Question

An analog signal has a constant magnitude spectrum upto 4KHz. After 4KHz, the spectrum attenuates at 15dB/octave. Sketch the spectrum.

a. Case 1:The signal goes through a system with an ideal anti aliasing LP filter, with sampling rate at 8KHz. Sketch the spectrum of the signal after passing it through such a filter. Use kHz at the unit of x axis. Note the periodicity and conjugate symmetry of the spectrum.

b. Case 2: There is no anti aliasing filter, so we decide to sample at 12KHz. Sketch the spectrum and mark the amount of aliasing by shading the area. Use kHz at the unit of x axis. Note the periodicity and conjugate symmetry of the spectrum.

c. In case 2, we wish to suppress the aliased components (between 4k and 6k) by more than 50 dB. What should the maximum attenuation level at the edge of stop band be for such a filter?

Answer 1

* ideal antialiasing filter will have the cut off frequency of f_{s /2.}

_* There is no aliasing for the case(a).

* There is aliasing for the case (b).

* What matters in the case of aliasing is the amount of aliasing at a frequency w.r.t to the original component at the same frequency.

* Here we will see that aliased component at 4kHz is 14 dB below the original component, but at 6kHz it is almost same as original component. So we need to strongly attenuate the component at 6kHz.