Monday, 14 November 2022

DSP Equations In Latex

I was recently documenting some DSP equations in Latex and couldn't find any suitable examples so I've put them together and thought I'd share.

The Fourier Transform

\large \mathscr{F} \normalsize (x(t))=\int_{-\infty}^{\infty}x(t)e^{-j \omega t}dt


$$\large \mathscr{F} \normalsize (x(t))=\int_{-\infty}^{\infty}x(t)e^{-j \omega t}dt$$

The Discrete Time Fourier Transform

X(k) = \sum_{n=0}^{N-1}x(n).e^{-j 2 \pi nk/N},\; for\; 0 \le k \le N-1


$$X(k) = \sum_{n=0}^{N-1}x(n).e^{-j 2 \pi nk/N},\; for\; 0 \le k \le N-1$$

FIR Filter

y(n) = \sum_{n=0}^{N-1}h(k).x(n-k)


$$y(n) = \sum_{n=0}^{N-1}h(k).x(n-k)$$

IIR Filter

y(n) = \sum_{k=0}^{N}a_{k}.y(n-k) + \sum_{r=0}^{M}b_{r}.x(n-r)


$$y(n) = \sum_{k=0}^{N}a_{k}.y(n-k) + \sum_{r=0}^{M}b_{r}.x(n-r)$$

Roots Of Quadratic Equation $ax^{2} + bx + c = 0$

x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}


$$x=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$


To align equations with the equals sign, embed in the following blocks, use "&=" for the alignment and separate each line by ending with " \\".



VSCode doesn't support equation numbering auto increment and Colab doesn't support "equation*" or "aligned*" for disabling equation numbers. Colab requires "aligned" not "align".

Latex References