A signal processing device comprising: an amplifier configured to amplify a sensor signal supplied from a sensor that is configured to receive a wireless signal reflected by an object; an A/D converter configured to convert the sensor signal amplified by the amplifier into a digital sensor signal and to output the digital signal; and a signal processor configured to convert the sensor signal output from the A/D converter into a frequency-domain sensor signal by Discrete Cosine Transform processing, and operate as an adaptive filter for removing a background signal from the sensor signal in the frequency domain, wherein the signal processor comprises: a DCT converter configured to convert the sensor signal supplied from the A/D converter into a frequency-domain sensor signal by the Discrete Cosine Transform processing; and a filtering unit configured to adaptively-estimate the background signal based on the frequency-domain sensor signal from the DCT converter and a reference signal which is white noise, and to remove the background signal from the frequency-domain sensor signal from the DCT converter; wherein the filtering unit comprises: a filter configured to remove the background signal from the sensor signal in the frequency domain based on a variable filter coefficient to produce an output signal; a subtracter configured to calculate difference between the output signal from the filter and the reference signal to obtain an error signal; and an adaptive processor configured to estimate the background signal based on the error signal, and to update the filter coefficient according to the estimated background signal, wherein the signal processor has selectively switchable first and second modes, the signal processor is configured, in the first mode, to estimate the background signal contained in the sensor signal based on the error signal, and to update the filter coefficient according to the estimated background signal, and in the second mode, to stop the updating processing of the filter coefficient, and to remove the background signal from the sensor signal in the frequency domain, characterized in that the signal processor is configured, when determining that the error signal has converged while operating in the first mode, to switch from the first mode to the second mode. an amplifier configured to amplify a sensor signal supplied from a sensor that is configured to receive a wireless signal reflected by an object; an A/D converter configured to convert the sensor signal amplified by the amplifier into a digital sensor signal and to output the digital signal; and a signal processor configured to convert the sensor signal output from the A/D converter into a frequency-domain sensor signal by Discrete Cosine Transform processing, and operate as an adaptive filter for removing a background signal from the sensor signal in the frequency domain, a DCT converter configured to convert the sensor signal supplied from the A/D converter into a frequency-domain sensor signal by the Discrete Cosine Transform processing; and a filtering unit configured to adaptively-estimate the background signal based on the frequency-domain sensor signal from the DCT converter and a reference signal which is white noise, and to remove the background signal from the frequency-domain sensor signal from the DCT converter; a filter configured to remove the background signal from the sensor signal in the frequency domain based on a variable filter coefficient to produce an output signal; a subtracter configured to calculate difference between the output signal from the filter and the reference signal to obtain an error signal; and an adaptive processor configured to estimate the background signal based on the error signal, and to update the filter coefficient according to the estimated background signal, wherein the signal processor has selectively switchable first and second modes, the signal processor is configured, in the first mode, to estimate the background signal contained in the sensor signal based on the error signal, and to update the filter coefficient according to the estimated background signal, and in the second mode, to stop the updating processing of the filter coefficient, and to remove the background signal from the sensor signal in the frequency domain, characterized in that the signal processor is configured, when determining that the error signal has converged while operating in the first mode, to switch from the first mode to the second mode.