A signal processing system for a vibrating structure angular rate sensor having a vibrating structure, a primary drive transducer for causing the vibrating structure angular rate sensor to oscillate at a resonant frequency, and a primary pick off transducer for detecting oscillation of the vibrating structure angular rate sensor at the resonant frequency; wherein the signal processing system comprises: a digital signal processing system configured to set a drive signal frequency for the primary drive transducer; a voltage controlled oscillator configured to receive an input indicative of the resonant frequency and to generate a first periodic signal at a first multiple of the resonant frequency; a first phase locked loop, configured to receive the first periodic signal, and to generate a second periodic signal at a second multiple of the resonant frequency, wherein the second multiple is greater than the first multiple; an analog-to-digital converter configured to sample a primary pick off signal from the primary pick off transducer at a first rate set by the first periodic signal and to generate a primary pick off data input to a digital signal processing system, wherein the second periodic signal is used as a clock signal by the ADC when generating the primary pick off data input to the digital signal processing system; and a digital-to-analog converter configured to receive the drive signal frequency from the digital signal processing system at a second rate set by the second periodic signal and to generate a drive signal waveform to be applied to the primary drive transducer, wherein the drive signal waveform is generated at a first rate set by the first periodic signal and the second periodic signal is used as a clock signal by the DAC when generating the drive signal waveform. a digital signal processing system configured to set a drive signal frequency for the primary drive transducer; a voltage controlled oscillator configured to receive an input indicative of the resonant frequency and to generate a first periodic signal at a first multiple of the resonant frequency; a first phase locked loop, configured to receive the first periodic signal, and to generate a second periodic signal at a second multiple of the resonant frequency, wherein the second multiple is greater than the first multiple; an analog-to-digital converter configured to sample a primary pick off signal from the primary pick off transducer at a first rate set by the first periodic signal and to generate a primary pick off data input to a digital signal processing system, wherein the second periodic signal is used as a clock signal by the ADC when generating the primary pick off data input to the digital signal processing system; and a digital-to-analog converter configured to receive the drive signal frequency from the digital signal processing system at a second rate set by the second periodic signal and to generate a drive signal waveform to be applied to the primary drive transducer, wherein the drive signal waveform is generated at a first rate set by the first periodic signal and the second periodic signal is used as a clock signal by the DAC when generating the drive signal waveform.