hello welcome to the digital signal 你好，欢迎来到数字信号
processing video lectures my name is 正在处理视频讲座，我叫
Jeffrey Herman and I will be your an 杰弗里·赫曼，我将是你的
online instructor for this course to 此课程的在线讲师
begin this lecture series I will do a 开始本系列讲座，我将做一个
quick review of what you would have 快速回顾一下您将拥有的东西
learned in your analog signal processing 从您的模拟信号处理中学到的
course and then introduce you to the 课程，然后向您介绍
terminology and systems of digital 数字术语和系统
signal processing in analog signal 模拟信号中的信号处理
processing you learned that a system 处理您了解到的系统
consists of an input filter and output 由输入过滤器和输出组成
we use the subscript a to denote that 我们用下标a表示
the signals x and y our analog signals 信号x和y是我们的模拟信号
in this example we show how a low-pass 在这个例子中，我们展示了低通
filter removes the high-frequency 滤波器去除高频
components or the squiggles from X sub a X sub a的分量或花形
of T to produce a low frequency signal Y T产生低频信号Y
sub a of T T的子
we are able to directly examine the 我们可以直接检查
frequency content of signals such as X X等信号的频率成分
sub a of T by using the Fourier 通过使用傅立叶T的子a
transform shown above the frequency 频率上方显示的变换
domain signal is represented by X sub a 域信号由X sub a表示
of Omega where Omega is measured in 在欧米茄中测量欧米茄
radians per seconds similarly we are 弧度/秒类似
able to transform X sub a of Omega back 能够将Omega的X sub a转换回
to the time domain by using the inverse 通过使用倒数到时域
Fourier transform here we see an example 傅立叶变换在这里我们看到一个例子
Fourier transform signal I want to point 我想指出的傅立叶变换信号
out one important feature of the signal 信号的一个重要特征
the magnitude of the Fourier transform 傅立叶变换的幅度
goes to zero beyond certain frequencies 在某些频率之外变为零
the signal is said to be and limited in 信号被认为是并限制在
digital signal processing be concerned 关注数字信号处理
only with such band-limited signals we 只有在这种带宽受限的信号下，我们
denote the band limit with the capital 用大写表示频段限制
letter B 字母B
when we have a band limited signal we 当我们有一个频带受限的信号时
can approximate the analog signal X sub 可以近似模拟信号X sub
a of T with the digital signal X sub n T的a与数字信号X sub n
the N tells us the X as a function of N告诉我们X是
samples and rather than a function of 样本，而不是函数
time T we create this digital signal by 时间T，我们通过以下方式创建此数字信号
sampling the signal at periodic 定期采样信号
intervals of time when there's high 高的时间间隔
frequency content in the signal these 这些信号中的频率含量
intervals of time must be small if these 如果这些时间间隔必须很小
intervals are too large and lose vital 间隔太大而失去生命
information about the signal 有关信号的信息
notice how the sampled signal on the 请注意，
right does not fully show the high 正确并不能完全显示出高
frequency content of XM a of teeth 牙齿XM a的频率含量
when there's only low frequency content 当只有低频内容时
like Y sub a of T these intervals can be 像T的Y sub a一样，这些间隔可以是
larger with the same time intervals as a 较大的时间间隔与
previous example we can accurately 前面的例子我们可以准确地
recreate y sub a of T with both periodic 用两个周期重新创建T的y sub a
intervals this sampling process is 此采样过程的时间间隔
represented schematically by a switch 用开关示意表示
that opens and closes periodically with 它会定期打开和关闭
period T every time the switch closes 开关每次闭合时的周期T
the value of x sub a of T is measured 测量T的x sub a的值
and quantized into a binary number that 并量化成一个二进制数
is stored in registers or computer 存储在寄存器或计算机中
memory for example this sample here is 内存，例如这里的示例是
stored as a zero in memory in the next 在下一个内存中存储为零
sample is stored as a 3 the value stored 样本存储为3的值存储
is a memory become our discrete time 是记忆成为我们离散的时间
signal X of n n的信号X
when we have a signal that has been 当我们有一个信号已经
limited to B radians per second or F 限制为每秒B弧度或F
Hertz we can perfectly recreate the 赫兹我们可以完美地再现
original analog signal if the sampling 原始模拟信号（如果采样）
frequency is high enough specifically we 频率足够高，特别是我们
can recreate the analog signal if the 可以重新创建模拟信号，如果
sampling frequency F sub s is greater 采样频率F sub s更大
than 2 F the critical sampling frequency 高于2 F的临界采样频率
where F sub s equals to F it's called F sub s等于F的地方叫做
the Nyquist frequency notice that F sub 奈奎斯特频率通知F sub
s is inversely related to T so small s与T成反比
intervals of time for T will equate to T的时间间隔等于
higher sampling frequencies typically we 通常，较高的采样频率
want to sample at a higher frequency 想要以更高的频率采样
than the night cluster you can see if we 比夜晚的星团，你可以看到我们
have sampled at or above the Nyquist 在奈奎斯特或以上采样
frequency we can perfectly recreate the 频率，我们可以完美地重建
analog signal X of a of T by multiplying T的a的模拟信号X乘以
every sample by a sinc function centered 每个样本均以正弦函数为中心
on that sample and adding the resulting 在那个样本上，并添加结果
sinc functions together the sinc sinc一起起作用
function is defined as the sine of T 函数定义为T的正弦
divided by T where the sinc function 除以T，其中sinc函数
equals 1 when T is 0 当T为0时等于1