The FIR filter’s structure main right and wrong recursive structure, has not output the input the feedback. And the FIR filter are very easy to obtain the strict linear phase characteristic, avoids processing the signal to produce the phase distortion. But the linear phase manifests in the time domain is merely h (n) in the time detention, this characteristic in profile transmission systems and so on image signal processing, data transmission is very important. In addition, he will not have the choking phenomenon, can avoid the strong signal submerging the weak signal, therefore especially qualify signal strong and the weak phase difference disparate situation. Its main deficiency is, it good performance is trades take the high exponent number as the price. Therefore, under the guarantee same performance’s premise, reduces its exponent number is one of diligently FIR digit filter design important attributes.
The following introduction realizes the FIR filter’s general pattern using Matlab and the DSP chip.
1 FIR filter’s design method
Usually uses the window function method to design the FIR filter method to be simple, but these filter’s design is not most superior. The first pass band and the stop-band fluctuation is basically equal, although general need δ2<δ1, but cannot control these parameters separately in the window function method. Moreover regarding the majority of window box number, in the pass band or the stop-band fluctuation is not even, usually leaves when the intermediate belt will reduce. If permission fluctuation in the entire pass band uniform distribution, will have the small peak value fluctuation.
The optimized design is takes all sampling value the variable, under some optimized criterion, carries on the most superior result which through the computer the iterative computation obtains. Its optimized criterion may use the error criteria. But the practice proved that the application biggest error minimum criterion and so on ripple imminent method is a more practical method, applies when he designs, the exponent number, the pass band and the stop-band edge as well as error’s weighting function may the free choice, be very flexible, the design obtains filter, its error in the entire frequency range uniform distribution, thus may propose imminently by the lowest exponent number target request.
Supposes treats designs filter’s amplitude-frequency characteristic is HdA (Omega), obtains actually filter’s amplitude-frequency characteristic is HA (Omega), the goal is causes HA (Omega) well imminent HdA (Omega). And so on ripple best consistent imminent are according to the design requirements, derives group of conditions, causes in the entire imminent frequency region the imminent erroneous absolute value to be smallest, defines weighting function W (Omega), W (Omega) may take the different value under the different frequency band, available he decides each frequency band probable error’s weight freely. When optimization design, W (Omega) is the known function, like this, weighted error function E (Omega) may define is:
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