System for digital sweep type spectrum analysis with up/down frequency provides measurements of frequency spectrum of complex analog baseband input signal. The signal is quantized into three levels with fs based on the bandwidth of the input signal. Four multiplexers, a first block of registers and a block of adders perform operations equivalent to complex multiplication of the quadrature components. Two complex signals with up and down shifted spectrum are produced by the adders. The quadrature components are inputted to the accumulators with reset, which act as low-pass filters and accumulate several samples at a constant frequency fLO of the local oscillator. Levels of two accumulated complex samples are estimates of input signal spectrum in two frequency points +fLO and −fLO. A sweep controller changes a frequency of the local oscillator from zero up to fs/2. Estimates of the input signal spectrum are generated sequentially in range −fs/2 to +fs/2.