Noise attenuation properties of non-recursive FIR filters
J M De Freitas · Measurement Science and Technology · 2003
The noise filtering properties of digital filters are studied using the classic analogue Butterworth model. We derive simple expressions for the noise power output associated with low-pass, band-pass, high-pass, band-reject and types III and IV M th-order digital differentiating filters in terms of their frequency characteristics. These results allow the user to quantify the extent of noise reduction, and hence the improvement in signal-to-noise ratio inherent in the application of a digital filter, or combinations of such filters, as a function of its bandwidth. In one application involving over-sampled fringes obtained from a white light Fabry–Perot interferometer, we show that it is possible to obtain 85% reduction in noise from a low-pass filter with normalized cut-off frequency of 0.15. In preliminary applications involving differentiators we observed significant noise reduction when applied to the said fringes.