# Calculating the Average Roll-off of an Anti-Aliasing Filter

Updated Apr 26, 2023

• NI-9234
• PXI-4496
• PXI-4472

## Issue Details

I would like to know the roll-off parameter of an anti-aliasing filter, but I don't find it in the datasheet of the corresponding data acquisition hardware. How can I calculate the roll-off parameter?

## Solution

The anti-aliasing filter is an analog low-pass filter. There are two possible ways to calculate an average, estimated roll-off parameter for a low pass-filter. Both methods need two points from the magnitude frequency response curve:

• Either the -3 dB cutoff frequency point and the stopband minimal frequency point.
• Or the passband maximal frequency point and the stopband minimal frequency point.
The frequency-coordinates and magnitude-coordinates of the two points in both cases make it possible to calculate the slope of the magnitude frequency response curve in the vicinity of the Nyquist frequency.

Example calculation for the NI-9234, based on the passband and the stopband parameters:

1. According to the datasheet the passband ends at 0.45 x Fs, where Fs denotes the sampling frequency. Here the magnitude is characterized by the flatness parameter, i.e. -0.04 dB...+0.04 dB.
2. The stopband starts at 0.55 x Fs, and the rejection here is -100 dB.
3. The frequency change between the two points is lg(0.55/0.45)=0.0872 Decade, which is 0.290 Octave.
4. The magnitude change can be estimated in this case to be -100 dB.
5. Finally we get the average roll-off as the quotient of the magnitude change and the frequency change: Roll-off=-1147 dB/Decade=-345 dB/Octave.