Convolution of discrete and continuous time signals

[swuster]

Not a specific question per se but...

Is it possible to convolve a discrete-time signal with a continuous-time one?

if you have x(n) and y(t) can you calculate the convolution of x and y (say, by taking y(t) for t in the set of integers or by treating each x(n) as its value multiplied by the delta function) or is there something inherently wrong about this?

 

[Petr Mugver]

A discrete-time signal x(nT), where T is the sampling period, is a special case of a continuous-time signal, as you can write

x(t)=\sum_{n}x(nT)\delta(t-nT)

so if y(t) is a continuous-time signal, the convolution is

x(t)\otimes y(t)=\sum_{n}x(nT)\delta(t-nT)\otimes y(t)=\sum_{n}x(nT)y(t-nT)

(you have to assume this converges).