Three factors affecting the structure of filter implementation

When the digital signal is filtered, the filter coefficients are calculated according to the characteristics of the signal, and the structure to realize the filter is also considered. Generally, people tend to pay more attention to the solution of filter coefficients, and often ignore the implementation structure of filters. Theoretically, the same filter, with different implementation structures, results in exactly the same. But in engineering practice, different implementation structure, the results may vary greatly. Moreover, in different applications, the implementation structure of the filter also has different requirements. What is this all about?

On the one hand, in the theoretical analysis, there is a basic assumption that the data is infinitely accurate, but in the actual digital system, the number is finite precision, which is usually said word length is limited. For example, a filter has a factor of 0.999, which can be quantified to 0.998985 when the actual system is implemented. Thus, the actual implementation of the filter and the theoretical analysis of the filter performance will be different. In addition, in different applications, the operating speed of the system requirements are not the same, the cost requirements of the system is not the same, at this time, we should try to choose the appropriate implementation structure.

So, in engineering practice, in the end what factors affect the choice of filter implementation structure? In general, there are three main factors: operational complexity, storage demand, and finite word length.

The complexity of operation is mainly the requirement of computation quantity. In the real-time system, it is hoped that the operation efficiency is as high as possible, in the filter design stage, the order of the filter should be as low as possible. In the filter structure selection stage, it is hoped that the same order of the filter, the required arithmetic operation as little as possible. For example, in engineering practice, the FIR filter usually requires a linear phase, when the coefficients of the filter is symmetric, if directly with the transverse structure, the required arithmetic operation and fir order n is proportional. However, if the improved lateral implementation structure is used to make full use of the symmetry of the coefficients, the arithmetic operation required is proportional to the N/2. In this way, the computation of different implementation structures is one-fold.

Storage demand is mainly designed to the cost of the system hardware resources, thus affecting the cost of the system. When the implementation structure is chosen, it is hoped that the required storage capacity is as small as possible. Or the above example, under two different structures, the storage requirements of the filter coefficients are also one-fold. In the case of not many filter coefficients, such differences may not be very large, but if the filter coefficients are many, then the cost of system resources will be more obvious. Moreover, in some occasions, such as radar sonar and other military applications, the price factor is relatively not very important, but in the mobile phone and other commercial competition, the price factor is fatal, the system resources savings will have important value.

The effect of finite word length is another very important consideration when the filter realizes the structure selection. Some implementation structures are easy to understand and easy to implement, but are sensitive to the effects of finite word length. For example, for IIR filters, if the pole is located near the unit circle, the quantization error of the system can easily cause the pole to change from the unit circle to the unit circle, which leads to the instability of the system. At this time, it is important to adopt an implementation structure that is insensitive to the effect of finite word length.

In addition, whether it is easy to parallel operation and whether pipeline operation can be realized often affects the implementation structure of the filter.

Three factors affecting the structure of filter implementation