Problem1: 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?