英语翻译Letusnowworkthisoutinaslightlymoreformalway.Consideradiscretesignalthatconsistsof8samplevalues.Inthepreviousexample:x=(x1,x2,...,x8)=(1,3,5,7,2,−1,−3,−2).ThespaceV0ofallsuchsignalsisinfa

Question

英语翻译
Let us now work this out in a slightly more formal way.Consider a discrete signal that
consists of 8 sample values.In the previous example:
x = (x1,x2,...,x8) = (1,3,5,7,2,−1,−3,−2).
The space V0of all such signals is in fact the space R8,namely the space of all 8-tupples.Note
that this is a Euclidean space with inner product X,Y = XtY .This space can be described
by the natural basis {ϕ0k}8k=1,where ϕ0k=ekis the kth column of the 8 × 8 unit matrix:
the columns of the matrix [E(0)] = I8.Thus,setting H(0)= I8,x = x(0)= [H(0)]tX(0).
Such a basis vector can be represented graphically as a 1 × 1 block at position k.The
values xkare the coordinates of x with respect to these basis vectors.We denote this
coordinate vector as X = X(0)= [1,3,5,7,2,−1,−3,−2]t.Note that the basis is orthonormal
since

Answer 1

现在让我们工作此用一个有一点更加正式的方式.认为一个离散信号那
包括8样品价值.在先例中：
x = (x1、x2,…,x8) = (1,3,5,7,2,−1,−3,−2).
空间V0of所有这一类信号实际上是空间R8,即空间所有8-tupples.笔记
那个这是与内积x,Y = XtY的欧几里德的空间.这空间可以被描述
在自然依据{ϕ0k} 8k=1,ϕ0k=ekis 8 × 8单位矩阵的kth专栏：矩阵[E (0)的] the专栏 = I8.因此,设置H (0) = I8,x = x (0) = [H (0)]tX (0).
就如依据传染媒介可以图解地代表作为一个1个× 1块在位置k.
values xkare x座标关于这些依据传染媒介的.我们表示此
coordinate传染媒介作为X = X (0) = [1,3,5,7,2,−1、−3,−2] T.注意依据是规格化正交的
since