半带滤波器（Half-band FIR Filter）

下图为半带滤波器的一般频率响应:

图3-19

The magnitude frequency response is symmetrical about quarter sample frequency
radians. The sample rate is normalized to radians/sec. The passband and stopband
frequencies are positioned such that

（幅频响应在四分之一采样频率左右是对称的 弧度。采样率归一化为 弧度/秒。通带和阻带频率的关系是这样的）

The passband and stopband ripple, and respectively, are equal . These properties are reflected in the filter impulse response. It can be shown (in Digital Signal Processing in Communication Systems [Ref 3]) that approximately half of the filter coefficients are zero for an odd number of taps, as shown in Figure 3-20 for an 11-tap half-band filter.

（通带纹波和阻带纹波分别相等。这些特性反映在滤波器的脉冲响应中。它可以（用数字信号表示在通信系统中的处理[Ref 3])，即大约一半的滤波器对于奇数个抽头，系数为零，如图3-20所示为对于11个抽头，系数为零的半带滤波器。）

 

图 3-20

The interleaved zero values in the coefficient data can be exploited to realize an efficient
realization, as shown in Figure 3-21. Note that the FIR Compiler also exploits coefficient  symmetry for half-band filter structures, although this is not shown in Figure 3-21.

（利用系数数据中的交错零值，可以实现一种高效的计算方法实现，如图3-21所示。注意，FIR编译器还利用了半带滤波器结构的系数对称性，尽管图3-21中没有显示这一点。）

图 3-21

The half-band filter selection in the compiler is intended for this purpose. This filter is
available in the Coefficient Structure field of the user interface.

（编译器中的半带滤波器选择就是为此目的而设计的。这个过滤器是可在用户界面的系数结构字段中找到。）
IMPORTANT: You must supply the complete list of filter coefficients, including the 0 value  samples, when using the half-band filter.

（重要提示:使用半带滤波器时，必须提供完整的滤波器系数列表，包括0值样本。）
The filter coefficient file format is discussed in greater detail in Filter Coefficient Data.

（在滤波系数数据中，对滤波系数文件格式进行了较为详细的讨论。）