2586bb22-8f44-444d-a1ae-833887c848c4 23 4 5 decimal

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

Convolution Integral(s)

Smath 5346 uninstalled version

From C:\Smath+Maxima\2014 11 16 Smath and Maxima

1. Open the "uninstalled" version above 2. click "Run" 3. Open the work sheet. It will work.

Smath 5346 installed version,NO LM

T 2 :

t h 0 t 0 ≤ e t -^cases :

# # cases

# # # cases

t x 0 t 0 ≤ 0 t 6 ≥ 1 cases :

# # # # # cases

t f u x t u - h * u 0 t int eval :

Convolving Integral components

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

System output [RC response]

x f x x 2 1 sys

t h # cases :

as you type [,] for the 2nd place holder, you get the construction to be filled in.

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

Optimiz: NONE a b t pulse 1 s / a s * - exp b s * - exp - (* t 0 > assume s t invlaplace maple :

a b t pulse a s * - exp b s * - exp - s / t 0 > (assume s t invlaplace maple

a b x f x a - sign x b - sign - 2 / : convolving function ≡

α β x g x α - sign x β - sign - 2 / : convolved function ≡

a 1 - : b 1 : 21 line

https://en.wikipedia.org/wiki/Convolution

slide 1.5 - :

α 0 slide + : β b a - (slide + : 21 line

t g 0 t α ≤ 0 t β ≥ 1 cases :

sliding window 
of integration α β 21 mat 1.5 - 0.5 21 mat

t f 0 t a ≤ 0 t b ≥ 1 cases :

t Int u f u g * u a t int eval :

t Σ t Int t 0 ≤ t Int - 2 + t β ≤ 0 cases :

Classical Triangular [pulses]

x Σ a 0 a 1 b 1 b 0 4 2 mat α 0 α 1 β 1 β 0 4 2 mat 3 1 sys

t Int u f t u - g * u 0 t int eval :

x Int a 0 a 1 b 1 b 0 4 2 mat α 0 α 1 β 1 β 0 4 2 mat 3 1 sys

t Int u f u t - g * u 0 t int eval :

x Int a 0 a 1 b 1 b 0 4 2 mat α 0 α 1 β 1 β 0 4 2 mat 3 1 sys