Question

A signal has the functional form f(t) = 5sin(40πt) and is sampled at a rate of 30 samples per second. What false alias frequency would you expect in the discrete data? What sampling rate would avoid aliasing this signal?

Answer 1

; from this equation we can find the input signal frequency(f_in):

or, ()

hence, f_in= 20 Hz.

goven sample rate, f_s= 30 Hz

the fromula for alias frequency: ; where N= any integer greater or equal zero.

for alias frequency, we have to bring the term Nf_s as closer to f_in.

so, if we choose N=0; Nfs= 0 Hz; if N=1; Nf_s= 30Hz which is more closer to f_in than N=0 term.

hence, false alias frequency,(Ans).

the maximum frequency of this signal is f_in=20Hz, hence the sampling rate would be just double of input frequency, to avoid aliasing this signal.

hence sampling rate= (2*20)= 40 samples /second.(Ans).