequence. 1 1. In digital signal processing, downsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. In practice, sampling is performed by applying a continuous signal … tors, decimation and interpolation filters, and digital filter banks, are reviewed, along with the interconnection prop- erties of the building blocks. I Decimation, I Interpolation, I Non-integer sample rate conversion, I Multistage sample rate conversion. “Interpolation”, in the DSP sense, is the process of upsampling followed by filtering. Multirate DSP Using Decimation and Interpolation 2.1. Apps. About this page. In multirate Digital Signal Processing (DSP), interpolation is required wh enever it is necessary to increase the sampling r ate of a digital signal. endstream endobj 133 0 obj <>stream The radix-4 DIF algorithm increases the execution speed of the FFT. h�T�Mo� ���>n�Bh�JQK5)�}h�v��t��Hz�`�j�����l��ݾ�� 0 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. %%EOF (However, you can do interpolation prior to decimation to achieve an overall rational factor, for example, “4/5”; see Part 4: Resampling.) Decimation and Interpolation 1. 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. 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. 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���! system are decreasing (decimation) and increasing (interpolation) the sampling-rate of a signal. It will be published Monday, April 28. 2007-11-20T15:00:19Z ... First, we study the basic operations of decimation and interpolation, and show how arbitrary rational sampling-rate changes can be implemented with them. • Interpolation – Increase the sampling rate of a discrete-time signal. Should I multiply the output signal for each stage by a constant value? Cascaded Integrator-Comb (CIC) filters are a class of linear phase FIR filters comprised of a comb part and an integrator part. decimation and interpolation in the multirate digital signal processing systems. 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. 2007-11-30T07:41:46Z Finally a number of multiplierless 5th and 10th order elliptic filter designs are presented which are applicable to efficient polyphase interpolation and decimation. Learn more about image processing, interpolation, decimation MATLAB Forums More Forums comp.dsp . 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 3.26 for L = 3 with the assumption of ideal decimation and interpolation filters. In section Ill, some applica- tions of multirate DSP are indicated, in digital audio sys- tems, in subband coding, and in voice privacy systems. [�b What shall I do to get the initial signal's amplitude. (However, you can do interpolation prior to decimation to achieve an overall rational factor, for example, “4/5”; see Part 4: Resampling.) ��,2L��L�`�*)wDr��է��| 0;H2N�$��~��4�,��H���1�@� � " About this page. The CIC Decimation block performs a sample rate decrease (decimation) on an input signal by an integer factor. 13. Perform decimation and linear or higher-order interpolation without introducing aliasing. Read a .wav file and match with their respective spectrograms. Introduction The decimator is a device that reduces the sampling rate by an integer factor of M, whereas the … Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals. 2. For decimation, the LPF serves to eliminate high frequency components in the spectrum. X'�{�ۇ��������{�]z�ԛ���o]+C� 5�&�@�ި?2���� ��Iv��,t��T����ɾ�C���=�-�{�����'�2�ޓC��� �e9�*^�$�߈�-�^�cK��M���m���̡5�/��VŵK�������a�*M����%�]��=$��j5��Z�t��R��oT�_[zUt�^+��^����n���0�w^���I:ޅ�t���_�Rn&��v����I�q�*�}�) Heavy Lowpass filtering 12: Polyphase Filters •Heavy Lowpass filtering •Maximum Decimation Frequency •Polyphase decomposition •Downsampled Polyphase Filter •Polyphase Upsampler •Complete Filter •Upsampler Implementation •Downsampler Implementation •Summary DSP and Digital Filters (2016-9045) … The main use of interpolation is to create a high definition video image from a low definition image. Mathematical interpolation vs. interpolation in DSP vs. decimation • In mathematics, interpolation stands for constructing a smooth curve that travels through all given points. In section Ill, some applica- tions of multirate DSP are indicated, in digital audio sys- tems, in subband coding, and in voice privacy systems. Solution: Decimation and Interpolation are two techniques used to alter the sampling rate of a sequence. Thanks Habib Decimation filters should not have attenuation. 2.4.7 How do I test a FIR decimator? q 595.20 0 0 841.92 0.00 4.08 cm 1 g /Obj183 Do Q endstream endobj 57 0 obj <>/Height 3508/Type/XObject>>stream ߟ�DDDH[)9C��9��zYP����{�9zl?���^`2@�},�����ȻV���~��>G��d(�du����,KB@�P_i� �]P7��6�Vu��V��b""���������ԈlR�H�*�q^��8����$�����S�s����nx(2�!�����R p�������#�d��{ DDDDD2�dc:�&{!���$0�t� x**\�^�*�2�(C� d�l6! IEEE, … 4 . ��) Ќ�T� �����*e2�1�,Z&DA"f�X �Q���Z�EYl,z��9��0�V��ר�%�2&�Z#��BFe%����ڦ�}c� ]Ð*��,�x���9�$�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� Multirate DSP Using Decimation and Interpolation 2.1. Increasing the number of samples per unit time, sometimes called upsampling, amounts to interpolation. 15. Whereas in sampling we start with a Resample uniform or nonuniform data to a new fixed rate. 2.1.5 Which signals can be downsampled? ��#��i��� �Dp�зn����=1�T(+K����T��?��_K D/������WIt���\%���H��dN���f�^�_�}$��Ap��.�G�?�0Z_]0C��l5Z_ i/��J�;��t�-���|/�z�[B9W��5���P���Z��ici8��D���r Department of Digital Signal Processing Master of Science in Electronics Multirate Systems Homework 1 Decimation and interpolation Dr. Gordana Jovanovic Dolecek Ojeda Loredo Fernando June/15/2015 Sta. 2. uuid:e6871ea1-e89d-f045-b544-dd56d540b131 Chapter 2, p. 31-39. The interpolation filter has many zeros in its input signal, as illustrated by the direct interpolation filter structure on the left in Figure 2. ;���84 These coefficients are to be used with dsp.FIRDecimator (L=1), dsp.FIRInterpolator (M=1), and dsp.FIRRateConverter (general case). ���T�����8$�!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��?��$U���!�< ?��@���Ț���8)u�u�� eÑ���u�q�ƒmׯ�����Ր&9�?o�91�DG�U�LٴG��q׈�Qs#�p��$"%@(#�!���0���j�5}�$6 �qE2Hک����A! – Low sampling rate reduces storage and computation requirements. ֈ("�k�(m'��8�ݮ��� �| �tW+";>Dq�H��b;y�. 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 Digital Signal Processing - September 2010. If we upsample by factor L to get v[m], the desired portion of V(ejω) is the spectrum in −π L, �? • 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”. Solution: Decimation and Interpolation are two techniques used to alter the sampling rate of a sequence. > [1/2 1 1/2] is a typical filter to interpolate between samples and is the > same as straight line averaging at a midpoint. This parallel operation allows ... general tree structure and its frequency resolution are displayed in Fig. 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 Rather than cascading an anti-imaging filter for interpolation with an anti-aliasing filter for decimation, we imple- ment one filter with the minim A so-designed lowpass filter is lin-ear phase, but periodically time-varying. 14. This is the basic point of view we have taken in this paper. • Interpolation – Increase the sampling rate of a discrete-time signal. In this case, we must use a process called decimation to reduce the sampling rate of the signal. h��T;o�@��Wl�s�o�]A�K).�r�� The major DSP vendors provide examples of FIR decimators in their data books and application notes; check their web sites. Mathematical interpolation vs. interpolation in DSP vs. decimation • In mathematics, interpolation stands for constructing a smooth curve that travels through all given points. The group delay variation can be minimised by adding all-pass equaliser sections. 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). Set alert. We begin in Section I1 with the mathematical (and signal processing) framework of Decimation, interpolation, downsampling, upsampling, antialiasing filter. 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 Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals. To start consider changing the rate of a signal by a factor of 2. Figure 1. h޼UYO�@�+��ҽ�޵�"� �#�iAZ��$Kp�đc$��;���QZ������ ��$�J ���"B"�Id�j�� signal processing algorithms that involve more than one sampling rate. DSP operations can use either floating-point or fixed-point formats. 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. Implementation of I/D sampling rate converters. ��OB4����Ԙ�OZM�4�[��Z�'K�Z ս��Z�K���k��o�g�{*��Y�"��]8����]ukI�ӓu��a}���r�i$�J׿���I������꿯���+�{���:I?T���k��/����/[�_O}/KkK��������k���������^���UuV�W���]%�v�������U�;)]Ҵ��Z�vP����'K�z��u��׵�q~kk���+��A+���=5� ��K��-���'K��WɲP4��A�V�?^ Download as PDF. Choosing a filter implementation that is appropriate for the targeted application helps ensure proper operation at minimum cost with respect to the L/M. Rabiner, "Multirate Digital Signal Processing," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1983. 16. �K����� t�Ɏ /���M����%���}$�+�����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 The block supports real and complex fixed-point inputs. 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 i.e. 13. 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. 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