from
Step response
by Abdelmonem Dekhil
Calculation of the response of strictly proper SISO systems by the convolution integral
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| response.m |
f u n c t i o n y = r e s p o n s e ( n u m , d e n , t , u )
% P r o g r a m f o r c a l c u l a t i o n o f t h e r e s p o n s e o f s t r i c t l y p r o p e r S I S O s y s t e m s
% t o a r b i t r a r y i n p u t b y t h e c o n v o l u t i o n i n t e g r a l .
% n u m = n u m e r a t o r p o l y n o m i a l c o e f f i c i e n t s o f t r a n s f e r f u n c t i o n
% d e n = d e n o m i n a t o r p o l y n o m i a l c o e f f i c i e n t s o f t r a n s f e r f u n c t i o n
% ( C o e f f i c i e n t s o f ' n u m ' a n d ' d e n ' a r e s p e c i f i e d a s a r o w v e c t o r , i n
% d e c r e a s i n g p o w e r s o f ' s ' )
% t = r o w v e c t o r o f t i m e p o i n t s ( s p e c i f i e d b y t h e u s e r )
% u = v e c t o r o f i n p u t v a l u e s a t t h e t i m e p o i n t s c o n t a i n e d i n t .
% y = c a l c u l a t e d r e s p o n s e
% C a l c u l a t e t h e t i m e - s t e p : -
d t = t ( 2 ) - t ( l ) ;
m = s i z e ( t , 2 )
t f = t ( m ) ;
% C a l c u l a t e t h e c o n v o l u t i o n i n t e g r a l : -
y = z e r o s ( s i z e ( t ) ) ;
G = y ;
[ g , T ] = i m p r e s p ( n u m , d e n , t ( 1 ) , d t , t f ) ;
f o r i = 1 : m
y = y + d t * u ( i ) * [ G ( 1 : i - 1 ) g ( 1 : m - i + 1 ) ] ;
e n d
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