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我们提供的信号和系统signals and systems及其相关学科的代写，服务范围广, 其中包括但不限于:
调和函数 harmonic function
椭圆方程 elliptic equation
抛物方程 Parabolic equation
双曲方程 Hyperbolic equation
非线性方法 nonlinear method
变分法 Calculus of Variations
几何分析 geometric analysis
偏微分方程数值解 Numerical solution of partial differential equations
信号代写|信号和系统作业代写signals and systems代考|Synchronous demodulation
The objective of demodulation is to reconstruct $m(t)$ from $s(t)$. Analyzing the spectrum $S(\omega)$ of the modulated signal $s(t)$, the following method extracts the information-bearing signal $m(t)$ from $s(t)$.
(1) Frequency shift the modulated signal $s(t)$ by $\omega_{c}\left(\right.$ or $-\omega_{c}$ ). If the modulated signal is frequency-shifted by $\omega_{c}$, one of the side bands is shifted to zero frequency, while the second side band is shifted to $2 \omega_{c}$. Conversely, if the modulated signal is frequency-shifted by $-\omega_{c}$, the two side bands are shifted to zero and $-2 \omega_{c}$.
(2) In order to remove the side band shifted to the non-zero frequency, the result obtained in Step (1) is passed through a lowpass filter having a pass band of $\left(-\omega_{\max } \leq \omega \leq \omega_{\max }\right)$. The output of the lowpass filter consists of a scaled version of the modulating signal and an impulse at $\omega=0$. The impulse represents the dc component and is removed by subtracting a constant value in the time domain as shown in Step (3).
(3) A constant voltage equal to the dc component is subtracted from the output of the lowpass signal.
信号代写|信号和系统作业代写signals and systems代考|Synchronous demodulation with non-zero epochs
In synchronous demodulation, the epoch $\phi_{c}$ of the modulating carrier is assumed to be identical to the epoch of the demodulating carrier. In practice, perfect synchronization between the carriers is not possible, which leads to distortion in the signal reconstructed from demodulation. To illustrate the effect of distortion introduced by unsynchronized carriers, consider the following modulated signal:
$$
s(t)=A \cos \left(\omega_{c} t+\phi_{c}\right)+A k m(t) \cos \left(\omega_{c} t+\phi_{c}\right),
$$
as derived in Eq. (8.2). Assume that the demodulator carrier is given by
$$
c_{2}(t)=A \cos \left(\omega_{c} t+\theta_{c}(t)\right)
$$
which has a time-varying epoch $\theta_{c}(t) \neq \phi_{c}$. Using $c_{2}(t)$, the demodulated signal is given by
$d(t)=s(t) c_{2}(t)=\left[A \cos \left(\omega_{c} t+\phi_{c}\right)+A k m(t) \cos \left(\omega_{c} t+\phi_{c}\right)\right] \cos \left(\omega_{c} t+\theta_{c}(t)\right)$
which simplifies to
$$
d(t)=\underbrace{\frac{A}{2}[1+k m(t)] \cos \left(\phi_{c}-\theta_{c}(t)\right)}{d{\text {low }}(t)}+\underbrace{\frac{A}{2}[1+k m(t)] \cos \left(2 \omega_{c} t+\phi_{c}+\theta_{c}(t)\right)}{d{\text {high }}(t)} .
$$
信号代写|信号和系统作业代写SIGNALS AND SYSTEMS代考|Asynchronous demodulation
In amplitude modulation, the information-bearing signal $m(t)$ modulates the magnitude of the carrier signal $c(t)$. This is illustrated in Figs. 8.2(c) and (d), where the envelope of the amplitude modulated signal follows the information component $[1+\mathrm{km}(t)$ ]. In asynchronous demodulation, we reconstruct the information signal $m(t)$ by tracking the envelope of the modulated signal.
Figure $8.5$ (a) shows a parallel $R C$ circuit used to reconstruct the informationbearing signal $m(t)$ from the amplitude modulated signal $s(t)$ applied at the input of the RC circuit. The diode acts as a half-wave rectifier removing the negative values from the modulated signal, while the capacitor $C$ tracks the envelope of the AM signal by charging to the peak of the sinusoidal carrier during the positive transition of the signal. During the negative transitions of the carrier, the capacitor discharges slightly, but is again recharged by the next positive transition. The process is illustrated in Fig. 8.5(b), where the demodulated signal is represented by a solid line. We observe that the demodulated signal closely follows the envelope of the modulated signal and is a good approximation of the information-bearing signal.
信号和系统代写
信号代写|信号和系统作业代写SIGNALS AND SYSTEMS代考|SYNCHRONOUS DEMODULATION
解调的目的是重建米(吨)从s(吨). 分析光谱小号(ω)调制信号的s(吨)，下面的方法提取信息承载信号米(吨)从s(吨).
1对调制信号进行频移s(吨)经过ωC(或者−ωC）。如果调制信号频移ωC，其中一个边带移到零频率，而第二个边带移到2ωC. 相反，如果调制信号频移−ωC，两个边带被移到零并且−2ωC.
2为了去除偏移到非零频率的边带，步骤中得到的结果1通过具有通带的低通滤波器(−ω最大限度≤ω≤ω最大限度). 低通滤波器的输出由调制信号的缩放版本和在ω=0. 脉冲表示直流分量，并通过在时域中减去一个常数值来去除，如步骤中所示3.
3从低通信号的输出中减去一个等于直流分量的恒定电压。
信号代写|信号和系统作业代写SIGNALS AND SYSTEMS代考|SYNCHRONOUS DEMODULATION WITH NON-ZERO EPOCHS
在同步解调中，纪元φC假设调制载波的 epoch 与解调载波的 epoch 相同。实际上，载波之间的完美同步是不可能的，这会导致从解调中重建的信号失真。为了说明由非同步载波引入的失真影响，请考虑以下调制信号：
s(吨)=一种因(ωC吨+φC)+一种ķ米(吨)因(ωC吨+φC),
如在方程式中得出。8.2. 假设解调器载波由下式给出
C2(吨)=一种因(ωC吨+θC(吨))
它有一个时变的时代θC(吨)≠φC. 使用C2(吨)，解调信号由下式给出
d(吨)=s(吨)C2(吨)=[一种因(ωC吨+φC)+一种ķ米(吨)因(ωC吨+φC)]因(ωC吨+θC(吨))
简化为
$$
d(t)=\underbrace{\frac{A}{2}[1+k m(t)] \cos \left(\phi_{c}-\theta_{c}(t)\right)}{d{\text {low }}(t)}+\underbrace{\frac{A}{2}[1+k m(t)] \cos \left(2 \omega_{c} t+\phi_{c}+\theta_{c}(t)\right)}{d{\text {high }}(t)} .
$$
信号代写|信号和系统作业代写SIGNALS AND SYSTEMS代考|ASYNCHRONOUS DEMODULATION
在幅度调制中，信息承载信号米(吨)调制载波信号的幅度C(吨). 这在图 1 和图 2 中进行了说明。8.2C和d，其中幅度调制信号的包络跟随信息分量[1+ķ米(吨)]。在异步解调中，我们重构信息信号米(吨)通过跟踪调制信号的包络。
数字8.5 一种显示一个平行RC用于重构信息承载信号的电路米(吨)从调幅信号s(吨)施加在RC电路的输入端。二极管充当半波整流器，从调制信号中去除负值，而电容器C通过在信号的正向转换期间充电到正弦载波的峰值来跟踪 AM 信号的包络。在载流子的负跃迁期间，电容器轻微放电，但在下一次正跃迁时再次充电。该过程如图 8.5 所示b，其中解调信号由实线表示。我们观察到解调信号紧跟调制信号的包络，是信息承载信号的良好近似。
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