分享知识，结识志同道合的朋友https://troyzhou.top/zh-cnhttps://troyzhou.top/notes/mri/mri_logs/tse-sequence-modification-20260409/https://troyzhou.top/notes/mri/mri_logs/tse-sequence-modification-20260409/修改TSE序列，添加Spoiler收尾梯度和激发脉冲层选梯度时遇到梯度幅值超限报错，以及波形衔接处出现明显瑕疵的排查过程。Thu, 09 Apr 2026 00:00:00 GMTMRI / 实验日志https://troyzhou.top/blog/welcome-to-my-site/https://troyzhou.top/blog/welcome-to-my-site/从 Obsidian 到 Astro，用两个月的时间搭起了这个个人站。记录搭建初衷、技术选型和未来计划。Wed, 08 Apr 2026 00:00:00 GMT随笔https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/biomedical-signal-processing/lecture-4/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/biomedical-signal-processing/lecture-4/求阶跃/冲激响应：默认是零状态响应 Tue, 31 Mar 2026 00:00:00 GMT大二下 / 生物医学信号处理https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/biomedical-signal-processing/lecture-5/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/biomedical-signal-processing/lecture-5/FIR系统的b系数就是h[n] Tue, 31 Mar 2026 00:00:00 GMT大二下 / 生物医学信号处理https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E5%BE%AE%E8%A7%82%E7%BB%8F%E6%B5%8E%E5%AD%A6/lecture-5/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E5%BE%AE%E8%A7%82%E7%BB%8F%E6%B5%8E%E5%AD%A6/lecture-5/Total Cost = Variable Cost + Fixed Cost Tue, 31 Mar 2026 00:00:00 GMT大二下 / 微观经济学https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E6%95%B0%E5%AD%97%E7%94%B5%E8%B7%AF/lecture-4/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E6%95%B0%E5%AD%97%E7%94%B5%E8%B7%AF/lecture-4/竞争-冒险： Tue, 31 Mar 2026 00:00:00 GMT大二下 / 数字电路https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/mcs-51/%E7%9F%A5%E8%AF%86%E6%A2%B3%E7%90%861/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/mcs-51/%E7%9F%A5%E8%AF%86%E6%A2%B3%E7%90%861/1 寄存器vs锁存器 Mon, 30 Mar 2026 00:00:00 GMT大二下 / MCS-51单片机https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/mcs-51/%E7%9F%A5%E8%AF%86%E6%A2%B3%E7%90%862/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/mcs-51/%E7%9F%A5%E8%AF%86%E6%A2%B3%E7%90%862/1. 寻址空间：程序存储器。指令的操作数直接存储在程序存储器中，根据指令的不同，操作数可以为8位或者16位。 Mon, 30 Mar 2026 00:00:00 GMT大二下 / MCS-51单片机https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/mcs-51/%E7%9F%A5%E8%AF%86%E6%A2%B3%E7%90%863/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/mcs-51/%E7%9F%A5%E8%AF%86%E6%A2%B3%E7%90%863/概况：数据传送指令一共有29条，用到的助记符有8种，可以概括为5类： Mon, 30 Mar 2026 00:00:00 GMT大二下 / MCS-51单片机https://troyzhou.top/notes/mri/mri-seq/01-fid-se/https://troyzhou.top/notes/mri/mri-seq/01-fid-se/FID全称：Free Induction Decay 也就是自由感应衰减，是核磁共振成像中最基础的信号。 Thu, 26 Mar 2026 00:00:00 GMTMRI / MRI Seqhttps://troyzhou.top/notes/mri/mri-seq/02-steam-press/https://troyzhou.top/notes/mri/mri-seq/02-steam-press/磁共振波谱（MRS）利用“化学位移”现象，将特定体素内的信号按分子频率差异拆解，从而定量分析组织中的各种代谢产物。它不产生传统的解剖图像，而是提供一张反映生化信息的“代谢指纹”频谱图，从分子水平揭示疾病的病理生理变化。 Thu, 26 Mar 2026 00:00:00 GMTMRI / MRI Seqhttps://troyzhou.top/notes/mri/mri-seq/03-gre/https://troyzhou.top/notes/mri/mri-seq/03-gre/在正式Gx梯度之前，我们会施加一个面积为Gx一半的反向梯度。通过这个梯度，我们可以让回波中心正好位于ADC的中心。 Thu, 26 Mar 2026 00:00:00 GMTMRI / MRI Seqhttps://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/biomedical-signal-processing/lecture-1/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/biomedical-signal-processing/lecture-1/函数：定义域到值域的映射 Tue, 24 Mar 2026 00:00:00 GMT大二下 / 生物医学信号处理https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/biomedical-signal-processing/lecture-2/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/biomedical-signal-processing/lecture-2/熟悉斜坡，阶跃，单位冲激函数的关系 Tue, 24 Mar 2026 00:00:00 GMT大二下 / 生物医学信号处理https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/biomedical-signal-processing/lecture-3/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/biomedical-signal-processing/lecture-3/\delta函数的筛选特性： Tue, 24 Mar 2026 00:00:00 GMT大二下 / 生物医学信号处理https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E5%BE%AE%E8%A7%82%E7%BB%8F%E6%B5%8E%E5%AD%A6/lecture-1/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E5%BE%AE%E8%A7%82%E7%BB%8F%E6%B5%8E%E5%AD%A6/lecture-1/定义： 经济主体如何配置稀缺资源，以及这些选择如何影响社会的学科 Tue, 24 Mar 2026 00:00:00 GMT大二下 / 微观经济学https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E5%BE%AE%E8%A7%82%E7%BB%8F%E6%B5%8E%E5%AD%A6/lecture-2/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E5%BE%AE%E8%A7%82%E7%BB%8F%E6%B5%8E%E5%AD%A6/lecture-2/最优化假设： 人们总会做出最优化的选择 Tue, 24 Mar 2026 00:00:00 GMT大二下 / 微观经济学https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E5%BE%AE%E8%A7%82%E7%BB%8F%E6%B5%8E%E5%AD%A6/lecture-3/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E5%BE%AE%E8%A7%82%E7%BB%8F%E6%B5%8E%E5%AD%A6/lecture-3/关于偏好的符号描述： Tue, 24 Mar 2026 00:00:00 GMT大二下 / 微观经济学https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E6%95%B0%E5%AD%97%E7%94%B5%E8%B7%AF/lecture-1/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E6%95%B0%E5%AD%97%E7%94%B5%E8%B7%AF/lecture-1/常用数制 Tue, 24 Mar 2026 00:00:00 GMT大二下 / 数字电路https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E6%95%B0%E5%AD%97%E7%94%B5%E8%B7%AF/lecture-2/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E6%95%B0%E5%AD%97%E7%94%B5%E8%B7%AF/lecture-2/真值表，逻辑表达式，卡诺图 Tue, 24 Mar 2026 00:00:00 GMT大二下 / 数字电路https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E6%95%B0%E5%AD%97%E7%94%B5%E8%B7%AF/lecture-3/https://troyzhou.top/notes/%E5%A4%A7%E4%BA%8C%E4%B8%8B/%E6%95%B0%E5%AD%97%E7%94%B5%E8%B7%AF/lecture-3/1. 信号的双向传输：两个相反的三态门，使用控制端+非门控制 Tue, 24 Mar 2026 00:00:00 GMT大二下 / 数字电路https://troyzhou.top/notes/mri/mri_basics/10-fast-imaging-method/https://troyzhou.top/notes/mri/mri_basics/10-fast-imaging-method/同一切层由于频率编码/相位编码，需要多次重复采集才能填满k-space. Wed, 11 Mar 2026 00:00:00 GMTMRI / MRI基础https://troyzhou.top/notes/%E8%AF%BB%E4%B9%A6%E7%AC%94%E8%AE%B0/%E6%B5%AA%E6%BD%AE%E4%B9%8B%E5%B7%85/%E6%B5%AA%E6%BD%AE%E4%B9%8B%E5%B7%85/https://troyzhou.top/notes/%E8%AF%BB%E4%B9%A6%E7%AC%94%E8%AE%B0/%E6%B5%AA%E6%BD%AE%E4%B9%8B%E5%B7%85/%E6%B5%AA%E6%BD%AE%E4%B9%8B%E5%B7%85/Mon, 09 Mar 2026 00:00:00 GMT读书笔记 / 浪潮之巅https://troyzhou.top/notes/mri/mri_basics/11-imperfections-and-artifacts/https://troyzhou.top/notes/mri/mri_basics/11-imperfections-and-artifacts/这里最重要的概念就是K-space的权重，我这里拿弛豫导致的衰减权重为例： Sun, 08 Mar 2026 00:00:00 GMTMRI / MRI基础https://troyzhou.top/notes/mri/mri_basics/08-spatial-encoding-k-space/https://troyzhou.top/notes/mri/mri_basics/08-spatial-encoding-k-space/Gy(n) = -G{yp} + (n-1)G{yi} Tue, 03 Mar 2026 00:00:00 GMTMRI / MRI基础https://troyzhou.top/notes/mri/mri_basics/09-image-characteristics/https://troyzhou.top/notes/mri/mri_basics/09-image-characteristics/视野（FOV) 由采样的步长决定，采样的步长越大，看到的视野越广： Tue, 03 Mar 2026 00:00:00 GMTMRI / MRI基础https://troyzhou.top/notes/mri/mri_basics/07-rf-pulse-design/https://troyzhou.top/notes/mri/mri_basics/07-rf-pulse-design/概述 ：RF Pulse在翻转角小于60°时使用傅里叶变换作为工具，在翻转角为90°，180°时使用SLR(Shinnar-Le Roux)作为工具 Sun, 01 Mar 2026 00:00:00 GMTMRI / MRI基础https://troyzhou.top/notes/mri/mri_basics/03-basic-contrast-mechanisms/https://troyzhou.top/notes/mri/mri_basics/03-basic-contrast-mechanisms/T1描述的是质子如何将吸收的能量释放给周围的分子结构（lattice），从而回到平衡态。周围分子的运动节奏和质子进动频率越接近，T1时间就越短。 Thu, 26 Feb 2026 00:00:00 GMTMRI / MRI基础https://troyzhou.top/notes/mri/mri_basics/04-in-vivo-contrast-mechanisms/https://troyzhou.top/notes/mri/mri_basics/04-in-vivo-contrast-mechanisms/原理： 人体不同组织的导磁率略有不同，这导致不同组织的自选频率不同，产生一种宏观失相。 Thu, 26 Feb 2026 00:00:00 GMTMRI / MRI基础https://troyzhou.top/notes/mri/mri_basics/05-gradient-and-spin-echo-pulse-sequence/https://troyzhou.top/notes/mri/mri_basics/05-gradient-and-spin-echo-pulse-sequence/梯度场差异会导致空间自选速度差异，施加反向梯度场可以纠正这种差异，让相位重新聚焦。 Thu, 26 Feb 2026 00:00:00 GMTMRI / MRI基础https://troyzhou.top/notes/mri/mri_basics/06-rf-pulses/https://troyzhou.top/notes/mri/mri_basics/06-rf-pulses/sinc函数的带宽与时间带宽积TBW的关系，以及SAR指标说明。Thu, 26 Feb 2026 00:00:00 GMTMRI / MRI基础https://troyzhou.top/notes/mri/mri_basics/01-pulse-sequence/https://troyzhou.top/notes/mri/mri_basics/01-pulse-sequence/在MRI成像中，为了填满k space,需要将基本脉冲序列重复几十次甚至上百次，而每一次的“相位编码梯度”（phase encoding gradient)的强度都会改变。 Wed, 25 Feb 2026 00:00:00 GMTMRI / MRI基础https://troyzhou.top/notes/mri/mri_basics/02-mri-signal-equation/https://troyzhou.top/notes/mri/mri_basics/02-mri-signal-equation/1. 离共振（off resonance)：质子的进动频率偏离了MRI系统设定的中心频率。离共振有很多原因，而化学位移是其中最重要的一个。 Wed, 25 Feb 2026 00:00:00 GMTMRI / MRI基础https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/%E5%90%91%E9%87%8F%E5%8F%89%E4%B9%98%E7%9A%84%E8%A1%8C%E5%88%97%E5%BC%8F%E8%AE%B0%E5%BF%86%E6%B3%95/%E5%90%91%E9%87%8F%E5%8F%89%E4%B9%98%E7%9A%84%E8%A1%8C%E5%88%97%E5%BC%8F%E8%AE%B0%E5%BF%86%E6%B3%95/https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/%E5%90%91%E9%87%8F%E5%8F%89%E4%B9%98%E7%9A%84%E8%A1%8C%E5%88%97%E5%BC%8F%E8%AE%B0%E5%BF%86%E6%B3%95/%E5%90%91%E9%87%8F%E5%8F%89%E4%B9%98%E7%9A%84%E8%A1%8C%E5%88%97%E5%BC%8F%E8%AE%B0%E5%BF%86%E6%B3%95/给定向量 \mathbf{a}=[ax,ay,az]^T 和 \mathbf{b}=[bx,by,bz]^T\ Wed, 15 Oct 2025 00:00:00 GMT数学杂记 / 向量叉乘的行列式记忆法https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/%E5%A6%82%E4%BD%95%E5%88%A4%E6%96%AD%E4%BA%8C%E5%85%83%E5%87%BD%E6%95%B0%E8%BF%9E%E7%BB%AD/%E5%A6%82%E4%BD%95%E5%88%A4%E6%96%AD%E4%BA%8C%E5%85%83%E5%87%BD%E6%95%B0%E8%BF%9E%E7%BB%AD/https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/%E5%A6%82%E4%BD%95%E5%88%A4%E6%96%AD%E4%BA%8C%E5%85%83%E5%87%BD%E6%95%B0%E8%BF%9E%E7%BB%AD/%E5%A6%82%E4%BD%95%E5%88%A4%E6%96%AD%E4%BA%8C%E5%85%83%E5%87%BD%E6%95%B0%E8%BF%9E%E7%BB%AD/设函数 z = f(x, y) 在点 (x0, y0) 的某个邻域内有定义。 Sun, 12 Oct 2025 00:00:00 GMT数学杂记 / 如何判断二元函数连续https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/0-0-%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0%E7%9B%AE%E5%BD%95/0-0-%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0%E7%9B%AE%E5%BD%95/https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/0-0-%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0%E7%9B%AE%E5%BD%95/0-0-%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0%E7%9B%AE%E5%BD%95/微积分梳理 Sat, 27 Sep 2025 00:00:00 GMT数学杂记 / 0-0 数学杂记目录https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/ln-z-%E5%92%8Cln-z-%E7%9A%84%E5%8C%BA%E5%88%AB/ln-z-%E5%92%8Cln-z-%E7%9A%84%E5%8C%BA%E5%88%AB/https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/ln-z-%E5%92%8Cln-z-%E7%9A%84%E5%8C%BA%E5%88%AB/ln-z-%E5%92%8Cln-z-%E7%9A%84%E5%8C%BA%E5%88%AB/Ln(z) (大写L): 代表 复对数函数 (Complex Logarithm)。 Sat, 27 Sep 2025 00:00:00 GMT数学杂记 / Ln(z)和ln(z)的区别https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/ln-z-%E5%A4%8D%E6%95%B0%E5%AF%B9%E6%95%B0/ln-z-%E5%A4%8D%E6%95%B0%E5%AF%B9%E6%95%B0/https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/ln-z-%E5%A4%8D%E6%95%B0%E5%AF%B9%E6%95%B0/ln-z-%E5%A4%8D%E6%95%B0%E5%AF%B9%E6%95%B0/复数 z 的对数 Ln(z) 定义为：Ln(z) = ln|z| + i(Arg(z) + 2kπ)，其中 k 为任意整数。 Sat, 27 Sep 2025 00:00:00 GMT数学杂记 / Ln(z) 复数对数https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/%E4%B8%89%E8%A7%92%E4%B8%8E%E5%8F%8C%E6%9B%B2%E5%87%BD%E6%95%B0%E7%9A%84%E8%BD%AC%E6%8D%A2%E5%85%B3%E7%B3%BB/%E4%B8%89%E8%A7%92%E4%B8%8E%E5%8F%8C%E6%9B%B2%E5%87%BD%E6%95%B0%E7%9A%84%E8%BD%AC%E6%8D%A2%E5%85%B3%E7%B3%BB/https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/%E4%B8%89%E8%A7%92%E4%B8%8E%E5%8F%8C%E6%9B%B2%E5%87%BD%E6%95%B0%E7%9A%84%E8%BD%AC%E6%8D%A2%E5%85%B3%E7%B3%BB/%E4%B8%89%E8%A7%92%E4%B8%8E%E5%8F%8C%E6%9B%B2%E5%87%BD%E6%95%B0%E7%9A%84%E8%BD%AC%E6%8D%A2%E5%85%B3%E7%B3%BB/由欧拉公式： Sat, 27 Sep 2025 00:00:00 GMT数学杂记 / 三角与双曲函数的转换关系https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/%E5%B7%B2%E7%9F%A5%E4%BA%8C%E5%85%83%E5%87%BD%E6%95%B0%E5%81%8F%E5%AF%BC%E6%95%B0-%E5%A6%82%E4%BD%95%E6%B1%82%E5%8E%9F%E5%87%BD%E6%95%B0/%E5%B7%B2%E7%9F%A5%E4%BA%8C%E5%85%83%E5%87%BD%E6%95%B0%E5%81%8F%E5%AF%BC%E6%95%B0-%E5%A6%82%E4%BD%95%E6%B1%82%E5%8E%9F%E5%87%BD%E6%95%B0/https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/%E5%B7%B2%E7%9F%A5%E4%BA%8C%E5%85%83%E5%87%BD%E6%95%B0%E5%81%8F%E5%AF%BC%E6%95%B0-%E5%A6%82%E4%BD%95%E6%B1%82%E5%8E%9F%E5%87%BD%E6%95%B0/%E5%B7%B2%E7%9F%A5%E4%BA%8C%E5%85%83%E5%87%BD%E6%95%B0%E5%81%8F%E5%AF%BC%E6%95%B0-%E5%A6%82%E4%BD%95%E6%B1%82%E5%8E%9F%E5%87%BD%E6%95%B0/当已知一个二元函数的两个偏导数时，可以通过积分来求得原函数。这在求解全微分方程中是一个核心步骤。以下是详细的求解方法和步骤。 Sat, 27 Sep 2025 00:00:00 GMT数学杂记 / 已知二元函数偏导数，如何求原函数https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/%E5%BE%AE%E7%A7%AF%E5%88%86%E6%A2%B3%E7%90%86/%E5%BE%AE%E7%A7%AF%E5%88%86%E6%A2%B3%E7%90%86/https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/%E5%BE%AE%E7%A7%AF%E5%88%86%E6%A2%B3%E7%90%86/%E5%BE%AE%E7%A7%AF%E5%88%86%E6%A2%B3%E7%90%86/一、定义： Sat, 27 Sep 2025 00:00:00 GMT数学杂记 / 微积分梳理https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/sec%E7%A7%AF%E5%88%86/sec%E7%A7%AF%E5%88%86/https://troyzhou.top/notes/%E6%95%B0%E5%AD%A6%E6%9D%82%E8%AE%B0/sec%E7%A7%AF%E5%88%86/sec%E7%A7%AF%E5%88%86/Tue, 16 Sep 2025 00:00:00 GMT数学杂记 / sec积分