NAME THE TYPES OF DIGITAL FILTERS STRUCTURES AND STRUCTURES BACKGROUND?

Background needed for structure formation

Normally there are four types of digital filter structures.The structural step in digital signal processing comes at very after the basic functionalities of filters.For example,I wan to design a digital filter,firstly I will check the nature of filter either filter is finite impulse response or infinite impulse response.Of course according to these categories of filters our requirements will be different.As we know FIR filters are stable,feed forward,have linear phase,similarly group delay for FIR filters is constant.On the other hand scenario is totally different,for IIR filters our phase is nonlinear,system is feed backward,may or may not be stable and furthermore group delay for IIR filters may or may not be constant.One very interesting thing for both FIR and IIR filters is that FIR is MOVING AVERAGE SYSTEM whereas IIR filter is AUTO REGRESSIVE SYSTEM.

moving average filter

Two important points about filters structures
a) filter hardware should be reduced
b) phase should be linear

Normally IIR filter is designed due to reduced hardware as infinite impulse response filter has least number of adders and multipliers and it is in compact form so it is preferred to design no doubt it has nonlinear phase whereas phase for finite impulse response is linear in nature.Furthermore,LOW PASS FILTER is designed firstly due to its universality as any filter can be manufactured using low pass filter.

Classification of structures

Digital filter structures are classified into following catrgories given below,

• direct form
• cascaded form
• parallel form
• transposed form

Why structure is important for digital filters?

The structure formation for digital filter is of supreme importance as before going to manufacture final any hardware project it is good and benefitted to check this hardware circuit on any software of need.If we prepare soft model of the project before finalizing hardware we will be able to check its casuality and stability that this soft structure of the project is stable as only stable system can provide some output.In this way pre structuring of the hardware will tell us the performance of our project.And it will be obvious that our project is feasible or not.

Filter realization

After a filter is designed, it must be realized by developing a signal flow diagram that describes the filter in terms of operations on sample sequences.

A given transfer function may be realized in many ways. Consider how a simple expression such as {\displaystyle ax+bx+c} ax+bx+c could be evaluated – one could also compute the equivalent {\displaystyle x(a+b)+c} x(a+b)+c. In the same way, all realizations may be seen as "factorizations" of the same transfer function, but different realizations will have different numerical properties. Specifically, some realizations are more efficient in terms of the number of operations or storage elements required for their implementation, and others provide advantages such as improved numerical stability and reduced round-off error. Some structures are better for fixed-point arithmetic and others may be better for floating-point arithmetic.

Direct form I

A straightforward approach for IIR filter realization is direct form I, where the difference equation is evaluated directly. This form is practical for small filters, but may be inefficient and impractical (numerically unstable) for complex designs. In general, this form requires 2N delay elements (for both input and output signals) for a filter of order N.

Biquad filter DF-I.svg

Direct form II

The alternate direct form II only needs N delay units, where N is the order of the filter – potentially half as much as direct form I. This structure is obtained by reversing the order of the numerator and denominator sections of Direct Form I, since they are in fact two linear systems, and the commutativity property applies. Then, one will notice that there are two columns of delays ( {\displaystyle z^{-1}} z^{-1}) that tap off the center net, and these can be combined since they are redundant, yielding the implementation as shown below.

The disadvantage is that direct form II increases the possibility of arithmetic overflow for filters of high Q or resonance It has been shown that as Q increases, the round-off noise of both direct form topologies increases without bounds. This is because, conceptually, the signal is first passed through an all-pole filter (which normally boosts gain at the resonant frequencies) before the result of that is saturated, then passed through an all-zero filter (which often attenuates much of what the all-pole half amplifies).

Biquad filter DF-II.svg

Cascaded second-order sections

A common strategy is to realize a higher-order (greater than 2) digital filter as a cascaded series of second-order "biquadratric" (or "biquad") sections[6] (see digital biquad filter). The advantage of this strategy is that the coefficient range is limited. Cascading direct form II sections results in N delay elements for filters of order N. Cascading direct form I sections results in N + 2 delay elements, since the delay elements of the input of any section (except the first section) are redundant with the delay elements of the output of the preceding section.Courtesy of wikipedia,,,,