Anti-aliasing Filter, Group Delay & Phase Match

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Anti-Aliasing Filter and the Use of Sigma-Delta Converters
The anti-aliasing filter is an important part in the dynamic signal analyzer input front end. It is used to filter out unwanted high frequency content before the analog signal is converted to the digital domain. Without an anti-aliasing filtering, high frequency noise is aliased into lower frequency spectrum during the digitization process which can lead to misinterpretation of the data. In the old days, the anti-aliasing filters were realized purely in the analog domain. Typically, a 6 or 8th -order Butterworth filter was used in order to achieve reasonable attenuation of high frequency noise.

The important parameters of an anti-aliasing filter include the cutoff frequency, flatness of the filter passband, attenuation of its stopband, and the linearity of its phase in the useful frequency range.

The drawbacks of analog anti-aliasing filter are several folds:

(1). The fa/fs ratio is low, where fa is the analyzer cutoff frequency and fs is the sampling frequency. Usually the value of fa/fs is about 0.2 to 0.3. This required that the instruments needed to sample at 80 kHz or higher in order to get a useful frequency up to 20 kHz.

(2). The phase characteristics of analog filters are not consistent therefore the phase match between each input channels are not good. It can range from a few degrees to as much as ten degrees or more up to 20 kHz.

(3). The phase of analog filters is not linear. A non-linear phase in a filter will result in distortion in the time domain. For example an impulse signal passing through a filter will have a very different peak reading and changed shape in time domain.

(4). The attenuation of an analog low pass filter is usually in the magnitude of -65 dB or less. Therefore the anti-aliasing effect is poor. When the anti-aliasing effect is not good, the system dynamic range and total harmonic distortion specs will suffer.

A revolution started in the mid nineties when the semiconductor industry introduced a new technology, the sigma delta A/D converter. In 1994, Crystal Instruments was among the very first companies in the world using the sigma-delta A/D converter in the dynamic signal analyzer. This innovation eliminated the need of large size analog filters and made it possible to put a four channel signal analyzers into a package the size of a PCMCIA card while realizing significant improvements in the anti-aliasing filter performance.