The filtering removes the undesired spectral images. Rational rate changers change the sampling rate by a factor of lm rational decimation system university of california at berkeley general structure l fn is a lowpass. A class of digital filters for decimation and interpolation conference paper pdf available in ieee transactions on acoustics speech and signal processing 292. In order to reconstruct the correct interpolating signal at the higher sampling rate. Then the techniques of decimation and interpolation enable this operation. In this episode i go over the concepts of decimation and interpolation or, down and up sampling of a sampled signal. Roles of decimation and interpolation in system identification. If we upsample by factor l to get vm, the desired portion of vej. This chapter shifts the emphasis to the design of the companion digital interpolation and decimation filters. Interpolation and decimation of digital signalsa tutorial. Perform decimation and linear or higherorder interpolation without introducing aliasing. Decimation filter an overview sciencedirect topics.
Step 1 requires a lowpass filter after increasing expanding the data rate, and step 2 requires a lowpass filter before decimation. Ieee transactions on 2, 155 an economical class of. Filter the resulting images from the up sample process 3. The lct domain analysis of decimation and interpolation to study the decimation and interpolation in the lct domain, in this section, we firstly give the definition of equivalent filter in the lct domain. Decimation and interpolation decimation filtering consider. Decimating, or downsampling, a signal xn by a factor of d is the process of creating a new signal yn by taking only every dth sample of xn. In this paper we present a tutorial overview of multirate digital signal processing as applied to systems for decimation and interpolation. Multirate digital signal processing university of newcastle upon tyne page 9. Decimation, interpolation, downsampling, upsampling, antialiasing filter. The continuity of first derivative means that the graph y sx will not. Gordana jovanovic dolecek ojeda loredo fernando june152015 sta. Then, the direct implementation structure for decimation and interpolation in the lct domain are derived based on the definition.
A class of digital filters for decimation and interpolation. Digital filter design for interpolation and decimation. Decimation refers to removing samples in between the existing vector of values. If h z and k z are multidimensional comb filters, then can the multidimensional. As a linear process, the dsp sense of interpolation is somewhat different from the math sense of interpolation, but the result is conceptually similar. Furthermore, the kth product is equal to one, so the sum is equal to yk and the interpolation conditions are satis.
Interpolation and decimation filters understanding delta. The frequency domain relationship between yn and xn can be shown to be the following. The band of the nyquist filter is typically set to be equal to the decimation factor, this centers the cutoff frequency at 1mfs2. Example of decimation and interpolation sample the signal xt 5sin 2000 t cos 20,000 t at 80 khz to form a discretetime signal xn, take every fourth sample of xn to form x sn and decimate x sn to form x dn. Low sampling rate reduces storage and computation requirements. In most applications involving multidimensional interpolation, an interpolation filter follows an expander as in figure 2. To decimate with no loss of information from the original data, the data must be oversampled to begin with. However, you can do interpolation prior to decimation to achieve an overall rational factor, for example, 45. Matlab program for interpolation and decimation m file 10. The interpolation filter used for the amplitude and phase path is derived from the basic cascaded integratorcomb cic structure 80 with a few significant modifications. As a first example we pass directly into an decimator with a signal having. Repeat another 2x interpolation to get 4x, and again for 8x cascading multiple 2x stages to increase interpolation is best due to efficient halfband filters. Then upsample x dn by a factor of four to form x in and compare it to xn. Us5339263a combined decimationinterpolation filter for.
Particular emphasis is placed on decimating and interpolating by a factor of two. In this paper, it is clarified that the decimation and interpolation have an effect on improving the numerical instability of leastsquares ls or predictionerror pe. It will be shown in section 111 that decimation and interpolation of signals are dual processesi. Multirate digital signal processing newcastle university staff. This will give us a smoother interpolating function. Resample uniform or nonuniform data to a new fixed rate. Linear interpolation the simplest form of interpolation is probably the straight line, connecting two points by a straight line. A signal can be downsampled without doing any filtering whenever it is oversampled, that is, when a sampling rate was used that was greater than the. The signal can be decimated more than once, using a gradual change in sampling frequency. Decimation, or downsampling, is the reverse operation of the sinc interpolation.
There is a unique straight line passing through these points. A combined decimation interpolation filter for adc and dac analogtodigital converter and digitaltoanalog converter provides a single filter which may be used both as a decimation filter and as an interpolation filter. As an example, the combined lowpass filter in the samplingrate converter. Insert a 0 between each sample zero stuffing up sampling 2. An example of samplingrate conversion would take place when data. The major focus of this paper is to analyze the different realization of interpolation decimation filter structures that supports wlan applications. I want to change the sampling rate of 8k to 300 via multirate processing. Fig 2a shows data that is nearly oversampled to produce a spectrum that has very little energy in the upper half of the nyquist interval. Decimation reduces the original sample rate of a sequence to a lower rate. The analysis of decimation and interpolation in the linear. A simple decimation example in the above system we will c onsider the pure decimator and the decimator with lowpass prefiltering. Interpolation and decimation of signals 301 or t t 4b is called decimation.
If px is evaluated at x xk, all the products except the kth are zero. Multiple stages for decimation or interpolation can reduce the number of lter coe cients in the lter speci cations. Pdf digital signal processing schemes for efficient interpolation. Decimation by irrational factor using cic filter and linear interpolation. Department of digital signal processing master of science in electronics multirate systems homework 1 decimation and interpolation dr. Gauss forward interpolation formula y 0 2 y 1 4 y 2 6 y 3 y 0 3 y 1 5 y 2 the value p is measured forwardly from the origin and 0 interpolation problem and the vandermonde determinant an alternative approach to the interpolation problem is to consider directly a polynomial of the form q nx xn k0 b kx k, 3. What is decimation and interpolation in signal processing. Antialiasing filter hn decimation xn d yn decimation in mutliple stages multistage.
Multirate dsp and its technique to reduce the cost of the. Learn more about image processing, interpolation, decimation matlab. The concepts of digital signal processing are playing an increasingly important role in the area of multirate signal processing, i. Pdf decimation and interpolation are the two basic building blocks in the multirate digital signal processing systems. I understand afer this it is lowpass filtered to remove the new alias images due to downsampling, but surely you you could lowpass filter after the downsampling and still end up with the same frequency output, i. Applications of multirate signal processing fundamentals decimation interpolation resampling by rational fractions multirate identities polyphase representations maximally decimated. Polyphase structure for decimation and interpolation filters. It gains simplicity and inexpensivenes by carefully selecting the tap weights of the filter, cascading multiple filters, time domain. Home proceedings volume 0697 article proceedings volume 0697 article. Cic filters are widely used for decimation and interpolation in communication systems. Interpolation increase the sampling rate of a discretetime signal. Pdf the analysis of decimation and interpolation in the linear. Multirate sampling simulation using matlabs signal. Pdf comparative analysis of interpolationdecimation fir.
Why compute filter output and then throw away samples. Pdf an economical class of digital filters for decimation and. Nyquist filters are attractive for decimation and interpolation due to the fact that a 1m fraction of the number of coefficients is zero. Boser 7 dsp ktc noise ktc noise of a 10nf capacitor is 0. For this purpose i need c code for interpolatiion and decimation. Similarly, in many applications involving multidimensional decimators, a decimation filter precedes the decimator as in figure 2.
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