引言
傅裡葉變換試圖將非週期信號也納入到傅裡葉的體系中。對於非週期信號,可以看成是週期無限長的週期信號。當週期無限大時,傅裡葉級數的頻率分量就變成了一個連續域。
非週期信號的表示:連續時間傅裡葉變換
首先以週期方波為例,即在一個週期內
\[x(t) = \begin{cases}1, |t| < T_1\\0,T_1 < |t| < T/2 \end{cases}
\]
若將其表示為傅裡葉級數,其傅裡葉級數的係數為
\[a_k = \frac{2sin(k\omega_0T_1)}{k\omega_0T}
\]
將其在頻域圖上畫出來,並逐漸增大週期T就可以得到下圖
![](data:image/png;base64,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)
可想而知,隨著T的增大,頻率越來越小,包絡線裡面的頻率越來越密集,最終形成一條連續的曲線。傅裡葉變換的工作就是要求出這條曲線,從而完成信號從時域到頻域的轉換。這就是對非週期信號建立傅裡葉級數表示的基本思想。
將\(\tilde{x}(t)\)看作是\(x(t)\)的一個週期,由於傅裡葉的級數表示是在一個週期內推出來的,所以對於非週期信號的一個週期,也有
\[\tilde{x}(t) = \sum^{+\infty}_{k = -\infty}a_ke^{jk\omega_0t}\tag{式1} \\a_k = \frac1T\int_{-\frac T2}^{\frac T2}\tilde{x}(t)e^{-jk\omega_0 t}dt
\]
由於非週期信號可以看成只有一個週期的信號,所以在週期之外,即\(|t| > T/2\)時,\(x(t) = 0\),而在週期之內,\(\tilde{x}(t) = x(t)\),則有
\[a_k = \frac1T\int_{k = -\infty}^{+\infty}x(t)e^{-jk\omega_0t}dt
\]
則可以得到
\[X(j\omega) = Ta_k = \int_{-\infty}^{+\infty}x(t)e^{-j\omega t}dt
\]
稱\(X(j\omega)\)為\(Ta_k\)的包絡。
再將\(a_k = \frac{X(j\omega)}{T}\)代入式1得
\[\tilde{x}(t) = \sum_{k=-\infty}^{+\infty}\frac1TX(jk\omega_0)e^{jk\omega_0t} = \frac1{2\pi}\sum_{k=-\infty}^{+\infty}X(jk\omega_0)e^{jk\omega_0t}\omega_0
\]
當\(T\rightarrow \infty\)時,\(\tilde{x}(t)\rightarrow x(t),\omega_0\rightarrow 0\),因此\(\omega_0\)可以看作一個微分,而右端式子可以看作一個積分式。則有
\[x(t) = \frac1{2\pi}\int_{-\infty}^{+\infty}X(j\omega_)e^{j\omega t}d\omega\tag{式4.8}
\]
而
\[X(j\omega) = \int_{-\infty}^{+\infty}x(t)e^{-j\omega t}dt\tag{式4.9}
\]
這兩式即稱為一對傅裡葉變換對。式4.9是將信號從時域變換到頻域,稱為時域信號的傅裡葉變換。式4.8則是從頻域變為時域,稱為頻域信號的傅裡葉逆變換。
在時域圖上,橫軸是時間t,縱軸則是由該時刻所有基本信號的線性組合。在頻域圖上,橫軸是頻率\(\omega\),縱軸則是某一頻率的基本信號的係數\(a_k\)。
可以看出,傅裡葉變換與週期信號的傅裡葉級數表示的結構還是很類似的。
傅裡葉變換的收斂
現研究用式4.8表示的\(x(t)\)和信號與實際的\(x(t)\)信號之間的誤差。用\(\hat{x}(t)\)表示式4.8為
\[\hat x(t) = \frac1{2\pi}\int_{-\infty}^{+\infty}X(j\omega_)e^{j\omega t}d\omega
\]
如果\(x(t)\)能量有限,即
\[\int^{+\infty}_{-\infty}|x(t)|^2dt < \infty
\]
則可以保證\(X(j\omega)\)是收斂的。
令\(e(t) = \hat{x}(t) - x(t)\),則
\[\int_{-\infty}^{+\infty}|e(t)|^2dt = 0
\]
如果\(x(t)\)能量有限,那麼雖然\(x(t)\)與它的傅裡葉表示\(\hat x(t)\)在個別點上有明顯的區別,但是在能量上沒有任何區別
狄利赫利條件,這組條件保證\(\hat x(t)\)除了個別不連續點外,其它點上都等於\(x(t)\)。
-
\(x(t)\)絕對可積
\[\int_{-\infty}^{+\infty}|x(t)|dt < \infty
\]
-
在任何有限個區間內,x(t)只有有限個最大值和最小值
-
在任何有限區間內,x(t)有有限個不連續點,並且在每個不連續點的值都是有限的。
週期信號的傅裡葉變換
週期信號的傅裡葉變換可以由週期信號的傅裡葉級數表示構造。
首先構造一個信號\(x(t)\),其傅裡葉變換\(X(j\omega)\)是一個面積為\(2\pi\),頻率為\(\omega_0\)的單位衝激。即
\[X(j\omega) = 2\pi \delta(\omega - \omega_0)
\]
則此時信號\(x(t)\)可以看成一個非週期信號,則利用非週期信號的傅裡葉變換得
\[\begin{aligned}x(t) &= \frac1{2\pi}\int_{-\infty}^{+\infty}2\pi\delta(\omega - \omega_0)e^{j\omega t}d\omega\\
&= e^{j\omega_0t}
\end{aligned}
\]
現在將\(X(j\omega)\)看成一組這樣的基本信號的線性組合
\[X(j\omega) = \sum^{+\infty}_{k = -\infty}2\pi a_k\delta(\omega - k\omega_0)
\]
則有
\[x(t) = \sum^{+\infty}_{k = -\infty}a_ke^{jk\omega_0t}
\]
上式正是一個週期信號的傅裡葉級數表示。
连续时间傅里叶变换性质
线性性质
\[ax(t) + by(t) \stackrel{F}{\longleftrightarrow} aX(j\omega) + bX(j\omega)
\]
时移性质
\[x(t-t_0) \stackrel{F}{\longleftrightarrow}e^{-j\omega t_0}X(j\omega)
\]
信号的时移不改变傅里叶变换的模
共轭和共轭对称性
共轭性质,若
\[x(t) \stackrel{F}{\longleftrightarrow}X(j\omega)
\]
则
\[x^*(t)\stackrel{F}{\longleftrightarrow}X^*(-j\omega)
\]
若x(t)为实函数,则\(X(j\omega)\)具有共轭对称性
\[X(-j\omega) = X^*(j\omega)
\]
若x(t)为实偶函数,则\(X(j\omega)\)也未实偶函数。若x(t)为实奇函数,则\(X(j\omega)\)为纯虚奇函数。
微分和积分
\[\frac{dx(t)}{dt}\stackrel{F}{\longleftrightarrow} j\omega X(j\omega)\\
\int_{-\infty}^{t}x(\tau)d\tau \stackrel{F}{\longleftrightarrow} \frac1{j\omega}X(j\omega) + \pi X(0)\delta(\omega)
\]
时间与频率的尺度变换
\[x(at)\stackrel{F}{\longleftrightarrow} \frac1{|a|}X(\frac{j\omega}{a})
\]
这里a是一个实常数
对偶性
\[x_1(t) = \begin{cases}1,|t|<T_1\\0,|t| > T_1 \end{cases} \stackrel{F}{\longleftrightarrow} X_1(j\omega) = \frac{2sin\omega T_1}{\omega}\\
x_2(t) = \frac{sinWt}{\pi t}\stackrel{F}{\longleftrightarrow}X_2(j\omega) = \begin{cases}1,|\omega|<W\\0,|\omega|>W \end{cases}
\]
信号的傅里叶变换和逆变换总有结构上的类似。
例如对于积分性质就可以导出对偶性质为
\[-\frac1{jt}x(t) + \pi x(0)\delta(t) \stackrel{F}{\longleftrightarrow} \int^\omega_{-\infty}x(\eta)d\eta
\]
帕斯瓦尔定理
\[\begin{aligned}\int_{-\infty}^{+\infty}|x(t)|^2dt &= \int_{-\infty}^{+\infty}x(t)\cdot x^*(t)dt\\&=\int_{-\infty}^{+\infty}x(t)\left[\frac1{2\pi}\int_{-\infty}^{+\infty}X^*(j\omega)e^{-j\omega t}d\omega \right]dt\\&=\frac1{2\pi}\int_{-\infty}^{+\infty}X^*(j\omega)\left[\int_{-\infty}^{+\infty}x(t)e^{-j\omega t}dt \right]d\omega\\&=\frac1{2\pi}\int_{-\infty}^{+\infty}X^*(j\omega)X(j\omega)d\omega\\&=\frac1{2\pi}\int_{-\infty}^{+\infty}|X(j\omega)|^2d\omega\end{aligned}
\]
表明一个周期信号的平均功率等于它的各次谐波分量的平均功率之和,而这些谐波分量的平均功率等于傅里叶级数系数的模的平方。
卷积性质
首先温习一下特征函数的定义:一个信号,若系统对于信号的响应仅仅是一个常数乘以输入,那么这个信号称为系统的特征函数,而这个常数称为特征值。
线性时不变系统的系统函数是复指数信号,若系统的单位冲激响应为h(t),则对于复指数信号\(e^{st}\),系统响应
\[y(t) = \int_{-\infty}^{+\infty}h(\tau)e^{s(t-\tau)}d\tau\\=e^{st}\int_{-\infty}^{+\infty}h(\tau)e^{-s\tau}d\tau
\]
所以特征值
\[H(s) =\int_{-\infty}^{+\infty}h(\tau)e^{-s\tau}d\tau
\]
当\(s = j\omega\)时,系统函数就称为该系统的频率响应,可以把频率响应\(H(j\omega)\)当做该系统单位冲激响应的傅里叶变换。则由叠加原理:
\[\frac1{2\pi}\sum_{k=-\infty}^{+\infty}X(jk\omega_0)e^{jk\omega_0 t}\omega_0\longrightarrow \frac1{2\pi}\sum^{+\infty}_{k=-\infty}X(jk\omega_0)H(jk\omega_0)e^{jk\omega_0t}\omega_0
\]
所以线性系统对x(t)的响应为
\[y(t) = \frac1{2\pi}\int_{-\infty}^{+\infty}X(j\omega)H(j\omega)e^{j\omega t}d\omega
\]
其傅里叶变换
\[Y(j\omega) = X(j\omega)H(j\omega)
\]
总结
\[y(t) = x(t)*h(t) \stackrel{F}{\longleftrightarrow}Y(j\omega) = X(j\omega)H(j\omega)
\]
单位冲激响应的傅里叶变换\(H(j\omega)\)控制着每一个频率的输入傅里叶变换复振幅的变化。
相乘性质
卷积性质说的是时域内的卷积对应于频域内的相乘。根据对偶性,我们也可以找到一个时域内的相乘对应频域内的卷积的性质
即
\[r(t) = s(t)p(t)\longleftrightarrow R(j\omega) = \frac1{2\pi}\int_{-\infty}^{+\infty}S(j\theta)P(j(\omega-\theta))d\theta
\]
一个信号与另一个信号相乘,可以理解为一个信号调制另一个信号的振幅,所以上式有时称为调制性质(modulation property)
System Characterized by Linear Constant-Coefficient Differential Equations
一类特别重要的连续时间线性时不变系统是输入输出满足如下形式的系统:
\[\sum^{N}_{k=0}a_k\frac{d^ky(t)}{dt^k} = \sum^M_{k=0}b_k\frac{d^kx(t)}{dt^k}
\]
两边取傅里叶变换并利用线性性质得:
\[\sum^N_{k=0}a_kF\left\{\frac{d^ky(t)}{dt^k} \right\} = \sum^M_{k=0}b_kF\left\{\frac{d^kx(t)}{dt^k} \right\}
\]
利用微分性质得
\[\sum^N_{k=0}a_k(j\omega)^kY(j\omega) = \sum^M_{k=0}b_k(j\omega)^kX(j\omega)
\]
所以有
\[H(j\omega) = \frac{Y(j\omega)}{X(j\omega)} = \frac{\sum^M_{k=0}b_k(j\omega)^k}{\sum^N_{k=0}a_k(j\omega)^k}
\]