According to an embodiment, a signal processing apparatus includes an estimation unit and an updating unit. The estimation unit is configured to estimate an auxiliary variable of a target section including first and second sections of input signals by using an approximating auxiliary function for approximating an auxiliary function having an auxiliary variable as an argument. The auxiliary function is determined according to an objective function that outputs a function value that is smaller as a statistical independence of separated signals into which input signals in time-series are separated by a demixing matrix is higher. The estimation unit is configured to estimate a value of the auxiliary variable of the target section based on the estimated auxiliary variable. The updating unit is configured to update the demixing matrix such that a function value of the approximating auxiliary function is minimized.