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-> The 采样 Theorem

As long as there are at least two 采样 每（一个） period of the 原始/原创 波形 we can assume that the 再合成 波形 will have the same 频率 But when there are fewer than two 采样 每（一个） period the 频率 and 也许 the 音色 of the 原始/原创 信号 is lost

The 采样 theorem 描述 the 关系 between the 采样 率 and the 频带宽度（带宽） of the 信号 being 传送 there are at least two 采样 每（一个） period of the 原始/原创 波形 To give a 實/具体 例如 suppose we introduce an 模拟 信号 at 26 KHz into an 模数（模拟—数字） 转化器 操作 at 50 KHz The 转化器 reads it as a 音 at 24 KHz since 50 -26 = 24 KHz

The essential point of the 采样 theorem can be stated 精确 as follows In order to be able to reconstruct a 信号 the 采样 频率 must be at least twice the 频率 of the 信号 being 采样

The highest 频率 that can be 产生 in a 数字 為耳/音频 系统 is called the 尼奎斯特 频率 In 樂/乐 应用（应用程序） the 尼奎斯特 频率 is 通常 in the upper 范围（排列） of 人类 听觉 above 20 KHz Then the 采样 频率 can be specified as being at least twice as much or above 40 KHz


--- Ideal 采样 Frequency

Many 人 听 信息 referred to as air in the 区域 around the 20 KHz 限制 on 人类 听觉 Neve 1992 Indeed Rudolf Koenig whose precise measurements set international 标准 for 声学 observed at age 41 that his own 听觉 extended to 23 KHz Koenig 1899 It seems strange that a new 数字 compact 碟盘 should have less 频带宽度（带宽） than a 留声机 录 made in the 1960s or a new 数字 為耳/音频 錄機/录机 should have less 频带宽度（带宽） than a twenty-year old 模拟 磁带 錄機/录机 Many 模拟 系统 can reproduce 频率 beyond 25 KHz 科学 experiments confirm the 效果 of 声 above 22 KHz from both 生理学 and 主观 观点 Oohashi et al 1991 Oohashi et al 1993

In 声波 合成 应用（应用程序） the lack of 频率 净空 in 标准 采样 rates of 44 1 and 48 KHz causes serious 问题 It requires that 合成 算法 产生 nothing other than 正弦 波 above 11 KHz 44 1 KHz 采样 率 or 12 KHz 48 KHz 采样 率 or foldover will 出现 This is because any 高频 组成 with 分音 beyond the 基（础） has a 频率 that 超过 the 尼奎斯特 率 The third 谐/泛音 of a 音 at 12 5 KHz for 例如 is 37 5 KHz which in a 系统 running at 44 1 KHz 采样 率 will reflect down to an 可听 6600 赫兹（he zi） 音 In 采样 and 音高移位 应用（应用程序） the lack of 频率 净空 requires that 采样 be 低通 滤 before they are pitch-shifted upward The trouble these limits impose is inconvenient

--- 抗混叠 and Anti-imaging Filters

In order to make sure that a 数字 声波 系统 作品 properly two 重要 滤器 are 包括 One 滤器 is placed before the ADC to make sure that nothing or as little as 可能 in the 输入 信号 occurs at a 频率 较高 than half of the 采样 频率 Logically enough such a 滤器 is called an 抗混叠 滤器

The other 滤器 is placed after the 数模转换器（数字—模拟转换器） Its 主要 功能（函数） is to change the 采样 储存 数字 into a 平滑 continuous 表示法 of the 信号