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本文以简明的方式导出了带通信号的一阶抽样频率,说明了若抽样频率为f_s,则精确恢复原信号的理想带通矩形滤波器的带宽是f_s/2.设带通信号的谱分量限制在f_1≤|f|≤f_1+W内,抽样频率在(2f_2)/m≤f_s≤(2f_1)/(m-1)(m是不大于f_2/W的正整数)内选择,则理想带通恢复滤波器的冲激响应是h(t)=T_s/πt[sin2πf_οt-sin2π(f_α-f_s/2)t]这里f_α=(m/2)f_s.当f_s=(4f_ο)/(2m-1)时,该滤波器对称于中心频率f_ο。
In this paper, the first-order sampling frequency of the bandpass signal is derived in a concise manner, which shows that the bandwidth of the ideal bandpass rectangular filter that accurately restores the original signal is f_s / 2 if the sampling frequency is f_s. The limit is within f_1 ≤ | f | ≤ f_1 + W and the sampling frequency is chosen within (2f_2) / m ≤ f_s ≤ (2f_1) / (m-1) (m is a positive integer not greater than f_2 / W) The impulse response of the band-pass restoration filter is h (t) = T_s / πt [sin2πf_οt-sin2π (f_α-f_s / 2) t] where f_α = (m / 2) f_s. When f_s = (4f_ο) / -1), the filter is symmetrical to the center frequency f_o.