We describe a data acquisition system based on two 10 MHz A/D-converters, a SHARC Digital Signal Processor (DSP), and a digital synthesizer used for triggering the A/D-converters. The temporal macrostructure of the data acquisition can be determined by external triggers or by timer interrupts from the DSP. In this way up to two million samples can be stored in DSP external memory. The samples are analyzed by directly fast Fourier transforming blocks of samples. In another mode we use software-based downmixing and filtering techniques to increase the resolution and zoom in on a small frequency band. Spectra of up to 5 MHz can be manipulated and displayed as waterfall plots or spectral maps on the host computer directly. Moreover, signals of up to 70 MHz can be analyzed by undersampling techniques. We use this system to analyze Schottky spectra from electron-cooled ion beams in CELSIUS and report drag rate measurements and observations of instabilities.