Before revision: Begin by defining a continuous-time signal from the sample values, as above but using delta functions instead of rect functions: The scaling by T , which arises naturally by time-scaling the delta function, has the result that the mean value of xs(t) is equal to the mean value of the samples, so that the lowpass filter needed will have a DC gain of 1.
After revision: Begin by defining a continuous-time signal from the sample values, as above but using delta functions instead of rect functions: he scaling by T , which arises naturally by time-scaling the delta function, has the result that the mean value of xs(t) is equal to the mean value of the samples, so that the lowpass filter needed will have a DC gain of 1.