Task 3. Speak about the Lattice Structure using Scheme 3.

Task 4. Study these verbs and phrasal verbs from the text:

to result in, to be delayed by, to be controlled by, to be continuous, to incorporate, to be required, to be restricted to, to be configured from, to output.

Now fill in each blank space with the appropriate phrasal verb in the correct form:

1. This filter has only a limited memory, which……………………… the number of delay stages and it …………the finite impulse response (FIR) or transversal filter design.

2. The input signal ………………… a number of delay elements, which may ……………..but in the present text ……………………….. discrete values.

3. This filter …………… only zeros (as there are no recursive feedback elements) and hence a large number of delay elements ……………. to obtain a sharp cutoff frequency response.

4. The FIR filter can ……………….. this generalized structure by replacing the undefined filter structure by a tapped delay line, which ………… a series of time-delayed signal samples.

Task 5. Answer the questions to Text B.

1. What is the way to overcome the drawback of potential instability in the filter?

2. What types of multipliers are used in nonrecursive filters?

3. What results in the finite impulse response (FIR) filter design?

4. What is the alternative FIR filter realization?

5. How can the lattice structure be considered?

6. What does the lattice structure provide?

7. What is the key attraction of the lattice structure?

Task 6. Home assignment. Summarize Text B “Nonrecursive Filters” using the given phrases. It’ll help you to make rendering.

The text is centered on…………………

It is reported about…………………………

Special attention is given to………………..

…………………………………is considered/emphasized.

In conclusion……………………..

Note: Don’t use subordinate clauses.

Task 7. Grammar Training. Translate the following sentences from English into Russian, mind “The Gerund”.

1. By designing an all-zero filter which uses only feed forward multipliers and is unconditionally stable we overcome the drawback of potential instability in the filter.

2. On multiplying by a set of stored weights we summed the products to form the output signal.

3. In 1971 Chang succeeded in unifying all approaches into a generalized equalizer or filter structure.

4. Using of this structure splits the signal into sets of forward (f) and backward (b) residual signal samples.

5. We discussed different methods of obtaining a sharp cutoff frequency response.

6. We know of the alternative FIR filter realization being the lattice structure which can be considered as a cascade of single tap prediction filter.

7. The researchers thought its (the filter) incorporating only zeros (as there are no recursive feedback elements) and hence a large number of delay elements are required to obtain a sharp cutoff frequency response.

8. Itakura and Saito succeeded in calculating Parcor coefficient values by recursive techniques in 1970 and both Makhoul and Mead have further suggested methods to simplify the algorithm computation.

Read Text C and express its main idea

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.

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