Realizable Anti-Aliasing Filters

Analog filtering before the ADC stage is intimately related to the definition of bandlimiting. 

Where the definition of bandlimiting involves the content of the signals that may be present, 

analog filtering before the ADC represents a signal-processing stage where certain frequencies 

can be attenuated. It is important to know both the signals that can be present before filtering and 

the amount of attenuation that the filter offers for different frequencies. With knowledge of both 

of these, the true spectrum of the signal to be digitized can be determined. Sampling at two times 

the maximum desired frequency presents a large and often impractical demand on the filter used 

before digitization (the anti-aliasing filter). Ideally, an anti-aliasing filter placed before an ADC 

would pass all of the desired frequencies up to some cutoff frequency and provide infinite 

attenuation for frequencies above the cutoff frequency. Then sampling at f

s

 = 2f

 would be two 

times the cutoff frequency and no spectrum overlap would occur. Unfortunately, practical, 

realizable filters cannot provide this type of “brickwall” response. The attenuation of real filters 

increases more gradually from the cutoff frequency to the stopband. Therefore, for a given cutoff 

frequency on a real filter, sampling at two times this cutoff frequency will produce some 

spectrum overlap. The steeper the transition from the passband to the stopband and the more 

attenuation in the stopband, the less the sampled signal will be distorted by spectrum overlap. In 

general, more complicated filters are required to achieve steeper transitions and higher 

attenuation in the stopband. Therefore, more complicated filters are required to reduce the 

distortion in the sampled signal due to spectrum overlap for a given sampling rate. Limitations 

on the practical implementation of analog filters make high-order, steep rolloff filters difficult to 

realize. Also, as the steepness of the rolloff is increased, the phase response tends to become 

more nonlinear. This can create distortion of the desired receive signal since different 

frequencies within a signal can be delayed in time by different amounts.