<p fontName="Arial">filter</p>

b5cb01c6-9e3a-4516-a917-9fbca6e49790 15 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

L H N xd U 0 : dx H L - N / : 12 mat i 1 N range U i el L dx - (dx i * + eval : for U 31 line :

x rnd 109^random 109^/ 11 line :

a b n xd d b a - n 1 - / : v n 1 matrix : k 1 n range : v k el k 1 - (d * : 14 mat a v + eval 21 line :

filter (b,a,x) filters the input data x using a rational transfer function defined by the 
numerator and denominator coefficients b and a. b a X filter b a X a length b length 12 mat max eval 1 matrix filter 11 line :

filter (b,a,x,zi) uses initial conditions zi for the filter delays. 
The length of zi must equal max(length(a),length(b))-1.
Final values modify given z. b a X Z filter na a length : nb b length : n na nb 12 mat max eval : 13 mat m X length : Y m 1 matrix : Z Z 0 stack : 13 mat B b na 1 matrix stack a 1 el / eval : A a nb 1 matrix stack a 1 el / eval : 12 mat k 1 m range Y k el B 1 el X k el * Z 1 el + eval : j 2 n range Z j 1 - el B j el X k el * Z j el + A j el Y k el * - eval : for 21 line for Z Z 1 n 1 - (range el : Y eval 61 line :

conv(u,v) returns the convolution of vectors u and v. 
If u and v are vectors of polynomial coefficients, convolving them 
is equivalent to multiplying the two polynomials. a b conv na a length : nb b length : 12 mat na nb > nb 1 > A a : A na nb + 1 - el 0 : 12 mat A a : if b 111 mat A filter 21 line na 1 > B b : B na nb + 1 - el 0 : 12 mat B b : if a 111 mat B filter 21 line if 21 line :

simplest lowpass filter

https://uk.mathworks.com/help/matlab/ref/filter.html

N 10 :

T 1 N range :

X T :

b 1121 mat :

a 111 mat :

Y b a X filter :

T X augment T Y augment 2 1 sys

Y 135791113151719101 mat

This example filters a matrix of data with the following rational transfer function.

X Clear 1

N 15 :

T 1 N range :

X 115 Random transpose :

a 1 0.2 - 21 mat :

b 111 mat :

Y b a X filter :

T X augment T Y augment 2 1 sys

N 100 :

T π - π N xd :

X T sin 0.25 1 rnd * + vectorize :

ws 5 :

b 1 ws / 1 ws 1 matrix + (* :

a 111 mat :

Y b a X filter :

T X augment T Y augment 2 1 sys

X 0.242186445999997 0.099493667470689 0.122666694314306 - 0.09793369408572 - 0.081250532914854 - 0.085032656874951 - 0.218346743684676 - 0.189865278315074 - 0.273543175851712 - 0.478357616228997 - 0.443072707542477 - 0.487368537748689 - 0.542622153928691 - 0.638648045171409 - 0.67337760952579 - 0.706810854624944 - 0.627613777002015 - 0.841244405043865 - 0.834325881966018 - 0.903057792638252 - 0.824837474295152 - 0.920736747378631 - 0.82715299722869 - 231 mat

Alvaro

XY T X augment :

xb XY 1 col : yb XY 2 col : N XY rows : 31 line

Prepare B39 Δx xb N el xb 1 el - (N / : ω 2 π N / * : u λ u xb 1 el - (ω Δx / * : 31 line

Fourier polynomial coefficients for B39 n 0 N range A n 1 + el 2 N 3 - / yb k 1 + el n k * ω * cos * k 0 N 1 - sum * eval : B n 1 + el 2 N 3 - / yb k 1 + el n k * ω * sin * k 0 N 1 - sum * eval : 21 line for

w 2 : length of B39 ≡

u B39 A 1 el 2 / A n 1 + el u λ n * cos * B n 1 + el u λ n * sin * + (n 1 w sum + 11 line :

XY x B39 2 1 sys