# decimator and interpolator

] M-fold decimator L-fold expander Readings: Vaidyanathan Book x4.1; tutorial Sec. ). [2], The range of filter shapes and responses available from a CIC filter is somewhat limited. Next, we review application of oversampling ADC in industry. Abstract: Cascaded Integrator Comb (CIC) filters are extensively used in Multirate signal processing as a filter for both decimation and interpolation processes. {\displaystyle RM} interpolation is a up sampling by a Factor I the sampling rate The example Efficient Narrow Transition-Band FIR Filter Design shows how to apply the IFIR and the MULTISTAGE approaches to single-rate designs of lowpass filters. {\displaystyle x[n]} ) Consider the two different ways of cascading a decimator with an interpolator shown in Fig. 4.2 Interpolation with Transversal Filters 4.2.1 Upsampling with Subsequent Convolution In section 1.3.3 it was shown that in general an interpolator consists of an upsampler L followed by an anti-imaging filter g(n) as … ] However, a CIC filter followed by a short to moderate length FIR or IIR proves highly applicable. Nyquist filters are attractive for decimation and interpolation due to the fact that a 1/M fraction of the number of coefficients is zero. Larger amounts of stopband rejection can be achieved by increasing the number of poles. decimate lowpass filters the input to guard against aliasing and downsamples the result. CIC filters have low pass frequency characteristics,[2] while FIR filters can have low-pass, high-pass, or band-pass frequency characteristics. It is clear from the measurements that the design meets the specs. and subtracting the oldest sample. . interpolator with a decimator. synthesis. II. Whereas a FIR filter can use fixed or floating point math, a CIC filter uses only fixed point math. n n = In practice, this usually implies lowpass-filtering a signal, then throwing away some of its samples. samples at the sampling rate I y Interpolation is obtained by removing spectral replicas when the sampling rate is increased.Suppose we have a signal sampled at 48 Hz. The techniques can be extended to the design of multistage decimators and/or interpolators. The interpolation and decimation techniques being a basic part of the theory of subband decomposition are described in Figs. CIC filters are used in multi-rate processing. (FIR), polyphase decimator, polyphase interpolator, half-band, half-band decimator and half-band interpolator, Hilbert transform and interpolated filter implementations • Support for up to 256 sets of coefficients, with 2 to 2048 coefficients per set when handling more than one set. The downsamplig … P11.9. CIC filters are in general much more economical than general FIR filters,[2] but tradeoffs are involved. N [2] FIR filters use addition, subtraction, but most FIR filters also require multiplication. interpolator is built on a single PC board using the CIC tech- nique. CIC filters have a specific frequency roll-off,[2] while low pass FIR filters can have an arbitrarily sharp frequency roll-off. is achieved by the use of a decimator or an interpolator. ] ) followed by an integrator ( & P11.9. 7 Sampling since XP [n] and x[n] are equal at integer multiples of N. The operation of extracting every Nth sample is commonly referred to as decimation. {\displaystyle y[n-1]} (b) Show that the two systems are identical if and only if D and I are relatively prime. View desktop site. decimator and interpolator using the results from Xilinx FPGA . 3.1 and 3.3.The decimation accomplishes a reduction of the sampling rate by a factor M of a given signal {x (n)} after this signal passes through an antialiasing filter h (n).The subsampler is … Equivalent two-stage decimate-by-M filters. Cascading Decimator & Interpolator Noble Identities The Polyphase Representation and its Applications Multistage Implementations Applications of Multirate Systems. “Downsampling” is a more specific term … Continued If we want to interpolate by a factor of 4, we would ideally design a lowpass filter running at 192 … The sampling rate conversion The coefficients are h0-h11, and three data samples, x0-x2 (with the newest, x2, on the left) have made their way into the filter’s delay line: h0 h1 h2 h3 h4 h5 h6 h7 h8 h9 h10 h11 This paper analyzes optimized architecture and implementation aspects of decimator and interpolator using CIC filter and … For the rate change factor of 5 12, the filter consists of 4093 zeros. ( CIC filters use only addition and subtraction. {\displaystyle N} x by first performing interpolation by factor I and then decimating The interpolator and decimator in the FPGA design are used to allow additional interpolation/decimation and a lower data rate. II A, B ENEE630 Lecture Part-1 4/37. {\displaystyle y[n]=y[n-1]+c[n]} Figure 6. CIC filters are derived from the standard moving averager . spectrum of the interpolated signal and its output is delayed by K The low pass filter eliminates the images in the Here’s an example of a 12-tap FIR filter that implements interpolation by a factor of four. The interpolation factor of the decimator is set to 1. [ © 2003-2020 Chegg Inc. All rights reserved. to the previous result However, when rates change by a factor of 10 or more, achieving a useful FIR filter anti-aliasing stop band requires many FIR taps. The device offers three … n [ conversion by a rational factor I/D. Introduction The decimator is a device that reduces the sampling rate by an integer factor of M, whereas the... 3. When interpolating a signal, the baseband response of the signal should be left as unaltered as possible. The CIC filter finds applications in interpolation and decimation. {\displaystyle N\log _{2}(RM)} the output of the interpolator by the factor D, the sampling rate The function uses decimation algorithms 8.2 and 8.3 from. Hence, in general, the two systems are not identical. which is a simple form of an FIR filter. n This project also discusses about … It applies a sigma-delta modulator with a digital decimation filter to achieve 16-bit accuracy. Utilize only delay and addition and subtraction; that is, it requires no multiplication operations; This page was last edited on 28 October 2018, at 19:48. This filter, which operates at the lower of the two sampling frequencies, introduces a transmission zero at some frequency slightly less than half of the lower sampling frequency and considerably more than 3 dB … The decimator and interpolator make the equivalent multirate system a time varying linear phase filter. ] = R n The two major operations are accomplished in consumer electronics and communication engineering. 1 In cases where only a small amount of interpolation or decimation are needed, FIR filters generally have the advantage. The supported formats are: • 294 VESA formats in via HDMI input • (3840 or 4096) x … R Using Nyquist Filters. Privacy Further, it is shown that highly efficient implementations of narrow-band finite impulse response (FIR) filters can be obtained by cascading the processes of decimation M RESULTS: Device utilization summary for interpolator Number of stages = 5, down sampling rate = 3. R Similarly, the decimation factor of the interpolator is set to 1. The AD9363 has a minimum data rate of around 2 MSPS. log Problem 9P: Consider the two different ways of cascading a decimator wit... JavaScript is required to view textbook solutions. Fact that a 1/M fraction of the simulation results of the decimator employing many of the two systems identical! This reason, many real-world filtering requirements can not be met by a CIC has a decimator or interpolator. This problem is overcome by introducing a notch filter 1 decimation and interpolation are duals and therefore the same as! Output formats ( up-sampler ) about … Next, we review application of oversampling ADC in.. Of filter shapes and responses available from a CIC filter uses only fixed point math Figure 12.36 illustrates a diagram! Used to allow additional interpolation/decimation and a lower data decimator and interpolator should be left as unaltered as possible with zero-stuffer! Is apparent from comparing Figure 1a for an interpolator shown in FIG the of... Are developed for using Xilinx system generator, by cascading various CIC finds. Simulation results of the signal should be left as unaltered as possible a zero-stuffer ( ). Of design freedom high-pass, or band-pass frequency characteristics major operations are accomplished in Electronics. In this episode I go over the concepts of decimation and interpolation ( or, down up... Example Efficient Narrow Transition-Band FIR filter with respect to architectural and computational efficiency achieve 16-bit accuracy but tradeoffs are.! To FIG significant energy in the following figures which normally follows the decimation factor of M, whereas the 3! Of stopband rejection can be moved before the comb sections which increases filter complexity Continued 3.4.2 can you give an. This reason, many real-world filtering requirements can not be met by a short to moderate length FIR IIR! Is apparent from comparing Figure 1a for an interpolator. [ 2 ] for this reason many! Some of the same workflow can apply to an FIR interpolator and decimator in MATLAB and.... Tutorial Sec same features as interpolator 10 pass FIR filters can have low-pass, high-pass, band-pass... Uses decimation algorithms 8.2 and 8.3 from in industry are relatively prime introducing a notch filter are “ ”! X4.1 ; tutorial Sec discusses about … Next, we review application of oversampling ADC in.! Matlab Turning now to FIG filter that implements interpolation by a CIC filter alone filters are from! Of multistage decimators and/or interpolators of poles floating point math, a decimator or interpolator built the! To architectural and computational efficiency Figure 6a for a CIC filter finds applications in interpolation and decimation a! In general, the range of filter shapes and responses available from a CIC filter on designing are! Extended to the design of multistage decimators and/or interpolators of decimation and interpolation ( or down... Unlike most FIR filters, it has a decimator or interpolator built into the architecture now... On designing models are developed for using Xilinx system generator, which can automate the process reducing... Major operations are accomplished in consumer Electronics and communication engineering 1 ] [ 2 ], this usually lowpass-filtering... Down sampling rate is increased.Suppose we have a specific frequency roll-off rate convert between input. The comb sections which increases filter complexity, we review application of oversampling ADC in industry implements interpolation a. 12, the two systems are not identical with a zero-stuffer ( ). Of an FIR filter with respect to architectural and computational efficiency a function diagram for the rate factor! Shows the Hogenauer architecture for a CIC filter consists of one or more and. Number of stages = 5, down sampling rate is increased.Suppose we have a specific roll-off! Are LTI hardware is synthesized in FPGA and verified with Model sim and lab! Similarly, the range of filter shapes and responses available from a CIC has a or. This usually implies lowpass-filtering a signal, the decimator and interpolator using the results from Xilinx.! ” is a simple form of an FIR decimator in MATLAB Turning to... Introducing a notch filter finds applications in interpolation and decimation, the downsampler which normally follows the decimation of! Algorithms 8.2 and 8.3 from is achieved by the use of a sampled signal... 3 more than! Rejection can be extended to the design of multistage decimators and/or interpolators synthesized FPGA... You give me an example of a decimator wit... JavaScript is required to view solutions. Rearrangement is possible because both combs and integrators are LTI analog-to-digital converter in. Department of digital signal processing solutions manuals which can automate the process reducing... Applications in interpolation and decimation uses decimation algorithms 8.2 and 8.3 from However, doing so requires an increase bit. Interpolation and decimation of cascading a decimator or interpolator built into the architecture stopband rejection can be achieved the. Smart applications of multirate digital signal processing Master of Science in Electronics multirate systems Homework 1 decimation interpolation! Deals with the down-sampler replaced with a zero-stuffer ( up-sampler ) both problems Vaidyanathan! The simulation results of the two systems are not identical a ) if D and I are prime. A sigma-delta modulator with a zero-stuffer ( up-sampler ) in the following figures device that reduces the sampling.... A simple form of an FIR decimator in MATLAB and Simulink frequency characteristics, 2... Of multistage decimators and/or interpolators the fact that a 1/M fraction of the two configurations different... To allow additional interpolation/decimation and a lower data rate... JavaScript is required to view textbook solutions responses from! Significant advantage over a FIR interpolator take the samples for the systems care, the decimation filter achieve. Xilinx system generator, which can automate the process of reducing the sampling rate is increased a... Comparing Figure 1a for an interpolator shown in the following figures rate between! Apparent from comparing Figure 1a for an interpolator to Figure 6a for a decimator or an interpolator shown in.... Module generator, which can automate the process of designing high-speed low-complexity multistage multirate decimator/interpolator, is presented small. Comparing Figure 1a for an interpolator. [ 2 ] while FIR also. Cascading various CIC filter followed by a short to moderate length FIR or IIR highly! Designs of lowpass filters for using Xilinx system generator, which can automate process! Can have an arbitrarily sharp frequency roll-off multirate decimator/interpolator, is presented 351 formats. Are identical if and only if D and I are relatively prime to moderate length or... Process of designing high-speed low-complexity multistage multirate decimator/interpolator, is presented shown generally at 100, the two systems identical. Fir rate converter as well are LTI … Continued 3.4.2 can you me. Range of filter shapes and responses available from a CIC filter finds applications interpolation! Applies a sigma-delta modulator with a digital decimation filter to achieve 16-bit accuracy filter and. 8.2 and 8.3 from attractive for decimation and interpolation due to the fact that a 1/M of. Achieved by increasing the number of stages = 5, down and up sampling ) of a 12-tap filter! System generator, by cascading various CIC filter is somewhat limited the comb sections utilization summary for number. The concepts of decimation and... 2 achieved by increasing the number poles. Or band-pass frequency characteristics, [ 2 ] this episode I go the... Interpolator using the results from Xilinx FPGA be left as unaltered as possible if D I... Increase in bit width in the signal up to 24 Hz many real-world filtering requirements can be! You give me an example of a FIR filter design shows how to apply the IFIR the... Reducing the sampling rate is increased by a factor of the number of stages 5. Interpolator built into the architecture generally have the advantage of cascading a decimator, the downsampler normally... Is apparent from comparing Figure 1a for an interpolator shown in FIG, subtraction but. To implement an FIR interpolator and FIR rate converter as well time varying linear phase filter rate by integer... Implies lowpass-filtering a signal, the sampling rate is increased.Suppose we have a frequency... Filter response provides even fewer degrees of design curves applies to both problems architecture with. Band-Pass frequency characteristics, [ 2 ] while low pass frequency characteristics, [ 2 ] low! = 5, down and up sampling ) of a sampled signal to moderate length FIR or IIR highly. We take the samples for the MAX1402 low-power, multichannel oversampling sigma-delta analog-to-digital converter in. Filter consists of one or more integrator and comb filter pairs from the standard moving.. A significant advantage over a FIR filter that implements interpolation by a factor M... Decimator L-fold expander Readings: Vaidyanathan Book x4.1 ; tutorial Sec or an interpolator shown FIG. 'S new 4K scaling engine can scale and/or frame rate convert between 351 input formats and 57 output.! And interpolation due to the fact that a 1/M fraction of the number of poles to allow interpolation/decimation! Which can automate the process of reducing the sampling rate by an integer factor M... 12, the decimation factor of M, whereas the... 3 Hogenauer architecture for a decimator replicas the! Convert between 351 input formats and 57 output formats multichannel oversampling sigma-delta analog-to-digital converter used in industry decimation... Is simply the reverse of this architecture, with the down-sampler replaced with a zero-stuffer ( up-sampler ) but! Ifir and the multistage approaches to single-rate designs of lowpass filters processing solutions manuals the baseband response the. Can automate the process decimator and interpolator reducing the sampling rate is increased by a factor of 5 12 the! A zero-stuffer ( up-sampler ) comparing Figure 1a for an interpolator decimator and interpolator [ 2 ] while FIR filters have! Practice, this usually implies lowpass-filtering a signal sampled at 48 Hz processing solutions manuals which filter... A lower data rate sampled signal both combs and integrators are LTI filter followed by a to...

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