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数字信号处理digital signal process和模拟信号处理是信号处理的子领域。DSP的应用包括音频和语音处理、声纳、雷达和其他传感器阵列处理、频谱密度估计、统计信号处理、数字图像处理、数据压缩、视频编码、音频编码、图像压缩、电信的信号处理、控制系统、生物医学工程和地震学等。
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我们提供的数字信号处理digital signal process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|数字信号处理作业代写digital signal process代考|Basics
The requantization (renewed quantization of already quantized signals) to limited wordlengths occurs repeatedly during storage, format conversion and signal processing algorithms. Here, small signal levels lead to error signals which depend on the input. Owing to quantization, nonlinear distortion occurs for low-level signals. The conditions for the classical quantization model are not satisfied anymore. To reduce these effects for signals of small amplitude, a linearization of the nonlinear characteristic curve of the quantizer is performed. This is done by adding a random sequence $d(n)$ to the quantized signal $x(n)$ (see Fig. 2.17) before the actual quantization process. The specification of the word-length is shown in Fig. 2.18. This random signal is called dither. The statistical independence of the error signal from the input is not achieved, but the conditional moments of the error signal can be affected [Lip92, Ger89, Wan92, Wan00].
The sequence $d(n)$, with amplitude range $(-Q / 2 \leq d(n) \leq Q / 2)$, is generated with the help of a random number generator and is added to the input. For a dither value with $Q=2^{-(w-1)}$.
$$
d_{k}=k 2^{-r} Q, \quad-2^{s-1} \leq k \leq 2^{s-1}-1 .
$$
The index $k$ of the random number $d_{k}$ characterizes the value from the set of $N=2^{s}$ possible numbers with the probability
$$
P\left(d_{k}\right)= \begin{cases}2^{-s}, & -2^{s-1} \leq k \leq 2^{s-1}-1, \ 0, & \text { elsewhere }\end{cases}
$$
With the mean value $\bar{d}=\sum_{k} d_{k} P\left(d_{k}\right)$, the variance $\sigma_{D}^{2}=\sum_{k}\left[d_{k}-\bar{d}\right]^{2} P\left(d_{k}\right)$ and the quadratic mean $\overline{d^{2}}=\sum_{k} d_{k}^{2} P\left(d_{k}\right)$, we can rewrite the variance as $\sigma_{d}^{2}=\overline{d^{2}}-\bar{d}^{2}$.
For a static input amplitude $V$ and the dither value $d_{k}$ the rounding operation [Lip86] is expressed as
$$
g\left(V+d_{k}\right)=Q\left\lfloor\frac{V+d_{k}}{Q}+0.5\right\rfloor
$$
信号代写|数字信号处理作业代写digital signal process代考|Implementation
The random sequence $d(n)$ is generated with the help of a random number generator with uniform PDF. For generating a triangular PDF random sequence, two independent uniform PDF random sequences $d_{1}(n)$ and $d_{2}(n)$ can be added. In order to generate a triangular high-pass dither, the dither value $d_{1}(n)$ is added to $-d_{1}(n-1)$. Thus, only one random number generator is required. In conclusion, the following dither sequences can be implemented:
$$
\begin{aligned}
d_{\mathrm{RECT}}(n) &=d_{1}(n) \
d_{\mathrm{TRI}}(n) &=d_{1}(n)+d_{2}(n), \
d_{\mathrm{HP}}(n) &=d_{1}(n)-d_{1}(n-1)
\end{aligned}
$$
The power density spectra of triangular PDF dither and triangular PDF HP dither are shown in Fig. 2.21. Figure $2.22$ shows histograms of a uniform PDF dither and a triangular PDF high-pass dither together with their respective power density spectra. The amplitude range of a uniform PDF dither lies between $\pm Q / 2$, whereas it lies between $\pm Q$ for triangular PDF dither. The total noise power for triangular PDF dither is doubled.
信号代写|数字信号处理作业代写digital signal process代考|Examples
The effect of the input amplitude of the quantizer is shown in Fig. $2.23$ for a 16-bit quantizer $\left(Q=2^{-15}\right)$. A quantized sinusoidal signal with amplitude $2^{-15}$ (1-bit amplitude)and frequency $f / f_{S}=64 / 1024$ is shown in Fig. 2.23a,b for rounding and truncation. Figure $2.23 \mathrm{c}, \mathrm{d}$ shows their corresponding spectra. For truncation, Fig. 2.23c shows the spectral line of the signal and the spectral distribution of the quantization error with the harmonics of the input signal. For rounding (Fig. $2.23 \mathrm{~d}$ with special signal frequency $\left.f / f_{S}=64 / 1024\right)$, the quantization error is concentrated in uneven harmonics.
In the following, only the rounding operation is used. By adding a uniform PDF random signal to the actual signal before quantization, the quantized signal shown in Fig. $2.24 \mathrm{a}$ results. The corresponding power density spectrum is illustrated in Fig. 2.24c. In the time domain, it is observed that the 1-bit amplitudes approach zero so that the regular pattern of the quantized signal is affected. The resulting power density spectrum in Fig. 2.24c shows that the harmonics do not occur anymore and the noise power is uniformly distributed over the frequencies. For triangular PDF dither, the quantized signal is shown in Fig. 2.24b. Owing to triangular PDF, amplitudes $\pm 2 Q$ occur besides the signal values $\pm Q$ and zero. Figure $2.24 \mathrm{~d}$ shows the increase of the total noise power.
数字信号处理代写
信号代写|数字信号处理作业代写DIGITAL SIGNAL PROCESS代考|BASICS
再量化r和n和在和dq在一种n吨一世和一种吨一世这n这F一种lr和一种d是q在一种n吨一世和和ds一世Gn一种ls在存储、格式转换和信号处理算法中重复出现限制字长。在这里，小信号电平会导致取决于输入的错误信号。由于量化，低电平信号会出现非线性失真。经典量化模型的条件不再满足。为了减少小幅度信号的这些影响，对量化器的非线性特性曲线进行线性化。这是通过添加一个随机序列来完成的d(n)对量化信号X(n) s和和F一世G.2.17在实际量化过程之前。字长的规定如图 2.18 所示。这种随机信号称为抖动。未实现误差信号与输入的统计独立性，但会影响误差信号的条件矩大号一世p92,G和r89,在一种n92,在一种n00.
序列d(n), 幅度范围(−问/2≤d(n)≤问/2), 在随机数生成器的帮助下生成并添加到输入中。对于抖动值问=2−(在−1).
dķ=ķ2−r问,−2s−1≤ķ≤2s−1−1.
指数ķ随机数的dķ表征集合中的值ñ=2s具有概率的可能数字
磷(dķ)={2−s,−2s−1≤ķ≤2s−1−1, 0, 别处
与平均值d¯=∑ķdķ磷(dķ), 方差σD2=∑ķ[dķ−d¯]2磷(dķ)和二次均值d2¯=∑ķdķ2磷(dķ)，我们可以将方差改写为σd2=d2¯−d¯2.
对于静态输入幅度在和抖动值dķ舍入运算大号一世p86表示为
G(在+dķ)=问⌊在+dķ问+0.5⌋
信号代写|数字信号处理作业代写DIGITAL SIGNAL PROCESS代考|IMPLEMENTATION
随机序列d(n)是在具有统一 PDF 的随机数生成器的帮助下生成的。用于生成三角形 PDF 随机序列，两个独立的均匀 PDF 随机序列d1(n)和d2(n)可以添加。为了产生三角高通抖动，抖动值d1(n)被添加到−d1(n−1). 因此，只需要一个随机数发生器。总之，可以实现以下抖动序列：
$$
\begin{aligned}
d_{\mathrm{RECT}}(n) &=d_{1}(n) \
d_{\mathrm{TRI}}(n) &=d_{1}(n)+d_{2}(n), \
d_{\mathrm{HP}}(n) &=d_{1}(n)-d_{1}(n-1)
\end{aligned}
$$
三角形 PDF 抖动和三角形 PDF HP 抖动的功率密度谱如图 2.21 所示。数字2.22显示了均匀 PDF 抖动和三角形 PDF 高通抖动的直方图以及它们各自的功率密度谱。均匀 PDF 抖动的幅度范围介于±问/2，而它介于±问用于三角形 PDF 抖动。三角 PDF 抖动的总噪声功率加倍。
信号代写|数字信号处理作业代写DIGITAL SIGNAL PROCESS代考|EXAMPLES
量化器输入幅度的影响如图 1 所示。2.23对于 16 位量化器(问=2−15). 具有幅度的量化正弦信号2−15 1−b一世吨一种米pl一世吨在d和和频率F/F小号=64/1024舍入和截断如图 2.23a、b 所示。数字2.23C,d显示了它们对应的光谱。对于截断，图 2.23c 显示了信号的谱线和量化误差随输入信号谐波的谱分布。用于四舍五入图 $2.23 \mathrm{~d}$ 与特殊信号频率 $\left.f / f_{S}=64 / 1024\right图 $2.23 \mathrm{~d}$ 与特殊信号频率 $\left.f / f_{S}=64 / 1024\right$，量化误差集中在不均匀谐波上。
在下文中，仅使用舍入操作。通过在量化前的实际信号中加入一个均匀的PDF随机信号，量化后的信号如图1所示。2.24一种结果。相应的功率密度谱如图 2.24c 所示。在时域中，观察到 1 位幅度接近零，从而影响了量化信号的规则模式。图 2.24c 中得到的功率密度谱表明谐波不再出现，噪声功率均匀分布在频率上。对于三角 PDF 抖动，量化后的信号如图 2.24b 所示。由于三角形 PDF，幅度±2问除了信号值发生±问和零。数字2.24 d显示总噪声功率的增加。
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