decimation and interpolation in dsp pdf

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. ��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��"$��d�Ćm��05餼��Y3 HP 9100C Digital Sender �K�$�1R�C��Yb�N�{��k^�|��Ʃ��T% 2007-11-30T07:41:46Z Theories and applications of polyphase decomposition for the decimation and interpolation in the FT and FRFT domain have %PDF-1.6 %�� Cascaded Integrator-Comb (CIC) filters are a class of linear phase FIR filters comprised of a comb part and an integrator part. In practice, sampling is performed by applying a continuous signal … 2007-11-20T15:00:19Z Crochiere and L.R. DSP operations can use either floating-point or fixed-point formats. Each TMS320C80 DSP parallel processor (PP) contains four major units operating in parallel. Consider an input signal x[n] that is ω0-bandlimited in the DTFT domain. decimation in frequency (DIF) fast Fourier transform (FFT) algorithm using the Texas Instruments (TITM) TMS320C80 digital signal processor (DSP). Perform decimation and linear or higher-order interpolation without introducing aliasing. %PDF-1.5 %�� 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�@��[ Ma. 15. – Higher sampling rate preserves ﬁdelity. If these components were not filtered out, they would alias when the reduction in sample rate is performed. 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). ��,2L��L�`�*)wDr��է��| 0;H2N�$��~��4�,��H��1�@� � " E�=�WnQl��W��u�8$��d<��4҇�+_��.�S/��J+�!Rʌ3+d� ��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˂=�$�G��o�K)h�G }��D� _��3�#�tl%�X��o��n�@wP��k x0�� C�/�Z��:B�I��aT2Ps!A�b��M��a|/�K �i}��N��J�~[��W��I!+K��w�l�Uun�m?�kNK��n��o��vZ��:ۥﺥz�&�g��D�Y6�޿�z��{Q�cK��t�l?Q�M��=a�߭[6��i8o��j��z��k�m��}ҷ��ݪUޭ��t��Wv�n�� v��C��K��wI��v��KI��}��Nҗ}��6��[��_ޓut��;��7_�'_��賧4��_�m&�'Y�K��{m/�Ն�Z �S�C7�ց~��/n��un��T�q?��f��.V#�տ��V��z2��k��ס��[��붖�Q|��:��I�? application/pdf ��#��i�� Dp�зn��=1�T(+K��T��?��_K D/��WIt��\%��H��dN��f�^�_�}$��Ap��.�G�?�0Z_]0C��l5Z_ i/��J�;��t�-��|/�z�[B9W��5��P��Z��ici8��D��r Perform decimation and linear or higher-order interpolation without introducing aliasing. (The filtering removes the undesired spectral images.) uuid:4be995db-6968-a44e-8d94-56cd6b0650c2 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. A so-designed lowpass filter is lin-ear phase, but periodically time-varying. This parallel operation allows ��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. The group delay variation can be minimised by adding all-pass equaliser sections. Decimation, interpolation, downsampling, upsampling, antialiasing filter. endstream endobj startxref polyphase lters I and Applications. • Digital Filter Design for Interpolation and Decimation: First we treat ﬁlter design for in-terpolation. Halfband FIR filters are implemented in dsp.FIRHalfbandInterpolator and dsp.FIRHalfbandDecimator. h�b```f``rd`2��@(�^�0�,�j`�*0)XaR��Ϯ�$d��K�/p�s1�90,Z�d�̙+gN[ $f. There are many more to topics and techniques in multirate digital signal processing including: I Implementation techniques, e.g. Signal Analyzer: Visualize and compare multiple signals and spectra: Functions. For decimation, the LPF serves to eliminate high frequency components in the spectrum. The sampling rate Fs refers to the input signal. 0 IEEE, … “Interpolation”, in the DSP sense, is the process of upsampling followed by filtering. Interpolation and decimation . The CIC Decimation block performs a sample rate decrease (decimation) on an input signal by an integer factor. Resample uniform or nonuniform data to a new fixed rate. C��H�,am�,sCB�a �� T��(d��P�2�@�1*:A2�@��:�� ԹL�P l@�� * a�5� ��4`xs8+p>agpe�^�Q�� Yi6�vXU(��(��#x]: |FW� �ׂo In digital signal processing, downsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. tors, decimation and interpolation filters, and digital filter banks, are reviewed, along with the interconnection prop- erties of the building blocks. �uy�Q4nJ�T� j�W��#� �U˚ h޼UYO�@�+��ҽ�޵�"� �#�iAZ��$Kp�đc$��;��QZ�� $�J ��"B"�Id�j�� 2.4.7 How do I test a FIR decimator? In multirate Digital Signal Processing (DSP), interpolation is required wh enever it is necessary to increase the sampling r ate of a digital signal. �hV1K�5�s! To Implement Decimation Process of any given sequence. In an analogous manner to decimation, when used for interpolation, Nyquist filters allow some degree of imaging. (6marks) (DEC’09-JAN’10) (Dec.12, 6m). The signal can be decimated more than once, using a gradual change in sampling frequency. That is, some frequencies above the cutoff frequency are not attenuated by the value of Ast. … � �-�]릪�Mۍ��w�cD�7S�,��7^�U8�z��b�8�a We begin in Section I1 with the mathematical (and signal processing) framework of Cf., e.g., least-squares approximation. • Decimation – Reduce the sampling rate of a discrete-time signal. To Implement I/D sampling rate converters. Then, we describe properties pertaining to the multirate systems, namely their valid inverse operations and the noble identities. Decimation and Interpolation 1. decimation and interpolation in the multirate digital signal processing systems. between the sampling playback rates so that you don't have to keep reloading code to the DSP! ��BQ:"8!|��e�� 9�!D��. St0Bi8��hn��Î��|�!�o�߯m'�t��`f�T�y�(_��Wyy$E�'��|�跋��o��W��|�iS�fvO/�z��^t�V�7yY�z�E��i�? ��VFѴG";#�l2��.�I@�n� ��̗�p�L� About this page. • 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”. Read a .wav file and match with their respective spectrograms. Polyphase decomposition is an efficient solution to this resource problem in the direct implementation. 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�� $E��7�� 6��i}��臷��S�?�q��鷯��N�?~:��d��I��>��Pʆ��c�"T�['�,'��_��*(��k�%��ԁ��5v��%.��AUa��}��lZ�~�)!�_��uu��z��*��־D�ɶ-*]��|jo��Q�k�Z�K��C>��"�"� S�Y�]}�ׯ��C�h_��;��7�}+�}{��?Iֿ��j�I��Uv\^�~�Ww��B��AX?In��_�7�_X��a� �[ ~D;�4Z��Z^��>��2^�w��\s�[�A�^@��a3�6T��F~Ƥ��*��6&y��+��?��<4��tD�w��L��`��OZrd�-~�%��0ߵ�� p��av�^��7W��`P��p2S]��e@i�K&280��eq�T xn�R�"AV��8�+�^�N)�,8�k в֫"l@��#��5��C�X��j�ۋ�È��jz �y 2�H��`}ia�u ��t5��@�B�(F�}mVC,� W=�"C`��!�9C��9��>�a��Y��*�ւ��1Bt:�Y�2�G2��f)8��Ԥ3(P�~�H U��Z��! endstream endobj 128 0 obj <> endobj 129 0 obj <> endobj 130 0 obj <>stream signal processing algorithms that involve more than one sampling rate. Download as PDF. ��OB4��Ԙ�OZM�4�[��Z�'K�Z ս��Z�K��k��o�g�{*��Y�"��]8��]ukI�ӓu��a}��r�i$�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. ־(��&��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 ! Resample uniform or nonuniform data to a new fixed rate. Figure 1. [�b Apps. Then the techniques of decimation and interpolation enable this operation, providing the ratio T1/T2 is a rational number i.e. To Implement Interpolation Process of any given sequence. To plot a time and frequency display of microphone plus a cosine using DSP. 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.. Chapter 2, p. 31-39. The Altera DSP Builder advanced blockset is a high-level synthesis tool that is integrated with the Mathworks Simulink tool. In this system, the decimation factor is always is equal to the interpolation fac-tor. • Interpolation – Increase the sampling rate of a discrete-time signal. K��o�$W_� �ჴA .��_�A��=�� 訍 �a�O��I��0�u�{� Mathematical interpolation vs. interpolation in DSP vs. decimation • In mathematics, interpolation stands for constructing a smooth curve that travels through all given points. Explain the decimation and interpolation process with an example. 16. 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 Finally a number of multiplierless 5th and 10th order elliptic filter designs are presented which are applicable to efficient polyphase interpolation and decimation. 15. Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals. Good questions! o��c��4�M�/K�� Ϻ��|�ሧ�B)��z�*�zRX0��eũ��u]��w�C��y�~��@�� Set alert. To start consider changing the rate of a signal by a factor of 2. Whereas in sampling we start with a Rather than cascading an anti-imaging ﬁlter for interpolation with an anti-aliasing ﬁlter for decimation, we imple- ment one ﬁlter with the minim ... First, we study the basic operations of decimation and interpolation, and show how arbitrary rational sampling-rate changes can be implemented with them. Purdue University: ECE438 - Digital Signal Processing with Applications 4 rate is lower than the sampling rate of the available data. 2.1.5 Which signals can be downsampled? Halfband filters are an efficient way of doing this. About this page. Implementation of Decimation Process. 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. 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 must incorporate the filtering operations for both interpolation and decimation, and hence it should ideally possess the frequency response characteristic filter. Therefore y(n) is simply x(Dn). 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. The radix-4 DIF algorithm increases the execution speed of the FFT. 2. 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. This is the basic point of view we have taken in this paper. Multiple stages for decimation (or interpolation) can reduce the number of lter coe cients in the lter speci cations. Chronological; Newest First; Reply by Jon Harris January 15, 2004 2004-01-15. o Constructing a curve that is as close as possible but does not include all the given points is referred to as approximation. Digital Signal Processing - September 2010. What shall I do to get the initial signal's amplitude. It also looks at multistage decimation and polyphase filters. Decimation by 8. 3.26 for L = 3 with the assumption of ideal decimation and interpolation filters. �QDv��B��. Introduction The decimator is a device that reduces the sampling rate by an integer factor of M, whereas the … 13. ... general tree structure and its frequency resolution are displayed in Fig. X'�{�ۇ��{�]z�ԛ��o]+C� 5�&�@�ި?2�� Iv��,t��T��ɾ�C��=�-�{��'�2�ޓC�� e9�*^�$�߈�-�^�cK��M��m��̡5�/��VŵK��a�*M��%�]��=$��j5��Z�t��R��oT�_[zUt�^+��^��n��0�w^��I:ޅ�t��_�Rn&��v��I�q�*�}�) (6marks) (DEC’09-JAN’10) (Dec.12, 6m). 141 0 obj <>/Filter/FlateDecode/ID[<96B5F680F483E53ADCD832CB0859C2A2>]/Index[127 25]/Info 126 0 R/Length 84/Prev 629771/Root 128 0 R/Size 152/Type/XRef/W[1 3 1]>>stream ��̫_2-�v#�?��W#�|��e��E�oR�C[b�e�޸_I�(�f�>��}��v:_غYڅ��z_�ic��kgcw��EU��u��k��_I��{^�M��}-t��V��'�^�]zW��gb�o��}[��O��69��խ��z��k��y��I��W��{��z��uֽ=�k��L��+;�S�>�� V��z��}7��Uls��0�o_FUt��;��'�0 &��/��Z /�'ҿ�}RX�� *_��sFAu��-��uM�W��A��ӂRL��ޗB��A ��+�]}�� A��z�_�W��o��?��Y�+m�ے�_�� t��ޭ��K��uqu�u��>��-d��k��5�u�PgH��Z�o��K��Y'�� ޭ��[zH;�ΡӺ�u~��uK; If we upsample by factor L to get v[m], the desired portion of V(ejω) is the spectrum in −π L, Rabiner, "Multirate Digital Signal Processing," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1983. "�DD8��_��b"""|��TV�G)��D��Yq@o |�rZiR�z��Z�� ʳq^w+B �� ~�>� �#�8�4��?�Uگ�it"""�AqА�O�B�!�� interpolation" method (interpolate to get the coeffeicents, then use them to interpolate the data) in their audio sample rate converter products. Decimation & Aliasing. The interpolation filter has many zeros in its input signal, as illustrated by the direct interpolation filter structure on the left in Figure 2. Implementation of Interpolation Process. 9.2 Decimation Decimation can be regarded as the discrete-time counterpart of sampling. INTRODUCTION TO DIGITAL SIGNAL PROCESSING Question No. Should I multiply the output signal for each stage by a constant value? ߟ�DDDH[)9C��9��zYP��{�9zl?��^`2@�},��ȻV��~��>G��d(�du��,KB@�P_i� �]P7��6�Vu��V��b""��ԈlR�H�*�q^��8��$��S�s��nx(2�!��R p��#�d��{ DDDDD2�dc:�&{!��$0�t� x**\�^�*�2�(C� d�l6! �>��;E�I�l��|߼�e�7��)��}��S��5:��WwW��bY'v:��fs��c��Q�rg��~g��!یKwpC9��N��ē�͔t��Bۿ�v�ucs @��,��̔��]�Jѓϕz�I�$��e�F7��y_��j ��{-b��*�0��-{]�R��zT��G_dH9v�E\�ڸ� ��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}�$6 �qE2Hک��A! The advanced blockset allows you to quickly design an algorithm, such as a high performance resampling filter, without regard for the hardware implementation details. tors, decimation and interpolation filters, and digital filter banks, are reviewed, along with the interconnection prop- erties of the building blocks. Tonantzintla, Puebla 2. h�T�Mo� ��>n�Bh�JQK5)�}h�v��t��Hz�`�j��l��ݾ�� This chapter investigates basics of multirate digital signal processing, illustrates how to change a sampling rate for speech and audio signals, and describes the polyphase implementation for the decimation filter and interpolation filter. 0�G��Td��-Q�Z��Z� 0�G�� 0�F@aj� 0�G�Tr��]�S�{�޿��-_��-Q��@aj��ҿ��w��m�ˢ��,�.6��@aj��2T|��`f,��A��)�}Q�^ d��1��,�#�2ʡQ�? In practice, sampling is performed by applying a continuous signal … Solution: Decimation and Interpolation are two techniques used to alter the sampling rate of a sequence. bC@P�n�>x>�Љ-�B[�M�:��Aw"uDpV��V�)�@�qE�A�D!�s�g�E�'!\�8�q�6I�d$��w��H��.Vo�B#5�pl#�@3R��a�� Gg��7�D��`�ADG�3��p_i��a��}H\/+ ,��|-�� _xd �e��?�usXZ�NA�sJaYP?d8�$�"&i.��pR�� 1 1. 1.1.1 Floating point Floating point is a method to represent real numbers. Set alert. The floating point unit in the Cortex®-M4 is only single precision, as it includes an 8-bit exponent field and a 23-bit fraction, for a total of 32 bits (see Figure 1). ��) Ќ�T� ��*e2�1�,Z&DA"f�X �Q��Z�EYl,z��9��0�V��ר�%�2&�Z#��BFe%��ڦ�}c� ]Ð*��,�x��9�$�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� 14. 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 h�bbd```b``��! 2007-11-30T07:41:46Z Their IIR counterparts, dsp.IIRHalfbandInterpolator and dsp.IIRHalfbandDecimatorcan be an even more efficient way of interpolating/decimating by 2. Decimating, or downsampling, a signal x(n) by a factor of D is the process of creating a ;��84 Explain the decimation and interpolation process with an example. 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 Both downsampling and decimation can be synonymous with compression, or they can describe an entire process of bandwidth reduction and sample-rate reduction. 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. Working of interpolation or decimation . 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. 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 Lizhe Tan, Jean Jiang, in Digital Signal Processing (Third Edition), 2019. Forums More Forums comp.dsp . 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. In the case of interpolation, the filter retains most of the spec… 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. This chapter shifts the emphasis to the design of the companion digital interpolation and decimation filters. Myself, I've experimented with cubic interpolation in audio applications and it sounded better than linear … 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. – Low sampling rate reduces storage and computation requirements. Decimation, interpolation, downsampling, upsampling, antialiasing filter. Solution: Decimation and Interpolation are two techniques used to alter the sampling rate of a sequence. uuid:e6871ea1-e89d-f045-b544-dd56d540b131 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. Document from Glenys o Constructing a curve that is as close as possible but does not include all the given points is referred to as approximation. The filter sample rate is 2x > the input series. Although the example uses decimation-by-2 stages, our approach applies to any integer decimation factor. Cf., e.g., least-squares approximation. • Interpolation – Increase the sampling rate of a discrete-time signal. Multirate DSP Using Decimation and Interpolation 2.1. Frequently, there is the need in DSP to change the sampling rate of existing data. endstream endobj 131 0 obj <>stream Xilinx DSP slices is presented. 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) … • Decimation – Reduce the sampling rate of a discrete-time signal. DSP and Digital Filters (2016-9045) Polyphase Filters: 12 – 1 / 10. Figure 1 illustrates a polyphase decimation filter at … 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. 16. 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. The block supports real and complex fixed-point inputs. (However, you can do interpolation prior to decimation to achieve an overall rational factor, for example, “4/5”; see Part 4: Resampling.) Multirate systems are sometimes used for sampling-rate conversion, which involves both decimation and interpolation. It can be applied for the derivation of new sampling theorems and the recovering bandlim-ited signal from nonuniformly sampled versions. �Z��Z�rTrW��-Q�Z��Z��-Q��?��?��? 13. endstream endobj 132 0 obj <>stream Learn more about image processing, interpolation, decimation MATLAB Both the interpolation and decimation filters incorporate a low-pass filtering function. – Higher sampling rate preserves ﬁdelity. 12. 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 HD video from non HD sources on a modern TV. These coefficients are to be used with dsp.FIRDecimator (L=1), dsp.FIRInterpolator (M=1), and dsp.FIRRateConverter (general case). 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. Increasing the number of samples per unit time, sometimes called upsampling, amounts to interpolation. However, this occurs only in the transition band of the filter. system are decreasing (decimation) and increasing (interpolation) the sampling-rate of a signal. �? Audio application such as to plot a time and frequency display of microphone plus a cosine using DSP. 12. {ۺ�^|ȶ�(�d5G!��vH��!�� D4ܡ��L�DBE��/�r�b(��P I have designed a decimation and interpolation filter, the amplitude after each decimation decreases. 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 I Decimation, I Interpolation, I Non-integer sample rate conversion, I Multistage sample rate conversion. > [1/2 1 1/2] is a typical filter to interpolate between samples and is the > same as straight line averaging at a midpoint. 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. L/M. 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. The major DSP vendors provide examples of FIR decimators in their data books and application notes; check their web sites. In this case, we must use a process called decimation to reduce the sampling rate of the signal. ֈ("�k�(m'��8�ݮ�� | �tW+";>Dq�H��b;y�. ��-Q��O�3� ��3_o�@� Thanks Habib Decimation filters should not have attenuation. 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. In section Ill, some applica- tions of multirate DSP are indicated, in digital audio sys- tems, in subband coding, and in voice privacy systems. 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. Record several seconds of a waveform into SRAM at 32 KHz and this time remove Mathematical interpolation vs. interpolation in DSP vs. decimation • In mathematics, interpolation stands for constructing a smooth curve that travels through all given points. i.e. It will be published Monday, April 28. 127 0 obj <> endobj Decreasing the number of samples per unit time, sometimes called downsampling, is decimation … Started by seb January 13, 2004. 14. Implementation of I/D sampling rate converters. 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 Yes it is possible to do something in between linear and a much higher-order FIR filter. endstream endobj 133 0 obj <>stream The reason for this LPF, however, is quite different for each case. h��T;o�@��Wl�s�o�]A�K).�r�� Furthermore, wikipedia interpolation: "Upsampling requires a lowpass filter after increasing the data rate, and downsampling requires a lowpass filter before decimation. Abstract: The concepts of digital signal processing are playing an increasingly important role in the area of multirate signal processing, i.e. %%EOF In section Ill, some applica- tions of multirate DSP are indicated, in digital audio sys- tems, in subband coding, and in voice privacy systems. {i}?��Ҧ�� This article is available in PDF format for easy printing. Multirate DSP Using Decimation and Interpolation 2.1. 11.2 Polyphase Filter Structure and Implementation. �!�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�� 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 g20�莈�Ddph/�ь� &��@b��M��wB��"�"��d6 2. Decimation (DDC) and Interpolation (DUC) Concepts TIPL 4701 Presented by Jim Seton Prepared by Jim Seton 1. Choosing a filter implementation that is appropriate for the targeted application helps ensure proper operation at minimum cost with respect to the The main use of interpolation is to create a high definition video image from a low definition image. 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. (However, you can do interpolation prior to decimation to achieve an overall rational factor, for example, “4/5”; see Part 4: Resampling.) 4 . In this paper we present a tutorial overview of multirate digital signal processing as applied to systems for decimation and interpolation. 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. Therefore, both operations can be accomplished by a single filter with the lower of the two cutoff frequencies. 151 0 obj <>stream ��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�� 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 called decimation to reduce the sampling rate of the signal. – Low sampling rate reduces storage and computation requirements. Therefore, for the input and output of the model concerned, the sampling rate is NOT changed, but it is changed within the model.