Existing spectrum sensing systems are commonly designed based on the famous Nyquist theorem. With the rapid development of radio frequency technology, the corresponding sampling frequency is so high that many problems may be brought about, such as the increasing hardware complexity, large volume of measurements and difficulties to meet the real time requirement etc. To tackle these problems caused by high sampling frequency, a novel scheme, adaptive modulated wideband converter, is proposed. By exploiting the band width of the narrow bands, the total sampling frequency is proved to be as low as four times of the sum of the narrow bands. There is a trade-off between the sampling complexity and the total sampling frequency for different choices of the repeating frequency of the random function. Sufficient conditions are derived to guarantee exact signal recovery from sub-Nyquist measurements. Conditions of full row rank of the equivalent unknown matrix are also explored to guarantee that the multiple signal classification can be adopted to implement the signal reconstruction. The simulations verify the analysis. This novel scheme can be used to implement front-end spectrum analysis for absorbing materials and detect the active channels in cognitive radio.