Signal-to-Noise Ratio (SNR)

Signal-to-Noise Ratio (SNR) 訊號雜訊比/訊雜比/訊噪比/信噪比

SNR = (signal power)/(noise power) = P_signal/P_noise
SNR_dB = 10log₁₀(SNR) = 10log₁₀(P_signal)-10log₁₀(P_noise) in decibels (dB)

Therefore, if P_signal > P_noise,

SNR > 1 and SNR_dB > 0 dB.

If SNR_dB < 0, P_signal < P_noise. In other words, when the SNR_dB is negative, the power of the signal is weaker than the power of background noise.

Reference

Signal-to-noise ratio/訊號雜訊比 (Wikipedia)

Matlab: Laplace Transform

The examples below demonstrate the Laplace transforms and inverse Laplace transforms using Matlab symbolic number or variable.

Laplace Transform

L{1} = 1/s

>> x = sym(1);
>> laplace(x)

ans =

1/s

L{t} = 1/s²

>> syms t
>> laplace(t)

ans =

1/s^2

Inverse Laplace Transform

L^-1{1/s} = 1

>> syms s
>> ilaplace(1/s)

ans =

1

L^-1{1/(s-a)} = e^at where a = 2

>> ilaplace(1/(s-2))

ans =

exp(2*t)

L^-1{a²/(s²+a²)} = sin(at) where a = 1

>> ilaplace(1/(s^2+1))

ans =

sin(t)

Reference

Zill, D., Wright, W. S., & Cullen, M. R. (2011). Advanced engineering mathematics. 4th Edition. Jones & Bartlett Learning. p 197-198.

laplace / ilaplace - MathWorks Documentation

Matlab: Differentiation of sine and cosine functions

To calculate the derivates of sin() and cos(), use the syms symbolic variable as below:

>> syms x
>> y = sin(x);
>> y_prime = diff(y)

y_prime =

cos(x)

>> y_prime_prime = diff(y_prime)

y_prime_prime =

-sin(x)

References

Matlab: Basic Differentiation and Integration with the syms symbolic variable
Basic Calculus Terms 基本微基分名詞

Basic Calculus Terms 基本微基分名詞

calculus 微積分

differentiation 微分
integration 積分

derivative 導數
integral 積分

References

Glossary of calculus (Wikipedia)
微積分常用述語中英文對照
Matlab: Basic Differentiation and Integration with the syms symbolic variable
Matlab: Differentiation of sine and cosine functions

Matlab: Basic Differentiation and Integration with the syms symbolic variable

To perform basic calculus calculations with Matlab, declare symbolic variables with syms command:

>> syms x;
>> y = 3*x^3+2*x^2-4*x+5;

Hence y = 3x³+2x²-4x+5.

For differentiation, the derivative of y is y' = diff(y):

>> y_prime = diff(y)

y_prime =

9*x^2 + 4*x - 4

Hence y' = dy/dx = 9x²+4x-4.

For integration, the integral of y is ∫ y dy = int(y):

>> y_integral = int(y)

y_integral =

(3*x^4)/4 + (2*x^3)/3 - 2*x^2 + 5*x

Consequently, ∫ y dy = (3x⁴)/4 + (2x³)/3 - 2x² + 5x + c.

References

Glossary of calculus (Wikipedia)
微積分常用述語中英文對照 (交大微積分教學小組)
Basic Calculus Terms 基本微基分名詞 (Study EECC)
Matlab: Differentiation of sine and cosine functions

Matlab: Simple structure with dot (.)

To create a basic form of structure in Matlab, simply use a dot (.) as below:

>> mystruct.name = "peter";
>> mystruct.age = 15;
>> mystruct.hobby = "swimming";
>> mystruct

mystruct =

  struct with fields:

     name: "peter"
      age: 15
    hobby: "swimming"