One problem with causal filters is that the response of the filter always lags the excitation. This problem cannot be eliminated if the filtering is done in real time but if the signal is recorded for later “off-line” filtering one simple way of eliminating the lag effect is to filter the signal, record the response and then filter that recorded response with the same filter but playing the signal back through the system backward. Suppose the filter is a single-pole filter with a frequency response of the form 
where 
is the cutoff frequency (half-power frequency) of the filter.
(a) What is the effective frequency response of the entire process of filtering the signal forward, then backward?
(b) What is the effective impulse response?
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