The operation of a longitudinal multibunch damping system using digital signal processing (DSP) techniques is shown via measurements from the Lawrence Berkeley Laboratory (LBL) Advanced Light Source (ALS). The feedback system (developed for use by PEP-II, ALS, and DAɸNE) uses a parallel array of signal processors to implement a bunch-by-bunch feedback system for sampling rates up to 500 MHz. The programmable DSP system allows feedback control as well as accelerator diagnostics. A diagnostic technique is illustrated which uses the DSP system to excite and then damp the beam. The resulting 12-ms time domain transient is Fourier analyzed to provide the simultaneous measurement of growth rates and damping rates of all unstable coupled-bunch beam modes.