Ideal Low-Pass Filter Output?
From the description I'll take you have a filter with 3 coefficients. (and the formulae are missing the symbol i). With a sample rate of 100 Hz you would require a filter of length 33 to make it cover the complete wave form of one cycle of 3 Hz signal. Just looking one tenth of a waveform a filter would have to do magic to attenuate (just) a 3Hz signal but leave 1Hz signals intact.

If you'll have octave or matlab, you might want to see the frequency response of your filter:

 `a=exp(i*pi*2/100);freqz([1,a*conj(a)],1)`


Here the 3dB cutoff is approximately at Fs/4 (one quarter of the sampling frequenzy).