Convolve exponential with rect

Hi,

I have a pretty trivial issue: I want to convolve a shifted rect
function with an exponential:

h(t) = 2pi/K e^(-2pi/K t)
p(t) = rect(t-1/2)

g(t) = (h*p)(t)

When I do the convolution with a discrete-time approximation numerically
in MATLAB (either conv or cconv) I get the blue line:

http://snag.gy/ZOhp5.jpg

When do the convolution analytically, I get

g(t) = e^(-2pi/K (t-1)) - e^(-2pi/K t)

which is the green line in the plot. Of course, discrete and continuous
convolutions are different but I would still expect a rough "match" when
I do fine time steps (in my case delta t = 1/1000).
I tried to add much zero padding, increase the time resolution etc. but
the result stays the same.

I "trust" the continuous result more but this shows the same result as
the discrete result:

http://lpsa.swarthmore.edu/Convolution/Convolution3.html#A_Rectangular_Pulse_and_an_Exponential

Did I do a trivial mistake when executing for continuous convolution?
Where does the difference come from?


Thanks
Peter

PS: This is a simple example, I observe the same thing for example for
higher order systems

On Monday, August 18, 2014 4:29:00 PM UTC-4, Peter Mairhofer wrote:
> Hi,
> 
> 
> 
> I have a pretty trivial issue: I want to convolve a shifted rect
> 
> function with an exponential:
> 
> 
> 
> h(t) = 2pi/K e^(-2pi/K t)
> 
> p(t) = rect(t-1/2)
> 
> 
> 
> g(t) = (h*p)(t)
> 
> 
> 
> When I do the convolution with a discrete-time approximation numerically
> 
> in MATLAB (either conv or cconv) I get the blue line:
> 
> 
> 
> http://snag.gy/ZOhp5.jpg
> 
> 
> 
> When do the convolution analytically, I get
> 
> 
> 
> g(t) = e^(-2pi/K (t-1)) - e^(-2pi/K t)
> 
> 
> 
> which is the green line in the plot. Of course, discrete and continuous
> 
> convolutions are different but I would still expect a rough "match" when
> 
> I do fine time steps (in my case delta t = 1/1000).
> 
> I tried to add much zero padding, increase the time resolution etc. but
> 
> the result stays the same.
> 
> 
> 
> I "trust" the continuous result more but this shows the same result as
> 
> the discrete result:
> 
> 
> 
> http://lpsa.swarthmore.edu/Convolution/Convolution3.html#A_Rectangular_Pulse_and_an_Exponential
> 
> 
> 
> Did I do a trivial mistake when executing for continuous convolution?
> 
> Where does the difference come from?
> 
> 
> 
> 
> 
> Thanks
> 
> Peter
> 
> 
> 
> PS: This is a simple example, I observe the same thing for example for
> 
> higher order systems

Clearly your continuous convolution is incorrect. Think about what you expect the correct continuous plot to be like near time 0; it isn't making a jump like that. What values of time is your g(t) supposed to be valid for?  I would expect an equation for time up to 0; another for time (0,1]; and another for time >1. If you scan and post your continuous convolution calculations, I think your mistake will be easily found.

Dirk

On 2014-08-18 15:12, bellda2005@gmail.com wrote:
> [...]
> Clearly your continuous convolution is incorrect. [...]
> I would expect an equation for time up to
> 0; another for time (0,1]; and another for time >1.

Thanks. I know I missed something trivial: H(t)

Peter