According to the Sampling Theorem, any signal can be accurately reconstructed from values sampled at uniform intervals as long as it is sampled at a rate at least twice the highest frequency present in the signal. Failure to satisfy this requirement will result in aliasing of higher-frequency components, meaning that these components will appear to have frequencies lower than their true values.
One way of avoiding the problem of aliasing is to apply a low-pass filter to the signal, prior to the sampling stage, to remove any frequency components above the "folding" or Nyquist frequency (half the sampling frequency). Such anti-aliasing filters are commonly built into the analog interface chips and codecs which convert analog input signals into digital form for processing by a digital signal processor (DSP). In many cases, these anti-aliasing filters are implemented using conventional analog circuitry. An alternative method is to use a digital anti-aliasing filter. This avoids the noise and drift problems inherent in analog filter circuits, and is the natural approach when the signal is going to be processed digitally anyway.
How can a digital filter be used to remove frequency components above the folding frequency, which is the highest frequency that can be handled by a sampled data system? The answer lies in the application of a technique called multirate digital signal processing, where different sampling rates are used at different stages in the processing of a signal. The anti-aliasing filter used in the FFT spectrum analyser applet (Java 1.1 version) works by "oversampling" the input signal at a rate of 48 kHz - six times the 8000 Hz sampling rate used by the spectrum analyser itself. Operating at the higher sampling rate, the anti-aliasing filter is a low-pass filter with a passband from 0 to 4000 Hz (the folding frequency). The output from the filter is "downsampled" by a factor of six, simply by throwing away five samples in every six, giving a stream of sampled values effectively at the lower sampling rate of 8000 Hz.
The 204-tap FIR anti-aliasing filter was designed using MATLAB, based on the Parks-McClellan method.
The filter specification is as follows:
The calculated frequency response of the filter is shown in the diagram.
Back to guidance notes on the Spectrum Analyser applet