# Multirate Digital Signal Control

The Hong Kong Polytechnic University Department of Electronic and Details Engineering EIE413 Digital Transmission Processing Individual Essay

Multirate Digital Sign Processing

Trainer: W. C. Siu By HAN Shilu 07828567D

EIE413 Digital Sign Processing

Multirate Digital Sign Processing

Abstract

In classic digital sign processing system, there is always merely one simple sampling rate (that is, the sampling frequency). The output transmission has the same sampling level with the insight. In modern day digital systems, however , there may be an

increasing need to method data for more than one sampling rate. At times the output from the system is instructed to have a different sampling rate of the input signal. It has lead the development of multirate digital signal control, which is a fresh sub-area in DSP. For instance , the testing rate intended for an audio CD (compact disc) is definitely 44. you kHz. If we like to transfer data from your CD to a DAT (digital audio tape) at a sampling level of twenty four kHz, we need to increase the rate of recurrence of the info first utilizing a multirate strategy. There are two primary alternatives we have in multirate finalizing. The first is decimation. The sampling rate fs of a presented signal times[n] is reduced. This approach is likewise called straight down sampling. The second is interpolation. We can increase the sampling rate fs of the offered signal times[n]. This approach is also known as up sample. In this section, we are going to discuss the general principles of decimation and interpolation in multirate processing and sampling change by non-integer factor.

Decimation by an Integer Factor

Decimation is simply the process of reducing the sampling frequency of your input sign to a ideal value. In this part, we shall confine our attention to a decrease by an integer factor M. For example , we now have an insight signal I actually = 1, 3, 5, 7, 9, 11, 13, 2, 4, 6, 8, 10, 12. The output transmission y[n] is by taking every Mth sample of the suggestions signal. In the event that M=4, we have to just take just about every fourth test of times[n] to obtain the preferred signal y[m] = 1, 9, 4, 12. According to Nyquist sampling theorem, we can say that aliasing is going to occur in the down tested signal as a result of reduced sampling rate. After the signal is definitely down experienced by a factor M, the brand new sampling consistency fsM becomes fs/M, in which fs is definitely the original testing frequency. The folding regularity after 1

EIE413 Digital Signal Processing

Multirate Digital Signal Digesting

down sample becomes fs/2M. If the initial signal provides frequency components than the new folding consistency, aliasing will probably be introduced to the outcome signal. To be able to solve the situation, it is necessary to process the original sign x[n] by using a lowpass filtering H(z) which has a cut-off regularity of fs/2M. The corresponding normalized cut-off frequency should be vc = (fs/2M) / fs = 1/2M. The strained output when it comes to z-transform can be written as W(z) sama dengan H(z)X(z). Where X(z) is definitely the z-transform from the original transmission x[n]. After passing through the lowpass filter, the value of the straight down sampled signal y(m) can be obtained from the blocked output: y(m) = w(mM). The process of down sampling by a factor of 3 is demonstrated in Figure 1A. And Figure 1B shows the corresponding spectral to get x(n), w(n) and y(m).

Figure 1A. Down testing with M=3.

Figure 1B. Spectral after down testing.

It has to be made the decision whether IIR or FIR should be intended for the lowpass filtering necessary. The use of a great IIR filtration has an obvious short approaching. Previous outputs are required to compute the Mth output. The computation is too complicated. All of us cannot take those advantage that individuals only have to compute every Mth output. If, however , a great FIR filtration system is used, we could do each of our computations at the rate of fs /M. We can obtain the desired output y(m) by equation: y(m) = w(mM) = в€‘.

Another advantage of an FIR filtering is that you can actually design a linear phase filter two

EIE413 Digital Signal Finalizing which is appealing in many cases....

References: 1 . E. C. Ifeachor and B. W. Jervis (1993), Digital Signal Control: a Practical Procedure (pp. 491-540), US: Addison-Wesley Publishing Business. 2 . Li Tan (2008), Digital Sign Processing: Principles and Applications (pp. 557-574), Burlington: Educational Press. three or more. Alok Jain, Rajiv Saxena, S. C. Saxena (2006), Anti-Image FIR Filters for Large Interpolation Factors, Recovered April 1, 2011, coming from http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V18-4J72XXH -1& _user=107833& _coverDate=11%2F30%2F2006& _rdoc=1& _fmt=high& _orig =gateway& _origin=gateway& _sort=d& _docanchor=& view=c& _searchStrId=171 0228721& _rerunOrigin=google& _acct=C000008378& _version=1& _urlVersion= 0& _userid=107833& md5=f472ea12b9f1ce655bf6ea92d17d691a& searchtype=a 4. E. Ambikairajah (2009), Multirate Digital Signal Control, Retrieved 03 31, 2011, from http://www.youtube.com/watch?v=hJ-bQODjpYg

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