Text c. Transformed-Based Filters
The final type of the filter we consider is that based on signal transformation techniques. It is well known in signal processing that a FIR filter can also be realized by multiplication in the frequency domain to implement "fast" convolution. Thus the filter can be implemented by Fourier transforming the input signal, multiplying by a set of stored complex frequency domain weights, followed by inverse Fourier transform processing. Although this appears at first sight to be more complicated than time-domain convolution, the reduced computational load of a fast Fourier transform (FFT) processor produces an overall simplification in the processor. It can be shown that for intermediate or large transform sizes (e.g., 128-point processors) the frequency-domain approach involves many fewer multiplications than the N parallel multiplications per sample period which are required to implement the N-point FIR-based convolution. Thus the frequency-domain technique offers wider filter bandwidth for a given speed of logic, but it does implement circular convolution and care is required to configure it for linear convolution, which is equivalent to FZR filtering. However, it has been extensively applied in radar systems in the design of matched filter-based receivers for the correlation of wideband coded waveforms.
Task 1. Compose a microtext using Scheme 1.
Scheme
1.
Task 2. Name the types of programmable filters (described in Texts A, B, C of this unit) which can be used in the design of the adaptive filters.
Task 3. Look through Texts A, B, C again and write some brief notes about significant features of all types of Programmable Filters.
Task 4. Answer the questions to Text C.
How can a FIR filter be realized to implement "fast" convolution?
What does the reduced computational load of a fast Fourier transform (FFR) processor produce?
What are the advantages and disadvantages of the frequency-domain technique?
Unit 3. Adaptive filters
Text A. Adaptive Infinitive Impulse Response Filters (IIF)
Text B. Adaptive Finite Impulse Response Filters (FIF)
Text a. Adaptive Infinitive Impulse Response Filters (iif)
Essential Vocabulary
multipath multipath interference reduction
to convolve convolution to converge pulse sorting scan mode
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Read and translate Text A using Essential Vocabulary
Text a. Adaptive Infinitive Impulse Response Filters (iif)
Any of the four programmable filter designs described earlier may now be incorporated as the programmable filter in Figure 1 (see Unit 1) to realize an adaptive filter. The advantages and disadvantages of the different filter designs are discussed briefly here to illustrate their areas of application.
Adaptive IIR filters have been principally applied to solve problems such as the reduction of multipath interference in radar and radio communication systems. Here the received signal comprises the original transmitted signal convolved with a channel response, which for multipath is an all-zero model. The adaptive receiver now models the inverse of the channel /Figure 2(b)/ to remove the interference. This is most efficiently accomplished using an all-pole adaptive filter model where the pole positions are adjusted until they coincide with the zeros in the channel.
This can also be accomplished with an adaptive FIR filter design, but it is more economical to use the recursive structure, as it implements an inverse filter structure, with a lower order of filter with fewer weights and it may reasonably be said that it will converge more rapidly than its transversal counterpart. However, the adaptive recursive filter requires a high degree of precision or accuracy in the digital circuit design to ensure stability of the filter. The adaptive processing technique based on IIR filters, is used in radar electronic support measure receivers for pulse sorting while adaptive Kalman filters are attractive for identifying the scan mode employed by specific emitters. They also find application in equalization and multipath reduction in high frequency (3 to 30 MHz) digital communication channels, where their high speed of convergence is of primary importance.
Task 1. Find and write down key terms and term groups from text A, translate them.
Task 2. Describe the operation of Adaptive IIR Filter using the terminology of Scheme 1.
Scheme 1.
Task 3. Here is a microdialogue. Read it carefully.
Situation: You are to discuss the logical Scheme 1 given above. Your friend or group-mate will help you.
A. Are you pleased with the given logical scheme?
B. Yes, I am. (No, I am not). I must say it is important to use the words in speech.
A. Is it tiring to compose it? (Is it easy to compose it?)
B. Yes, it is. (No, it is not).
Work in pairs. Give your own individual explanation of scheme work.
Task 4. Home assignment. Compose a dialogue to Text A. |
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Task 5. Look through Text A again and try to present it in shorts excluding excessive information and details.
Write down these sentences. The list of the verbs to be used: to include, to be represented by, to be characterized by, to be aimed at
Task 6. Answer the questions to Text A.
Where have Adaptive IIR filters been applied?
What problems can be solved by using Adaptive IIR filters?
Where do the adaptive Kalman filters find the application?
What is the primary importance of adaptive Kalman filters?