1. You wish to construct   an ideal lowpass filter with

Because the system you build is causal, you actually have

(a)  Find  H(f), and compare   it to the system  function  of the ideal  filter.

(b)   Find the output when the input  is

(c)   Find the error  (difference   between  output  and input)  for the input of part  (b).


2. Compare the step response of an RC circuit (output taken across the capacitor) with that of an ideal lowpass filter. Find the value of tift for the ideal filter (in terms of R and  C), which  mini- mizes  the integrated  square  error  between  the two step responses.

3. Design a Butterworth lowpass filter with a 3-dB cutoff at 500 Hz. The roll-off of the filter must be such that the amplitude response is attenuated by at least  50 dB  at a frequency   of 3 kHz.

4.   Design  a spectrum   analyzer   that  can  display   the  magnitude   of  the  Fourier  transform   of the function