Mathematical symbols 數學符號

∀ - for all

Reference

List of mathematical symbols (Wikipedia)

Tensor 張量

Array of numbers that may have
- scalar 純量
- vector 向量
- matrix 矩陣
- more dimensions.

Refernces

Lecture slides for Chapter 2 of Deep Learning, Ian Goodfellow
張量 (Tensor) - 金門大學陳鍾誠的網站

Data Center Locations - Google, Akamai, CloudFlare, Amazon CloudFront

Below data are recorded on August 19, 2017

Google - https://www.google.com/about/datacenters/inside/locations/index.html

• USA x 7
• Asia x 2 (Taiwan, Singapore)
• Europe x 4

      Taiwan 台灣 - Chunghua County 彰化縣

Akamai - https://www.akamai.com/us/en/locations.jsp

      Taiwan 台灣 - Taipei 台北市

CloudFlare - https://www.cloudflare.com/network/

• 116 data centers

      Taiwan 台灣 - Taipei 台北(亞洲第28個/全球第77個data center)

Amazon CloudFront Edge InfraStructure - https://aws.amazon.com/cloudfront/details/

• 22 edge locations / 11 regional edge caches

      Taiwan 台灣 - Taipei 台北

Rectifiers 整流器

rectifiers 整流器

half-wave rectifiers 半波整流器
full-wave rectifiers 全波整流器

diode rectifier 二極體整流器

Matlab: Play Demo Sounds

It is very easy to play some demo sounds with Matlab commands using the sound function.

To play a female speaker saying 'Matlab' type:

>> load mtlb
>> sound(mtlb,Fs)

Note that the workspace contains mtlb and Fs, so sound(mtlb,Fs) is called.

You may clear the workspace with the the clear command:

>> clear

To play a snippet of Handel's Hallelujah Chorus, type:

>> load handel
>> sound(y,Fs)

There are also other sounds you may load:

load chirp
load gong
load laughter
load train

References:

Formant Estimation with LPC Coefficients
Record and Play Audio
Sound + FFT

Vectors 向量

dot product / scalar product / inner product / projection product 點積/內積/純量積 a·b
A·B = |A| |B| cos(θ)
A_B = |A| cos(θ)

For vectors a = (a₁, a₂, ..., a_n) and b = (b₁, b₂, ..., b_n) ,

a·b = a₁b₁ + a₂b₂ + ... + a_nb_n

For example, vectors a = (1, 2, 3) and b = (0, 4, 5),

a·b = 1×0 + 2×4 + 3×5 = 23

Matlab code:

>> a = [1 2 3];
>> b = [0 4 5];
>> dot(a,b)

ans =

    23

cross product/vector product 點積/向量積 a×b

參考資料

內積與外積

Cent and Semitone 音分和半音

cent 音分
semitone/half step/half tone 半音
whole tone 全音
accidental 變音記號

1 semitone = 100 cents

octave 八度音

一個八度音 = 12個半音 = 5個全音 + 2個半音
Twelve-tone equal temperament (十二平均律)
- divide an octave into 12 equal parts

Number of Semitones between Two Frequencies (兩個頻率間相差的半音數):

n = abs(log₂(f₁/f₂)/log₂(2^(1/12))) = abs(12log₂(f₁/f₂))

Reference

How to find the number of semitones between two frequencies?