The construction and characteristics of the cylindrical ion pulse ionization chamber (CIPIC) with a working volume of 3.2 L are described. The chamber is intended to register alpha-particles from the $^{222}$Rn and its daughters decays in the filled air sample. The detector is less sensitive to electromagnetic pick-ups and mechanical noises. The digital pulse processing method is proposed to improve the energy resolution of the ion pulse ionization chamber. An energy resolution of 1.6% has been achieved for the 5.49 MeV alpha-line. The dependence of the energy resolution on high voltage and working media pressure has been investigated and the results are presented.