Is the result of convolution of a heaviside function with a sinc low pass with cut off at fc, say 25khz, band limited ((sin(2 x Pi x fc x i))/(Pi x i))?
I've been working it out in frequency domain (taking ft of the signals and multiplying them). The ft of the sinc is a rectangular function with cut off at +/-fc. If I pass a continuous 5khz sine, I get a 5khz sine at output, if I pass a continuous 30khz sine, I get a 0 at output, and if I pass an impulse I get a band limited impulse with components upto 25khz at my output. All these results are band limited.
What about heaviside function? I am unable to get the result to look Bandlimited. The Fourier transform of heaviside step function looks very complicated. What am I doing wrong.
I am unable to embed what I've tried but I am linking the equivalent:
- https://math.stackexchange.com/questions/736749/fourier-transform-of-sinc-function . This results in a rectangular function from -fc to +fc.
- http://www.thefouriertransform.com/pairs/sinusoids.php . The result is energy concentrated at frequency of the sinusoid. If this frequency is inside the rectangular function, after multiplication, I Will get the result as same as before multiplication. If this frequency is outside the rectangular function, I will get 0 as result.
- I am unable to come at a proper derivation for the heaviside function. It feels too complicated. Looking at resources. http://www.theochem.ru.nl/~pwormer/Knowino/knowino.org/wiki/Heaviside_step_function.html