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