LuvRene's Blog

Frequency ModulationPre-viewI’m glad that I still have time to write this blog in spite of so much things i need to do. The pressure of my grade is overweighted. But I feel lucky to have a little spare time to do something meaningful rather just playing games and wasting it. So back to the topic. In this blog, i will introduce a more useful modulation method called Frequency Modulation. DefinitionUnlike AM modulation which use the amplitude of the carrier signal to maintain the amplitude of...

Amplititude ModulationBasic IntroductionWhat is ModulationIf you want to understand what is modulation, you need to first know Why we need Modulation.As we all know, the frequency spectrum is limited and valueable which enable us to transmit signals at the same time without interference. But the signals we transmit is usually low frequency and long wave length ($ \lambda = \frac{c}{f} $). But due to its low frequency, it is easy to be interfered by other signals along the way it...

信号与系统 chapter 04-05 & 09-10 总结归纳Review在上一篇博客中，我们讲述了连续时间下的傅里叶变换以及对应的更为一般的情况，拉普拉斯变换。以及这两个变换在线性时不变系统中的表征和性质。其次我们讲述了离散时间下的傅里叶变换以及对应的更为一般的情况，Z变换。以及这两个变换在线性时不变系统中的表征和性质。无论是拉普拉斯变换还是Z变换都是对原输入信号添加一个增益后再进行傅里叶变换，为了满足添加增益后的输入信号能够收敛，我们对增益有一定的限制，由此引出了拉普拉斯变换和Z变换的收敛域的概念。 下面我们将开始介绍Chapter 06-08的内容，这也是我们最后的一部分内容。 Chapter 06幅度与相位表征系统函数在前文中，我们说线性时不变系统对于一个复指数信号的响应是等于信号自身乘上一个系统函数，对应的输入输出的傅里叶变换有$Y(s) = X(s)H(s)$,对于$H(s)$来说，既有幅度的信息，也有相位的信息，即我们可以将系统函数写成相量的形式，$ \lvert H(s) \rvert \arg(H(s))...

信号与系统 chapter 04-05 & 09-10 总结归纳Review在上一篇博客中，我们初步的接触了信号与系统，学习了一个简单但是重要的信号：单位冲激信号。对应的，我们学习了在线性时不变系统中如何用单位冲激信号表示一个信号，无论是连续还是离散。以及如果已知单位冲激响应如何求得系统对任何一个信号的响应。由此引入了卷积计算，系统对一个输入信号的响应就等价于输入信号与单位冲激响应做卷积。之后我们通过系统对复指数信号的响应引入了特征函数和特征值的概念，并且表示如果一个信号能够表示为一系列成谐波关系的复指数信号集，那么这个信号就可以写成傅里叶级数，而这样的信号的系统响应很容易求得。 连续时间的傅里叶级数$ x(t) = \sum_{k=-\infin}^{+\infin}a_{k}e^{jkw_{0}t} = \sum_{k=-\infin}^{+\infin}a_{k}e^{jk(\frac{2\pi}{T})t}, k = 0, 1, 2… $ （综合方程） $ a_{k} =...

信号与系统 chapter 01-03 总结归纳Tips：本博客中设计大量 Latex 公式，需要在浏览器中安装相应的插件支持 Latex 公式的显示Chapter 01:简单来说，章节一简单的介绍了一下什么是信号、什么是系统。以及介绍了一些常见的信号变化方式。那么我们需要关注的就是信号的分类，以下是几个非常重要的信号分支： 连续信号\离散信号 周期信号\非周期信号 第一类与第二类的信号可以相互组合，总共四种： 连续周期 连续非周期 离散周期 离散非周期 后续讨论的一切信号处理皆建立在这四类信号的基础上。不同的信号时域、频域的转换以及表现都不相同，对信号变化的响应也不相同。在这四种信号类型之外，介绍了一些常见的信号，如指数信号、正弦信号，表达式如下：$$ x(t) = Ae^{j\omega t} $$经过欧拉公式变形后，信号的表现形式如下：$$ x(t) = A(cos\omega_{0} t + j sin\omega_{0} t) $$ 可以发现，复指数信号是一个周期函数且可以展开为三角函数的形式，这也为我们后面的讨论定下了基础。其中 A...

STM32H723ZGT6 Development log01 - ADCWhat is ADCThe ADC, analog to digital conversion, is a tool to sample the analog values of voltage and transform to digital data. The range of digital data depends on the accuracy of ADC which can be 12bits, 14bits or even 16bits. The choices above are all provided in STM32H723ZGT6 and I personally recommend to use 14bits which mean $ 0-2^{14} $. Above all, ADC is a tool that can sample the analog values and transform to digital stored in STM32 so that we...

LanQiao Baseboard development’s log 03PWM Input Capture Mode for Frequency and Duty CalculationWhat is PWM Input Capture ModePWM input capture mode, is a special mode of TIM, which is especially useful in frequency measure. But you can’t use it occasionally because it needs a PWM input. Its original theory is below. How Can We Configure the Input Capture ModeYou should start the TIM input capture and rewrite the callback function. The original theory is when Timer detect the rising edge of...

LanQiao Baseboard development’s log 02PWM Output with Changeable DutyPWM Generate and OutputPWM, simply regarded as square signal, is important in many aspects like motor driven or any thing that can change effect by the level of voltage. So how can we generate a PWM signal? We can easily generate a PWM signal through our STM32’s TIM modules. The basic configure that you need to change is: First, Activate the TIM and choose a channel as PWM output channel. Attention! You need to choose CHx...

LanQiao Baseboard development’s log 01LED、LCD and Key quick startLED - LED Display and FloatingThe Pins to LED is show as followed.Pins Due to The pin from PC8 to PC15 is used by both LED and LCD so there is D1 between pins and LEDs so that when PD2 is set to High, the value of pins can be also set to LED. Instead, if the PD2 is set to low, the value of pins only affect the LCD’s value.So now we define the display function so that we can easily write the value of LED. 123456789#define...