A radar system for detecting the surroundings of a motor vehicle, having - transmitting means for emitting transmission signals with one or more transmitting antennas, - receiving means for receiving transmission signals reflected off objects with one or more receiving antennas, and - signal processing means for processing the received signals, wherein - the frequency of the emitted transmitting power is modulated in such a way that it comprises a series of K linear ramps of the same gradient, - the received signals of multiple combinations of transmitting and receiving antennas are acquired by mixing with an oscillator signal and sampling ∘ in parallel for each frequency ramp, and/or ∘ serially over in each case P consecutive frequency ramps which form a group of frequency ramps, that is to say K/P-times, - results of a first spectral analysis are calculated in each case via the sampled values for each frequency ramp and for respective combinations of transmitting and receiving antennas in the digital signal processing means, - over the K frequency ramps, the results of said first spectral analysis are stored for at least a part of their frequency supporting points which represent so-called distance gates, - thereafter, a second spectral analysis is calculated by way of the results of the first spectral analysis stored for each distance gate and for each combination of transmitting and receiving antennas over the frequency ramps and/or groups of frequency ramps, - and results of the second spectral analysis are further processed over the various combinations of transmitting and receiving antennas, in particular by means of a digital beam formation via a third spectral analysis, characterized in that - the results of the first spectral analysis are stored in a compressed form in order to reduce the storage space, wherein - the results of the first spectral analysis of multiple combinations of transmitting and receiving antennas experience the same scaling for each distance gate and frequency ramp and/or group of frequency ramps, and said scaling is stored at least once, - the thus scaled results of the first spectral analysis are quantized to a lower bit number than the bit number used in the signal processing means, in particular during the spectral analyses, and are stored with said reduced bit number, and - said compressed results of the first spectral analysis are decompressed prior to the calculation of the second spectral analysis. - transmitting means for emitting transmission signals with one or more transmitting antennas, - receiving means for receiving transmission signals reflected off objects with one or more receiving antennas, and - signal processing means for processing the received signals, - the frequency of the emitted transmitting power is modulated in such a way that it comprises a series of K linear ramps of the same gradient, - the received signals of multiple combinations of transmitting and receiving antennas are acquired by mixing with an oscillator signal and sampling ∘ in parallel for each frequency ramp, and/or ∘ serially over in each case P consecutive frequency ramps which form a group of frequency ramps, that is to say K/P-times, ∘ in parallel for each frequency ramp, and/or ∘ serially over in each case P consecutive frequency ramps which form a group of frequency ramps, that is to say K/P-times, - results of a first spectral analysis are calculated in each case via the sampled values for each frequency ramp and for respective combinations of transmitting and receiving antennas in the digital signal processing means, - over the K frequency ramps, the results of said first spectral analysis are stored for at least a part of their frequency supporting points which represent so-called distance gates, - thereafter, a second spectral analysis is calculated by way of the results of the first spectral analysis stored for each distance gate and for each combination of transmitting and receiving antennas over the frequency ramps and/or groups of frequency ramps, - and results of the second spectral analysis are further processed over the various combinations of transmitting and receiving antennas, in particular by means of a digital beam formation via a third spectral analysis, - the results of the first spectral analysis are stored in a compressed form in order to reduce the storage space, wherein - the results of the first spectral analysis of multiple combinations of transmitting and receiving antennas experience the same scaling for each distance gate and frequency ramp and/or group of frequency ramps, and said scaling is stored at least once, - the thus scaled results of the first spectral analysis are quantized to a lower bit number than the bit number used in the signal processing means, in particular during the spectral analyses, and are stored with said reduced bit number, and - said compressed results of the first spectral analysis are decompressed prior to the calculation of the second spectral analysis.