Question

The signal output from a certain process in an industry is described by the following equation

h (t) = 5 cos 2π1000 t + 7 cos 2π 2000 t + 2 cos 2π 3000 t.

If the above signal h(t) is sampled at the rate of 5000 samples/second, comment on the output obtained from the reconstruction process.

Answer 1

Ans)

Given

the frequencies in the above signal is

given sampling frequency of

as we can see that according to sampling theorem sampling frequency should be twice than signal frequency ,in above case for 3rd frequency it is less than that hence aliasing occurs which we prove later

the sampled signal is

using

Now from above we can see that third frequency term after sampling is same as second frequency term i.e due to aliasing

simplifying further

Now converting back i.e   reconstruction process

output obtained

from the above output we can say that due to aliasing third frequency term (3000 Hz) has now become 2000 Hz signal