Interpolation and decimation filters understanding delta. Insert a 0 between each sample zero stuffing up sampling 2. An example of samplingrate conversion would take place when data. Interpolation and decimation of signals 301 or t t 4b is called decimation. Pdf comparative analysis of interpolationdecimation fir. Pdf the analysis of decimation and interpolation in the linear. The band of the nyquist filter is typically set to be equal to the decimation factor, this centers the cutoff frequency at 1mfs2.
Step 1 requires a lowpass filter after increasing expanding the data rate, and step 2 requires a lowpass filter before decimation. 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. The analysis of decimation and interpolation in the linear.
Therefore, both operations can be accomplished by a single filter with the lower of the. To decimate with no loss of information from the original data, the data must be oversampled to begin with. If px is evaluated at x xk, all the products except the kth are zero. Interpolation filter an overview sciencedirect topics. Interpolation increase the sampling rate of a discretetime signal. There is a unique straight line passing through these points. As a linear process, the dsp sense of interpolation is somewhat different from the math sense of interpolation, but the result is conceptually similar. Polyphase structure for decimation and interpolation filters. Then the techniques of decimation and interpolation enable this operation. 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.
Similarly, in many applications involving multidimensional decimators, a decimation filter precedes the decimator as in figure 2. Roles of decimation and interpolation in system identification. Multirate dsp and its technique to reduce the cost of the. Subband coding is a method where the speech signal is subdivided into several frequency bands and each band is digitally encoded separately. A simple decimation example in the above system we will c onsider the pure decimator and the decimator with lowpass prefiltering. A class of digital filters for decimation and interpolation. 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.
It gains simplicity and inexpensivenes by carefully selecting the tap weights of the filter, cascading multiple filters, time domain. In this paper we present a tutorial overview of multirate digital signal processing as applied to systems for decimation and interpolation. This article discusses a not so wellknown rule regarding the filtering in multistage decimation and interpolation by an integer power of two. Multiple stages for decimation or interpolation can reduce the number of lter coe cients in the lter speci cations. As a first example we pass directly into an decimator with a signal having. Particular emphasis is placed on decimating and interpolating by a factor of two. This will give us a smoother interpolating function. Pdf an economical class of digital filters for decimation and. Low sampling rate reduces storage and computation requirements. Ieee transactions on 2, 155 an economical class of.
Applications of multirate signal processing fundamentals decimation interpolation resampling by rational fractions multirate identities polyphase representations maximally decimated. Linear interpolation the simplest form of interpolation is probably the straight line, connecting two points by a straight line. Matlab program for interpolation and decimation m file. The frequency domain relationship between yn and xn can be shown to be the following. 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. The filtering removes the undesired spectral images. Combine decimation and interpolation to get noninteger sample rate conversion. 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. Home proceedings volume 0697 article proceedings volume 0697 article. Nyquist filters are attractive for decimation and interpolation due to the fact that a 1m fraction of the number of coefficients is zero. 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.
Gordana jovanovic dolecek ojeda loredo fernando june152015 sta. What is decimation and interpolation in signal processing. Then upsample x dn by a factor of four to form x in and compare it to xn. 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. Perform decimation and linear or higherorder interpolation without introducing aliasing. 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. Decimation and interpolation decimation filtering consider. Digital filter design for interpolation and decimation. The signal can be decimated more than once, using a gradual change in sampling frequency. Decimation refers to removing samples in between the existing vector of values. In most applications involving multidimensional interpolation, an interpolation filter follows an expander as in figure 2. Resample uniform or nonuniform data to a new fixed rate.
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. Why compute filter output and then throw away samples. As an example, the combined lowpass filter in the samplingrate converter. Multirate digital signal processing university of newcastle upon tyne page 9. Decimation, or downsampling, is the reverse operation of the sinc interpolation.
If we upsample by factor l to get vm, the desired portion of vej. This section of matlab source code covers decimation or down sampling matlab code. Working of interpolation or decimation matlab answers. A class of digital filters for decimation and interpolation conference paper pdf available in ieee transactions on acoustics speech and signal processing 292. In this episode i go over the concepts of decimation and interpolation or, down and up sampling of a sampled signal. Then, the direct implementation structure for decimation and interpolation in the lct domain are derived based on the definition. 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. It will be shown in section 111 that decimation and interpolation of signals are dual processesi. Multirate sampling simulation using matlabs signal. The concepts of digital signal processing are playing an increasingly important role in the area of multirate signal processing, i. Furthermore, the kth product is equal to one, so the sum is equal to yk and the interpolation conditions are satis.
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. Learn more about image processing, interpolation, decimation matlab. This chapter shifts the emphasis to the design of the companion digital interpolation and decimation filters. Pdf digital signal processing schemes for efficient interpolation.
However, you can do interpolation prior to decimation to achieve an overall rational factor, for example, 45. Filter the resulting images from the up sample process 3. The continuity of first derivative means that the graph y sx will not. Optimizing the halfband filters in multistage decimation.
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. Pdf decimation by irrational factor using cic filter and. Matlab program for interpolation and decimation m file 10. For this purpose i need c code for interpolatiion and decimation. Antialiasing filter hn decimation xn d yn decimation in mutliple stages multistage. Decimation filter an overview sciencedirect topics. In order to reconstruct the correct interpolating signal at the higher sampling rate. Boser 7 dsp ktc noise ktc noise of a 10nf capacitor is 0. Decimation reduces the original sample rate of a sequence to a lower rate. Pdf decimation and interpolation are the two basic building blocks in the multirate digital signal processing systems. Us5339263a combined decimationinterpolation filter for. Interpolation, in the dsp sense, is the process of upsampling followed by filtering. 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. If h z and k z are multidimensional comb filters, then can the multidimensional.
Cic filters are widely used for decimation and interpolation in communication systems. Multirate digital signal processing newcastle university staff. Decimation, interpolation, downsampling, upsampling, antialiasing filter. 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.