(Currently Amended) A wavelength dispersion compensation apparatus comprising: a block division unit configured to segment an electric digital received signal obtained from a received optical signal into blocks of a certain length with an overlap of a length determined in advance with an adjacent block and output the blocks; a Fourier transform unit configured to perform Fourier transformation for each of the blocks output by the block division unit; a coefficient multiplication unit (33, 33a) configured to store a plurality of the blocks converted by the Fourier transform unit consecutively in time series, and further configured to apply different coefficients determined respectively based on all of: ∘ a wavelength dispersion compensation amount according to one of the frequency positions which are positions in a frequency domain of frequency component values contained in the plurality of the blocks output by the Fourier transform unit, ∘ a delay compensation amount, according to one of the frequency positions and one of the time positions which are positions in a processing order of the plurality of the blocks output by the Fourier transform unit at each unit time, ∘ an attenuation amount of a band-pass filter with a bandwidth centered at the frequency position of a frequency component value included in the plurality of the blocks that are stored, and generate one block with the coefficients applied, the one block with the coefficients applied being obtained by adding up frequency component values with the coefficient applied for each of the frequency positions; an inverse Fourier transform unit configured to perform inverse Fourier transformation on the one block with the coefficients applied that is generated by the coefficient multiplication unit; and an overlap cut unit configured to remove a part of the overlap from the one block with the coefficients applied that is converted by the inverse Fourier transform unit. a block division unit configured to segment an electric digital received signal obtained from a received optical signal into blocks of a certain length with an overlap of a length determined in advance with an adjacent block and output the blocks; a Fourier transform unit configured to perform Fourier transformation for each of the blocks output by the block division unit; a coefficient multiplication unit (33, 33a) configured to store a plurality of the blocks converted by the Fourier transform unit consecutively in time series, and further configured to apply different coefficients determined respectively based on all of: ∘ a wavelength dispersion compensation amount according to one of the frequency positions ∘ a wavelength dispersion compensation amount according to one of the frequency positions which are positions in a frequency domain of frequency component values contained in the plurality of the blocks output by the Fourier transform unit, ∘ a delay compensation amount, according to one of the frequency positions and one of the time positions which are positions in a processing order of the plurality of the blocks output by the Fourier transform unit at each unit time, ∘ an attenuation amount of a band-pass filter with a bandwidth centered at the frequency position of a frequency component value included in the plurality of the blocks that are stored, and generate one block with the coefficients applied, the one block with the coefficients applied being obtained by adding up frequency component values with the coefficient applied for each of the frequency positions; ∘ a delay compensation amount, according to one of the frequency positions and one of the time positions which are positions in a processing order of the plurality of the blocks output by the Fourier transform unit at each unit time, ∘ an attenuation amount of a band-pass filter with a bandwidth centered at the frequency position of a frequency component value included in the plurality of the blocks that are stored, and generate one block with the coefficients applied, the one block with the coefficients applied being obtained by adding up frequency component values with the coefficient applied for each of the frequency positions; an inverse Fourier transform unit configured to perform inverse Fourier transformation on the one block with the coefficients applied that is generated by the coefficient multiplication unit; and an overlap cut unit configured to remove a part of the overlap from the one block with the coefficients applied that is converted by the inverse Fourier transform unit.