3d46201d-74a1-400c-a31d-204cdd14f402 36 6 9 decimal

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

Convolution Integral(s)

t h t 0 ≤ 01 t * - exp if :

w 4 : pulse width ≡

t f t 0 ≤ 0 t w ≥ 01 if if :

t0 1 time :

T 2 : Demo ≡

Does not recognise 'T' in h(T-x)

x f x f T x - h * 2 x - h 3 1 sys

cnv Does not recognise integrand t 3 - 10 2.75 - range : i 1 t rows range Σ i el u f t i el u - h * u 0 t i el int : for t Σ augment 41 line :

u q e x f * x h * eval :

Observe: the transit carrier [u <= x], [t, x, u], [x <= t] Int(x):=Int(t)must NOT be redefined for other integrand

t Int u q u 0 x int eval :

shape_dn 3 :

x Int t Int :

t y e shape_dn t 1 - (* -^eval :

x up 0 x ≤ (x 1 ≤ (& (x Int if :

x dn 1 x ≤ x y if :

1 Int 1 y 21 mat 1121 mat

α 6 : stretch/shrink ≡

t up 1 α / t * up :

t dn 1 α / t * dn :

C t 010 0.01 range : i 1 t rows range Σ i el t i el Int eval : for t Σ augment 31 line :

RC response under square pulse shape_up: RemToDo

x up x dn α 2 α 0 2 2 mat 3 1 sys

Continuous convolution evolves within the square pulse. Tabulate 'C'

C w 0.5 w 0.5 - 2 2 mat 2 1 sys

up_dn t 01 0.01 range : i 1 t rows range up i el t i el Int eval : for UP t up augment : t 16 1.01 range : i 1 t rows range dn i el t i el y eval : for DN t dn augment : UP DN stack 71 line :

point 50 :

X up_dn point row 1 col :

Y up_dn point row 2 col :

up_dn point row 0.49 0.816 12 mat

Discrete Convolution Integral point t=1 is duplicated.

up_dn X Y + 14 red 1 5 mat 2 1 sys

1 time t0 - 282 sec *

http://lpsa.swarthmore.edu/Convolution/Convolution2.html