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.

Suggest any two remedial measures to avoid any problems that occurred during the

reconstruction process.

Answer 1

The very first measure to avoid any problem during signal reconstruction is proper sampling .

And for proper sampling ,the sampling frequency of signal must satisfy the Nyquist condition for signal reconstruction that is

  

  

where Fs is sampling frequency of signal and f_{max is the maximum frequency of the bandlimited  signal}

_{and Nyquist Frequency = 2* fmax}

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

here f1=1000 Hz ,f2=2000 Hz and f3=3000 Hz .

fmax= max(f1,f2,f3)

fmax= 3000 Hz

So

   Hz

Generally for proper sampling the Fs is kept 10 % greater than Nyquist Frequency

which will come round 6000 + 6000 *0.1

Fs =6600 Hz

2.

The second most important thing is to make any signal as band limited signal and for this anti-aliasing filter is used .

  The anti aliasing operation must be performed before the signal is sampled.

3.

There may one more problem that can occur during reconstruction of signal that is over sampling .

This problem occurs when you sample a signal much much higher than Nyquist Rate of sampling like

10 times the Nyquist Rate .

Then it becomes difficult to the filter that is used for reconstruction of the signal to properly analyse the signal .