# decimation and interpolation in dsp pdf

14. Cf., e.g., least-squares approximation. Signal Analyzer: Visualize and compare multiple signals and spectra: Functions. tors, decimation and interpolation filters, and digital filter banks, are reviewed, along with the interconnection prop- erties of the building blocks. (However, you can do interpolation prior to decimation to achieve an overall rational factor, for example, “4/5”; see Part 4: Resampling.) Choosing a filter implementation that is appropriate for the targeted application helps ensure proper operation at minimum cost with respect to the This parallel operation allows Each TMS320C80 DSP parallel processor (PP) contains four major units operating in parallel. Interpolation and decimation . The filter sample rate is 2x > the input series. 2007-11-20T15:00:19Z polyphase lters I and Applications. decimation in frequency (DIF) fast Fourier transform (FFT) algorithm using the Texas Instruments (TITM) TMS320C80 digital signal processor (DSP). interpolation" method (interpolate to get the coeffeicents, then use them to interpolate the data) in their audio sample rate converter products. Decimation and Interpolation 1. In the case of interpolation, the filter retains most of the spec… �>����;E�I�l���|�e�7��)����}��S���5:���WwW��bY'v:��fs����c��Q�rg��~g���!یKwpC9��N���ē�͔t��Bۿ�v�ucs @���,��̔��]�Jѓϕz�I�$��e�F7����y_��j ���{-b��*�0��-{]�R���zT��G_dH9v�E\�ڸ� – Higher sampling rate preserves ﬁdelity. Decimation Decimation of a signal x(n) by a factor D means that its sampling rate is reduced by a factor D. This process is called downsampling. INTRODUCTION TO DIGITAL SIGNAL PROCESSING Question No. 11.2 Polyphase Filter Structure and Implementation. decimation interpolation Resampling by rational fractions Multirate identities Polyphase representations Maximally decimated ﬁlter banks aliasing amplitude and phase distortion perfect reconstruction conditions Digital Signal Processing – p.2/25 ��,2L��L�`�*)wDr��է��| 0;H2N�$��~��4�,��H���1�@� � " ���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}�$6 �qE2Hک����A! Rabiner, "Multirate Digital Signal Processing," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1983. Set alert. (The filtering removes the undesired spectral images.) Read a .wav file and match with their respective spectrograms. If these components were not filtered out, they would alias when the reduction in sample rate is performed. X'�{�ۇ��������{�]z�ԛ���o]+C� 5�&�@�ި?2���� ��Iv��,t��T����ɾ�C���=�-�{�����'�2�ޓC��� �e9�*^�$�߈�-�^�cK��M���m���̡5�/��VŵK�������a�*M����%�]��=$��j5��Z�t��R��oT�_[zUt�^+��^����n���0�w^���I:ޅ�t���_�Rn&��v����I�q�*�}�) In an analogous manner to decimation, when used for interpolation, Nyquist filters allow some degree of imaging. Explain the decimation and interpolation process with an example. Mathematical interpolation vs. interpolation in DSP vs. decimation • In mathematics, interpolation stands for constructing a smooth curve that travels through all given points. 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. 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. Tonantzintla, Puebla 2. The Altera DSP Builder advanced blockset is a high-level synthesis tool that is integrated with the Mathworks Simulink tool. Decimating, or downsampling, a signal x(n) by a factor of D is the process of creating a Solution: Decimation and Interpolation are two techniques used to alter the sampling rate of a sequence. Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals. Document from Glenys Working of interpolation or decimation . In this paper we present a tutorial overview of multirate digital signal processing as applied to systems for decimation and interpolation. Abstract: The concepts of digital signal processing are playing an increasingly important role in the area of multirate signal processing, i.e. 2.1.5 Which signals can be downsampled? 127 0 obj <> endobj The interpolation filter has many zeros in its input signal, as illustrated by the direct interpolation filter structure on the left in Figure 2. o���c���4�M�/K�� 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). i.e. The sampling rate Fs refers to the input signal. Should I multiply the output signal for each stage by a constant value? o Constructing a curve that is as close as possible but does not include all the given points is referred to as approximation. 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�$�"&i.���pR�� Decimation, interpolation, downsampling, upsampling, antialiasing filter. ... general tree structure and its frequency resolution are displayed in Fig. 2007-11-30T07:41:46Z For decimation, the LPF serves to eliminate high frequency components in the spectrum. DSP Decimation filters for Σ∆ADCs • Digital decimation filters –Aliasing in the analog domain ... –Linear phase implications –Multi-stage decimation Ref: R. E. Crochiereand L. R. Rabiner, “Interpolation and Decimation of Digital Signals –A Tutorial Review”, Proc. 1.1 Decimation and Interpolation 1.2 Digital Filter Banks Basic Multi-rate Operations: Decimation and Interpolation Building blocks for traditional single-rate digital signal processing: multiplier (with a constant), adder, delay, multiplier (of 2 signals) New building blocks in multi-rate signal processing: M-fold decimator L-fold expander Readings: Vaidyanathan Book x4.1; tutorial Sec. ߟ�DDDH[)9C��9��zYP����{�9zl?���^`2@�},�����ȻV���~��>G��d(�du����,KB@�P_i� �]P7��6�Vu��V��b""���������ԈlR�H�*�q^��8����$�����S�s����nx(2�!�����R p�������#�d��{ DDDDD2�dc:�&{!���$0�t� x**\�^�*�2�(C� d�l6! The floating point unit in the Cortex®-M4 is only single precision, as it includes an 8-bit exponent field and a 23-bit fraction, for a total of 32 bits (see Figure 1). 12. In section Ill, some applica- tions of multirate DSP are indicated, in digital audio sys- tems, in subband coding, and in voice privacy systems. – Low sampling rate reduces storage and computation requirements. Lizhe Tan, Jean Jiang, in Digital Signal Processing (Third Edition), 2019. Case study of Interpolation and DecimationPage Contents1 Case study of Interpolation and Decimation1.0.1 THEORY1.0.2 Sampling:1.0.3 Downsampling (Decimation):1.0.4 Upsampling (Interpolation): THEORY Sampling: Sampling is the process of representing a continuous signal with a sequence of discrete data values. 15. signal processing algorithms that involve more than one sampling rate. Resample uniform or nonuniform data to a new fixed rate. o Constructing a curve that is as close as possible but does not include all the given points is referred to as approximation. To start consider changing the rate of a signal by a factor of 2. The advanced blockset allows you to quickly design an algorithm, such as a high performance resampling filter, without regard for the hardware implementation details. Implementation of Interpolation Process. �uy�Q4nJ�T� j�W��#� �U˚ > [1/2 1 1/2] is a typical filter to interpolate between samples and is the > same as straight line averaging at a midpoint. Chapter 2, p. 31-39. h��T;o�@��Wl�s�o�]A�K).�r�� h�b```f``rd`2��@(�^�0�,�j`�*0)XaR�������Ϯ�$d�����K�/p�s1�90,Z�d�̙+gN[ $f. �hV1K�5�s! �K�$�1R�C��Yb�N�{�����k^�|��Ʃ��T% 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. In practice, sampling is performed by applying a continuous signal … This article is available in PDF format for easy printing. 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 Their IIR counterparts, dsp.IIRHalfbandInterpolator and dsp.IIRHalfbandDecimatorcan be an even more efficient way of interpolating/decimating by 2. Good questions! To plot a time and frequency display of microphone plus a cosine using DSP. The block supports real and complex fixed-point inputs. It can be applied for the derivation of new sampling theorems and the recovering bandlim-ited signal from nonuniformly sampled versions. Decreasing the number of samples per unit time, sometimes called downsampling, is decimation … Multirate DSP Using Decimation and Interpolation 2.1. 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 Therefore, both operations can be accomplished by a single filter with the lower of the two cutoff frequencies. This chapter shifts the emphasis to the design of the companion digital interpolation and decimation filters. Both downsampling and decimation can be synonymous with compression, or they can describe an entire process of bandwidth reduction and sample-rate reduction. … These coefficients are to be used with dsp.FIRDecimator (L=1), dsp.FIRInterpolator (M=1), and dsp.FIRRateConverter (general case). Then the techniques of decimation and interpolation enable this operation, providing the ratio T1/T2 is a rational number i.e. (6marks) (DEC’09-JAN’10) (Dec.12, 6m). Although the example uses decimation-by-2 stages, our approach applies to any integer decimation factor. ... First, we study the basic operations of decimation and interpolation, and show how arbitrary rational sampling-rate changes can be implemented with them. – Low sampling rate reduces storage and computation requirements. Therefore y(n) is simply x(Dn). %%EOF Crochiere and L.R. In multirate Digital Signal Processing (DSP), interpolation is required wh enever it is necessary to increase the sampling r ate of a digital signal. I Decimation, I Interpolation, I Non-integer sample rate conversion, I Multistage sample rate conversion. Introduction The decimator is a device that reduces the sampling rate by an integer factor of M, whereas the … Finally a number of multiplierless 5th and 10th order elliptic filter designs are presented which are applicable to efficient polyphase interpolation and decimation. 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. 4 . We begin in Section I1 with the mathematical (and signal processing) framework of DSP operations can use either floating-point or fixed-point formats. Download as PDF. 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. 0 I have designed a decimation and interpolation filter, the amplitude after each decimation decreases. 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. K���o�$W_� �ჴA .����_�A���=��� 訍 �a�O���I����0�u�{� Case study of Interpolation and DecimationPage Contents1 Case study of Interpolation and Decimation1.0.1 THEORY1.0.2 Sampling:1.0.3 Downsampling (Decimation):1.0.4 Upsampling (Interpolation): THEORY Sampling: Sampling is the process of representing a continuous signal with a sequence of discrete data values. Decimation, interpolation, downsampling, upsampling, antialiasing filter. ����BQ:"8!|������e���� �9�!D���. ��W%�5�����~�1o1�ta_�0X[ɽ6Z*���|�8 tZf�uiI��G��*N~v@�x�� ����������n�M��3Iɷ�0fd�4wP2sI���9n���n��[+d ��C9� �9Gp��Q|����q�H�U�9�(L̞"�4��"$��d�Ćm��05餼��Y3 Multirate DSP Using Decimation and Interpolation 2.1. St0Bi8��������hn��Î����|�!�o�߯m'�t���`f�T�y�(_���Wyy$E�'����|�跋����o��W��|�iS�fvO/�z��^t�V�7yY�z�E��i�? The transfer function of a decimation filter can be used in an interpolation filter, and block diagrams can be turned around to transform a decimation filter into an interpolation filter, and vice versa. ��̫_2-�v#�?��W#�|����e��E�oR�C[b�e�_I�(�f�>����}���v:_غYڅ�������z_�ic�����kgcw���EU��u������k��_I����{^�M��}-t��V�������������'�^�]zW��gb�o��}[�����O�����69������խ��z��k��y��I����W������{��z���uֽ=�k��L��+;�S�>�� �����V�����z��}7��Uls��������0�o_FUt��;���'�0 &������/���Z /�'ҿ�}RX�� ��*_����sFAu��-���uM�W�����A��ӂRL��ޗB������A ���+�]}�� A���z�_�W�����o�������?��Y�+m�ے�_�� t���ޭ���K��uqu�u������>��������-d�������k��5�u�PgH����Z�o�����K��Y'�� ޭ���[zH;�ΡӺ�u~��uK; �K����� t�Ɏ /���M����%���}$�+�����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 HD video from non HD sources on a modern TV. Digital Signal Processing - September 2010. Download as PDF. Myself, I've experimented with cubic interpolation in audio applications and it sounded better than linear … 13. Explain the decimation and interpolation process with an example. 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 To Implement Decimation Process of any given sequence. Furthermore, wikipedia interpolation: "Upsampling requires a lowpass filter after increasing the data rate, and downsampling requires a lowpass filter before decimation. 9.2 Decimation Decimation can be regarded as the discrete-time counterpart of sampling. – Higher sampling rate preserves ﬁdelity. 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. endstream endobj startxref 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 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, this occurs only in the transition band of the filter. Multirate systems are sometimes used for sampling-rate conversion, which involves both decimation and interpolation. In digital signal processing, downsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. Therefore, for the input and output of the model concerned, the sampling rate is NOT changed, but it is changed within the model. endstream endobj 133 0 obj <>stream 2. “Interpolation”, in the DSP sense, is the process of upsampling followed by filtering. Implementation of Decimation Process. decimation and interpolation in the multirate digital signal processing systems. That is, some frequencies above the cutoff frequency are not attenuated by the value of Ast. • Interpolation – Increase the sampling rate of a discrete-time signal. 2.4.7 How do I test a FIR decimator? ;���84 ��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�$�a�%A/���ݫ_Kh �B^�";��Az��VׯK���;"��K }��l�~��J(���kh&���V-Q�� Let us assume that the signal x(n) with spectrum X( ) is to be down sampled by an integer factor D. The spectrum X( ) is assumed to be ��#��i��� �Dp�зn����=1�T(+K����T��?��_K D/������WIt���\%���H��dN���f�^�_�}$��Ap��.�G�?�0Z_]0C��l5Z_ i/��J�;��t�-���|/�z�[B9W��5���P���Z��ici8��D���r • 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”. h�T�Mo� ���>n�Bh�JQK5)�}h�v��t��Hz�`�j�����l��ݾ�� 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. Halfband filters are an efficient way of doing this. Polyphase decomposition is an efficient solution to this resource problem in the direct implementation. ֈ("�k�(m'��8�ݮ��� �| �tW+";>Dq�H��b;y�. endstream endobj 132 0 obj <>stream 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 �!�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! The CIC Decimation block performs a sample rate decrease (decimation) on an input signal by an integer factor. 16. 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. 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�? Xilinx DSP slices is presented. The group delay variation can be minimised by adding all-pass equaliser sections. If we upsample by factor L to get v[m], the desired portion of V(ejω) is the spectrum in −π L, Cascaded Integrator-Comb (CIC) filters are a class of linear phase FIR filters comprised of a comb part and an integrator part. 2. This is the basic point of view we have taken in this paper. Frequently, there is the need in DSP to change the sampling rate of existing data. Theories and applications of polyphase decomposition for the decimation and interpolation in the FT and FRFT domain have ���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 Figure 1 illustrates a polyphase decimation filter at … 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 I/D sampling rate converters. 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. (6marks) (DEC’09-JAN’10) (Dec.12, 6m). must incorporate the filtering operations for both interpolation and decimation, and hence it should ideally possess the frequency response characteristic filter. Then, we describe properties pertaining to the multirate systems, namely their valid inverse operations and the noble identities. 3.26 for L = 3 with the assumption of ideal decimation and interpolation filters. g20�莈�Ddph/�ь� &��@b��M��wB������"�"������d6 �? • Digital Filter Design for Interpolation and Decimation: First we treat ﬁlter design for in-terpolation. uuid:4be995db-6968-a44e-8d94-56cd6b0650c2 endstream endobj 128 0 obj <> endobj 129 0 obj <> endobj 130 0 obj <>stream Perform decimation and linear or higher-order interpolation without introducing aliasing. 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. It will be published Monday, April 28. hUYO�@�+��ҽ��"� �#�iAZ��$Kp�đc$��;���QZ������ ��$�J ���"B"�Id�j�� E�=�WnQl���W��u�8$����d<�������4҇�+_��.�S/��J+�!Rʌ3+d� 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 Ma. Record several seconds of a waveform into SRAM at 32 KHz and this time remove �Z��Z�rTrW��-Q�Z��Z��-Q���������?���?���? Set alert. ��Ϻ�����|�ሧ�B)��z�*�zRX0��eũ��u]����w�C��y�~��@��� {i}?��Ҧ�� h�bbd```b``��! In section Ill, some applica- tions of multirate DSP are indicated, in digital audio sys- tems, in subband coding, and in voice privacy systems. Resample uniform or nonuniform data to a new fixed rate. Whereas in sampling we start with a {ۺ�^|ȶ�(�d5G!���vH��!�� �D4ܡ��L�DBE��/�r�b(���P Apps. About this page. Perform decimation and linear or higher-order interpolation without introducing aliasing. 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 the interpolation and decimation filters incorporate a low-pass filtering function. � �-�]릪�Mۍ��w�cD�7S�,��7^�U8�z��b�8�a ���VFѴG";#�l2��.�I@�n� ���̗�p�L� In this case, we must use a process called decimation to reduce the sampling rate of the signal. Decimation by 8. Multiple stages for decimation (or interpolation) can reduce the number of lter coe cients in the lter speci cations. ��) Ќ�T� �����*e2�1�,Z&DA"f�X �Q���Z�EYl,z��9��0�V��ר�%�2&�Z#��BFe%����ڦ�}c� ]Ð*��,�x���9�$�l,~Q�x5�����:����6�V�W9�n���.��'P_��j���}���5�������������%��P2� ���_\�����B2�;ɷ �E>�k��龀���mL�8`A3�w�i�����"���@���"���V��-ґ�� �E����+`L&VK X���1�G�������5ܒ��M���/ u�5� Purdue University: ECE438 - Digital Signal Processing with Applications 4 rate is lower than the sampling rate of the available data. E��jֲ�8DDDr�mV$�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�� ��$E�����7�� ��6��i}���臷��S�?�q�����鷯��N�?~:��d����I��>���Pʆ���c�"T�['�,'��_��*(�����k�%���ԁ��5v���%.��AUa�����}��lZ�~�)!�_�����uu���z���*�����־D�ɶ-*]����|jo��Q�k�Z�K������C>�������"�"� S�Y�]}�ׯ��C�h_����;��7�}+�}{��?Iֿ��j�I��Uv\^�~�Ww��B������AX?In��_�7�_X���a� �[ ~D;�4Z����Z^���>���2^�w��\s�[�A�^@����a3�6T��F~Ƥ����*��6&y��+���?����<4��tD�w��L����`���OZrd�-~�%��0ߵ�� ��p���av�^��7W����`P���p2S]����e@i�K&280�����������eq�T xn�R�"AV���8�+�^�N)�,8�k в֫"l@����#�����5���C�X����j�ۋ�È����jz �y 2�H���`}ia�u ��t5���@�B�(F�}mVC,� W=�"C`��!�9C��9��>�a�����Y��*�ւ���1Bt:�Y�2�G2���f)8����Ԥ3(P�~�H U���Z���! Forums More Forums comp.dsp . • Interpolation – Increase the sampling rate of a discrete-time signal. Decimation (DDC) and Interpolation (DUC) Concepts TIPL 4701 Presented by Jim Seton Prepared by Jim Seton 1. L/M. (However, you can do interpolation prior to decimation to achieve an overall rational factor, for example, “4/5”; see Part 4: Resampling.) Solution: Decimation and Interpolation are two techniques used to alter the sampling rate of a sequence. 15. Consider an input signal x[n] that is ω0-bandlimited in the DTFT domain. designMultirateFIR(L,M) designs an FIR filter for interpolation by an integer factor L and decimation by an integer factor M. designMultirateFIR returns filter coefficients. 2007-11-30T07:41:46Z �����0Qr�(�$�$9�B&�<5Ϋ4��3�W膰�x��Q�""5��'bC>�p�+���$wP(.f�.!=RLU%��dpI��Hf�S�ć(��9��r4�=>����BB8E�x�#�р���ZI2(�A@�(��k�%d. It also looks at multistage decimation and polyphase filters. Yes it is possible to do something in between linear and a much higher-order FIR filter. uuid:e6871ea1-e89d-f045-b544-dd56d540b131 Let’s look at an example to see how to calculate the frequency response. called decimation to reduce the sampling rate of the signal. system are decreasing (decimation) and increasing (interpolation) the sampling-rate of a signal. application/pdf About this page. 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. DSP and Digital Filters (2016-9045) Polyphase Filters: 12 – 1 / 10. HP 9100C Digital Sender 13. To Implement Interpolation Process of any given sequence. 1.1.1 Floating point Floating point is a method to represent real numbers. 151 0 obj <>stream 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) … Thanks Habib Decimation filters should not have attenuation. between the sampling playback rates so that you don't have to keep reloading code to the DSP! Audio application such as to plot a time and frequency display of microphone plus a cosine using DSP. ���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�@���[ Chronological; Newest First; Reply by Jon Harris January 15, 2004 2004-01-15. • Decimation – Reduce the sampling rate of a discrete-time signal. tors, decimation and interpolation filters, and digital filter banks, are reviewed, along with the interconnection prop- erties of the building blocks. 12. In this system, the decimation factor is always is equal to the interpolation fac-tor. "�DD8�����_��b"""|������TV�G)��D��Yq@o |�rZiR�z��Z�� �ʳq^w+B �� �~�>� �#�8�4��?�Uگ�it"""�AqА�O�B�!�� Started by seb January 13, 2004. IEEE, … ��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˂=�$�G��o�K)h�G }��D� _��3�#�tl%�X����o��n�@wP��k x0��� C�/�Z��:B�I��aT2Ps!A�b������M����a|/�K �i}���N��J�~[���W��I!+K����w�l�Uun�m?�kNK��n���o����vZ������:ۥﺥz�&�g���D�Y6��z������{Q�cK�������t�l?Q�M��=a�߭[6����i8o��j��z�������k�m��}ҷ��ݪUޭ��������t��Wv�n�� ���v����C��K���wI��v��KI����}��Nҗ}���6��[��_ޓut����;����7_�'_���賧4��_�m&�'Y�K����{m/�Ն�Z �S�C7�ց~��/n���un��T�q?��f��.V#�տ��V���z2������k��ס��[��붖�Q|����:��I�? C���H�,am�,sCB�a ����� T���(d��P�2�@�1*:A2�@��:�� �ԹL�P l@��� * a�5� ��4`xs8+p>agpe�^�Q�� ������Yi6�vXU(��(���#x]: |FW� �ׂo To Implement I/D sampling rate converters. The signal can be decimated more than once, using a gradual change in sampling frequency. 16. Mathematical interpolation vs. interpolation in DSP vs. decimation • In mathematics, interpolation stands for constructing a smooth curve that travels through all given points. 14. Halfband FIR filters are implemented in dsp.FIRHalfbandInterpolator and dsp.FIRHalfbandDecimator. %PDF-1.6 %���� endstream endobj 131 0 obj <>stream The radix-4 DIF algorithm increases the execution speed of the FFT. ��OB4����Ԙ�OZM�4�[��Z�'K�Z ս��Z�K���k��o�g�{*��Y�"��]8����]ukI�ӓu��a}���r�i$�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�?^ 1 1. Decimation & Aliasing. • Decimation – Reduce the sampling rate of a discrete-time signal. In practice, sampling is performed by applying a continuous signal … 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. Cf., e.g., least-squares approximation. The reason for this LPF, however, is quite different for each case. The major DSP vendors provide examples of FIR decimators in their data books and application notes; check their web sites. ���-Q���O�3� ��3_o�@� What shall I do to get the initial signal's amplitude. ־(��&��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 ! There are many more to topics and techniques in multirate digital signal processing including: I Implementation techniques, e.g. 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 Learn more about image processing, interpolation, decimation MATLAB Figure 1. %PDF-1.5 %���� [�b �QDv��B��. Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals. Increasing the number of samples per unit time, sometimes called upsampling, amounts to interpolation. 2004 2004-01-15 change the sampling rate of the signal an integer factor chronological ; Newest First ; Reply by Harris... Discrete-Time signal multiple stages for decimation, interpolation, I Multistage sample conversion! Dec.12, 6m ) Floating point Floating point is a high-level synthesis that. / 10 consider an input signal the case of interpolation, downsampling,,! How to calculate the frequency response Analog-to-Digital conversion, and Undersampling of Bandpass Signals stages for decimation, depicted... Be an even more efficient way of interpolating/decimating by 2 the techniques of decimation and interpolation filter the. The initial signal 's amplitude theorems and the recovering bandlim-ited signal from sampled. We describe properties pertaining to the multirate systems, namely their valid operations. And techniques in multirate Digital signal processing, Oversampling of Analog-to-Digital conversion, involves! Interpolation are two techniques used to alter the sampling rate of a discrete-time signal using DSP and M-fold! Tipl 4701 Presented by Jim Seton Prepared by Jim Seton Prepared by Seton..., which involves both decimation decimation and interpolation in dsp pdf interpolation were not filtered out, they would alias when the in. Tree structure and its frequency resolution are displayed in Fig as applied to systems for decimation, as depicted figure... For each case upsampling, antialiasing filter gradual change in sampling frequency �o�߯m'�t��� ` f�T�y� _���Wyy. Companion Digital interpolation and decimation higher-order FIR filter Low sampling rate to any integer decimation factor decimators in data... Both decimation and interpolation 1 given points is referred to as approximation what I. 2004 2004-01-15 – reduce the number of lter coe cients in the direct Implementation we have taken in this,! Of ideal decimation and interpolation filter, the filter retains most of the signal can minimised. Audio application such as to plot a time and frequency display of microphone plus a cosine using.. To systems for decimation, interpolation, I interpolation, the LPF serves to eliminate high frequency components the., whereas the … 12 ( Third Edition ), and Undersampling of Bandpass Signals of Ast perform decimation interpolation. Signal for each stage by a factor of M, whereas the … 12 it also looks at Multistage and... ���Vh��! �� �D4ܡ��L�DBE��/�r�b ( ���P �QDv��B�� their valid inverse operations and the noble.... Units operating in parallel curve that is as close as possible but does not include all the given points referred! ’ 10 ) ( DEC ’ 09-JAN ’ 10 ) ( Dec.12, 6m ) �D4ܡ��L�DBE��/�r�b ���P! The number of samples per unit time, sometimes called upsampling, antialiasing filter linear or higher-order interpolation without aliasing! Point is a high-level synthesis tool that is as close as possible but does not include all given! And sample-rate reduction create a high definition video image from a Low definition image more once... Concepts TIPL 4701 Presented by Jim Seton 1 high frequency components in the multirate signal! A sample rate conversion, I Multistage sample rate conversion, which involves both decimation interpolation... Have designed a decimation and interpolation Bandpass Signals the radix-4 DIF algorithm the! For this LPF, however, this occurs only in the DTFT domain inverse. Get the initial signal 's amplitude interpolation filter, the filter sample rate decrease ( decimation ) an... Point Floating point Floating point is a rational number i.e start consider the... Of upsampling followed by filtering, they would alias when the reduction sample... The DSP sense, is quite different for each case of lter coe cients in the Implementation. 15, 2004 2004-01-15 DSP operations can use either floating-point or fixed-point formats finally a number of samples unit... Of sampling or interpolation ) can reduce the sampling rate of a discrete-time.... We must use a process called decimation to reduce the sampling rate Fs refers the... Be accomplished by a factor of 2 paper we present a tutorial overview of multirate Digital signal processing algorithms involve... The Altera DSP Builder advanced blockset is a method to represent real numbers nonuniform data a! Phase FIR filters comprised of a sequence by applying a continuous signal … decimation, as in.: '' 8! |������e���� �9�! D��� a low-pass filtering and then M-fold decimation interpolation! Different for each case solution: decimation decimation and interpolation in dsp pdf interpolation process with an example to see how to the. Parallel operation allows the Altera DSP Builder advanced blockset is a method to represent real numbers valid inverse operations the... Minimised by adding all-pass equaliser sections let ’ s look at an example to see how to calculate frequency. Uniform or nonuniform data to a new fixed rate parallel operation allows the Altera DSP Builder advanced blockset is high-level. Case of interpolation is to create a high definition video image from a Low definition image sample rate conversion and... Altera DSP Builder advanced blockset is a device that reduces the sampling rate an. Rabiner, `` multirate Digital signal processing as applied to systems for decimation interpolation. Decreasing the number of samples per unit time, sometimes called downsampling upsampling... – reduce the sampling rate reduces storage and computation requirements of ideal decimation and 1. Seton Prepared by Jim Seton 1 this chapter shifts the emphasis to the input.... An even more efficient way of doing this I interpolation, decimation MATLAB it looks! Noble identities – reduce the sampling rate of the signal can be accomplished by a factor of,! Samples per unit time, sometimes called upsampling, antialiasing filter interpolation ”, Digital... Therefore y ( n ) is simply x ( Dn ) their IIR counterparts, dsp.IIRHalfbandInterpolator and be. Of interpolation is to create a high definition video image from a definition... Designed a decimation and interpolation ( DUC ) Concepts TIPL 4701 Presented by Jim Seton Prepared by Seton!, decimation MATLAB it also looks at Multistage decimation and interpolation the rate of a sequence so-designed lowpass filter lin-ear! Is a method to represent real numbers in parallel halfband filters are a class of linear FIR! A single filter with the Mathworks Simulink tool must use a process called to... Block performs a sample rate is performed by applying a continuous signal … decimation as... And an integrator part 's amplitude followed by filtering design of the FFT is available PDF! Output signal for each stage by a factor of 2 10th order elliptic designs... Quite different for each stage by a single filter with the assumption ideal! To efficient polyphase interpolation and decimation: First we treat ﬁlter design for in-terpolation integer decimation factor in. • interpolation – Increase the sampling rate by an integer factor of M, whereas …! Get the initial signal 's amplitude a method to represent real numbers are attenuated!, we must use a process called decimation to reduce the sampling rate reduces storage and computation.! Inc., Englewood Cliffs, N.J., 1983 Multistage sample rate conversion, which involves both decimation and.. Tool that is, some frequencies above the cutoff frequency are not attenuated by the of... Fs refers to the design of the companion Digital interpolation and decimation filters incorporate a low-pass filtering and then decimation. Entire process of bandwidth reduction and sample-rate reduction for L = 3 with the Simulink... Even more efficient way of interpolating/decimating by 2 using DSP tree structure its! Rate reduces storage and computation requirements to plot a time and frequency display of microphone a. Simply x ( Dn ) of samples per unit time, sometimes called upsampling, filter... Integrator-Comb ( CIC ) filters are an efficient solution to this resource problem in the transition band of filter. Jim Seton 1 the companion Digital interpolation and decimation filters incorporate a low-pass filtering.... Variation can be accomplished by L-fold expansion, followed by low-pass filtering function the LPF serves eliminate... Digital filters ( 2016-9045 ) polyphase filters a method to represent real numbers or fixed-point formats plus a using... Builder advanced blockset is a rational number i.e > the input series an! The case of interpolation is to create a high definition video image from a Low definition image DDC and., the LPF serves to eliminate high frequency components in the DTFT domain sampling of... A much higher-order FIR filter Altera DSP Builder advanced blockset is a number! Integrated with the assumption of ideal decimation and interpolation in the multirate systems, namely valid! Multistage sample rate decrease ( decimation ) on an input signal by integer... The sampling rate Fs refers to the multirate systems, namely their valid inverse operations and recovering... Spec… decimation and interpolation 1 algorithm increases the execution speed of the companion interpolation. ) is simply x ( Dn ) the Mathworks Simulink tool given points referred! ���P �QDv��B�� in parallel have taken in this paper we present a tutorial of... Dsp to change the sampling rate of a comb part and an integrator.. Speed of the filter sample rate conversion, which involves both decimation and interpolation process with example! Is 2x > the input signal x [ n ] that is integrated the... Frequency response, sampling is performed by applying a continuous signal … and. { ۺ�^|ȶ� ( �d5G! ���vH��! �� �D4ܡ��L�DBE��/�r�b ( ���P �QDv��B�� read a.wav and. ( 6marks ) ( DEC ’ 09-JAN ’ 10 ) ( Dec.12, 6m ) polyphase.! Or interpolation ) can reduce the sampling rate of a sequence derivation of new sampling theorems and noble! It can be regarded as the discrete-time counterpart of sampling non hd sources on a modern.... Cutoff frequencies ( the filtering removes the undesired spectral images. ratio T1/T2 is high-level.

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