将f(x)= x 2 在（-π,π）上展开为傅里叶级数 A 0 为（）。

A . 0 B . 1 C . -1 D . 1／2

A . 0B . πC .https://assets.asklib.com/images/image2/2017051111193844963.jpg D .https://assets.asklib.com/images/image2/2017051111194477734.jpg

A . A B . B C . C D . D

A . 仅有https://assets.asklib.com/images/image2/2017051114231174259.jpg B .https://assets.asklib.com/images/image2/2017051114232954189.jpg C .https://assets.asklib.com/images/image2/2017051114233710779.jpg D .https://assets.asklib.com/images/image2/2017051114234885753.jpg

A .https://assets.asklib.com/psource/201510291530231830.jpg B .https://assets.asklib.com/psource/2015102915303768116.jpg C .https://assets.asklib.com/psource/2015102915305046680.jpg D .https://assets.asklib.com/psource/2015102915310234816.jpg

A .https://assets.asklib.com/psource/2015102816494294239.jpg B .https://assets.asklib.com/psource/2015102816495840213.jpg C .https://assets.asklib.com/psource/2015102816501252670.jpg D .https://assets.asklib.com/psource/2015102816502734467.jpg

A．s(0)=0 B．s(π)=1+π³ C．s(-π)=-1 D．s(-4)=-1

设x[n]是一个实值序列，其傅里叶变换X(ejω)=0，ω≥Π/4，现在想要得到一个信号y[n]，它的傅里叶变换在—Π≤ω≤Π内为 <img src='https://img2.51aidian.com/ask/2020-09-15/969024913064545.png' /> 图8-16所示的系统用于从x[n]得到y[n]。试确定要使该系统正常工作，图8-16中滤波器的频率响应H(ejω)必须满足什么限制. <img src='https://img2.51aidian.com/ask/2020-09-15/969024927046345.png' />

将函数<img src='https://img2.soutiyun.com/shangxueba/ask/18747001-18750000/18749367/2016071617013646896.jpg' />，在［-π，π］上展开成傅里叶级数，其形式为<img src='https://img2.soutiyun.com/shangxueba/ask/18747001-18750000/18749367/2016071617014226431.jpg' />（）<img src='https://img2.soutiyun.com/shangxueba/ask/18747001-18750000/18749367/2016071617014996704.jpg' /> A．A B． B C． C D． D

证明.若函数f(x)在区间[-π,π]可积,且a_k,b_k,是函数f(x)的傅里叶系数,则<img src='https://img2.soutiyun.com/ask/2020-11-13/974121166578095.jpg' />有不等式 <img src='https://img2.soutiyun.com/ask/2020-11-13/974121183156043.png' /> 后者称为贝塞尔①不等式.(证明1),讨论积分<img src='https://img2.soutiyun.com/ask/2020-11-13/974121199972005.png' />

A．f(x)是增函数，g(x)是减函数 B．f(x)是减函数,g(x)是增函数 C．f(x)与g(x)都是增函数 D．f(x)与g(x)都是减函数

将图3-7所示的三角形信号在时间区间(-π,π)上展开为有限项的三角傅里叶级数，使其与实际信号间的均方误差小于原信号f(t)总能量的1%。写出此有限项三角傅里叶级数的表达式。 <img src='https://img2.soutiyun.com/ask/2020-05-27/959440921240914.png' />

设函数f(x)=πx+x²(-π＜x＜π)的傅里叶级数为<img src='https://img2.soutiyun.com/ask/2021-01-11/97924161438348.png' /><img src='https://img2.soutiyun.com/ask/2021-01-11/979241624327048.png' /> 则其中系数b₃=().

将下列各周期函数f(x)展开成傅里叶级数，如果f(x)在一个周期的表达式为： <img src='https://img2.soutiyun.com/ask/2021-01-14/979481711875738.jpg' />

设S(x)是周期为2π的函数f(x)的Fourier级数的和函数.f(x)在一个周期内的表达式为<img src='https://img2.soutiyun.com/ask/2020-12-22/977479036798748.png' />写出S(x)在[-π,π]上的表达式.

已知f[n] =x[n]cos(πn/4) ， 其离散时间傅里叶变换为<img src='https://img2.soutiyun.com/ask/2020-09-14/968929174676685.png' />，在Ω的主值区间(-π，π)内。试确定序列x[n]，并概画出其序列图形。

将函数f(x)=x(x-π)展开成以2π为周期的傅里叶级数,并回答: (I)级数在点x=±π和x=2π分别收敛于何值？(II)<img src='https://img2.soutiyun.com/ask/2021-01-11/979241771846486.png' />

设周期函数f(x)的周期为2π.证明: (1)如果f(x-π)=-f(x),则f(x)的傅里叶系数a₀=0,a_2k=0,b_2k=0(k=1,2,…); (2)如果f(x-n)=f(x),则f(x)的傅里叶系数a_2k₊₁=0,b_2k₊₁=0(k=0,1,2,…).

设周期为2π的函数f(x)在[-π,π]上的Fourier系数为<img src='https://img2.soutiyun.com/ask/2021-02-02/981111657409235.png' />,求下列函数的Fourier系数<img src='https://img2.soutiyun.com/ask/2021-02-02/981111665834716.png' />: <img src='https://img2.soutiyun.com/ask/2021-02-02/981111673674165.png' />