Please guys Assume that you have 2 seconds T0 of a real sign

Assume that you have 2 seconds (=T_0) of a real signal x(t)and you sample it, with f_s = 1 KHz. Let X(k) denote the DPT of x(n). Determine the number of samples (=N). Find the maximum frequency (f_max) that x(t) can have .so that there will be no aliasing effect due to sampling? Assuming that N found in part-a is the DFT length, what is the frequency resolution between two adjacent DFT values in digital (delta Ohm) and in analog (delta f)? What analog (f) and digital (ohm) frequencies do the DFT component X (130)correspond to? Given, X (130) = -1 - j2. Determine the value of m for which X(m) is related (o X (26000). Find (he value of the corresponding X(m). Find Record Length (T_n) if the desired frequency resolution (delta f) is 0.1Hz. How many more samples or zeroes are needed to achieve deltaf = 0.1 Hz.

Solution

(a) Ts= sampling time=1/fs= 1 micro s

N= number of sample= To/Ts= 2*10^6

(b) fmax= fs/2=500 hz

(C)fd= frequency resolution in digital

fd=2/N=*10^-6

Fa= frequency resolution in analog

Fa=fs/N=1/2= 0.5