A smoothing apparatus comprising: a log spectral envelope generating unit configured to obtain a log spectral envelope sequence L 0 , L 1 , ..., L N-1 , which is an integer value sequence corresponding to binary logarithms of respective sample values of a spectral envelope sequence corresponding to a time series signal in a predetermined time segment and is an integer value sequence whose total sum is 0, where the time series signal is any one of an audio signal, a video signal, a seismic wave signal, or a biological signal; and a smoothing unit configured to obtain a smoothed spectral sequence ~X 0 , ∼X 1 , ..., ∼X N-1 by: with respect to a quantized spectral sequence ^X 0 , ^X 1 , ..., ^X N-1 obtained by quantization of respective sample values of a frequency domain spectral sequence for the time series signal, for ^X k , k is sample number, where k∈{0, ..., N-1} with L k corresponding to ^X k being a positive value, adopting ^X k with L k digits from its least significant digit in binary removed as a smoothed spectral value ∼X k ; for ^X k with L k corresponding to ^X k being a negative value, adopting ^X k with -L k digits added to its least significant digit in binary in accordance with a predefined rule as a smoothed spectral value ∼X k ; and when L k corresponding to ^X k is 0, adopting ^X k as a smoothed spectral value ~X k , wherein the predefined rule is a rule defined based on an order of sample numbers and an order of digit numbers such that removed digits become digits to be added without excess or deficiency. a log spectral envelope generating unit configured to obtain a log spectral envelope sequence L 0 , L 1 , ..., L N-1 , which is an integer value sequence corresponding to binary logarithms of respective sample values of a spectral envelope sequence corresponding to a time series signal in a predetermined time segment and is an integer value sequence whose total sum is 0, where the time series signal is any one of an audio signal, a video signal, a seismic wave signal, or a biological signal; and a smoothing unit configured to obtain a smoothed spectral sequence ~X 0 , ∼X 1 , ..., ∼X N-1 by: with respect to a quantized spectral sequence ^X 0 , ^X 1 , ..., ^X N-1 obtained by quantization of respective sample values of a frequency domain spectral sequence for the time series signal, for ^X k , k is sample number, where k∈{0, ..., N-1} with L k corresponding to ^X k being a positive value, adopting ^X k with L k digits from its least significant digit in binary removed as a smoothed spectral value ∼X k ; for ^X k with L k corresponding to ^X k being a negative value, adopting ^X k with -L k digits added to its least significant digit in binary in accordance with a predefined rule as a smoothed spectral value ∼X k ; and when L k corresponding to ^X k is 0, adopting ^X k as a smoothed spectral value ~X k , wherein with respect to a quantized spectral sequence ^X 0 , ^X 1 , ..., ^X N-1 obtained by quantization of respective sample values of a frequency domain spectral sequence for the time series signal, for ^X k , k is sample number, where k∈{0, ..., N-1} with L k corresponding to ^X k being a positive value, adopting ^X k with L k digits from its least significant digit in binary removed as a smoothed spectral value ∼X k ; for ^X k with L k corresponding to ^X k being a negative value, adopting ^X k with -L k digits added to its least significant digit in binary in accordance with a predefined rule as a smoothed spectral value ∼X k ; and when L k corresponding to ^X k is 0, adopting ^X k as a smoothed spectral value ~X k , wherein the predefined rule is a rule defined based on an order of sample numbers and an order of digit numbers such that removed digits become digits to be added without excess or deficiency. <EOS>