### Introduction

Teledyne LeCroy's Digital Filter Package (DFP2) option allows users to select any of 7 standard types as well as define a custom filter and apply the filter to measured data. A range of pass band limits and Transition (roll off) widths can be specified for the filters which are implemented as digital finite impulse response (FIR) filters. The range of band edge frequencies is a function of the scopes effective sampling rate. Using the available math traces it is possible to implement multi-stage, multi-rate filters to extend the range of the DFP package filter limits.

Consider the application shown in Figure 1.

This type of signal is common in switching power supply measurements. The measured waveform contains a 63 kHz pulse width modulated signal riding on top of a 60 Hz sinusoidal waveform. Removal of the 60 Hz component requires a high pass filter with a pass band edge above 60 Hz. This type of filter can be implemented in the DFP2 filter option. Using DFP2 at a 10 MS/s sample rate will require filters with a very large number of taps. In order to reduce the required filter size to a more useable value, the effective sampling rate must be reduced. There are two ways to accomplish this. The first is to reduce the length of the acquisition memory. The second is to decimate the data using the sparse math function. Reducing the sampling rate increases the possibility of aliasing the data, especially using harmonic rich signals like this one. To limit the possibility of aliasing, the data can be sampled at a high rate to prevent aliasing then low pass filtered, using a digital filter, before decimation. This combination of filtering and decimation prior to performing another filtering operation on the data is called 'multi-stage, multi-rate' digital filtering. It offers the ability to reduce the effective sampling rate with a minimum risk of aliasing, thus extending the useable range of the DFP2 option.

The multi-stage, multi-rate filter implementation of this example is shown in Figure 2. The upper trace is the acquired waveform sampled at 10 MS/s. The goal is to reduce the sample rate by 10:1. This is accomplished by first low pass filtering the acquired data with a bandwidth of less than 1/2 the desired effective sampling rate of 1MS/s.

Math trace F2 is signal after being low pass filtered with a bandwidth of 500 kHz. Math Trace F3 applies the sparse function. This math function is used to decimate waveform data. The decimation ratio of 10:1 is set by the Math dialog box entry "Sparsing Factor ". This can be accessed via the Math Setup menu. The resultant decimation is 10:1 and the effective sample rate is 1MS/s.

Math trace F4 is the set up for the high pass filter. The cutoff frequency is 200 Hz with a transition zone width of 50 Hz. Note that the 60 Hz component has been reduced significantly by the filtering process.

A comparison of the input and output frequency spectra in Figure 3 reveals the significant reduction in the 60 Hz component of 40 dB as shown in the right hand zoom trace comparison Note that the high pass filtering operation does not affect the spectral components above 300 Hz.

Multi-stage, multi-rate filtering provides a technique for increasing the useable range of the digital filters in the DFP option package. It allows more effective use of the filtering package.