There are two types of distortion :-
a)
Aliased Component Distortion : Aliased Component distortion can be corrected, if required by cascading another better lowpass filter.
b) Baseband Spectrum Distortion (Sinc
Distortion) : Baseband Spectrum Distortion is corrected by an Equalizer. An Equalizer is an LSI system with Fourier Transformable impulse response which acts like an inverse
1 / H ( f ) to another LSI system, at least in a certain range of frequencies. Equalizer is also used to correct channel imperfections in a communication system.
The higher the sampling rate fs, the less is the distortion in the spectral image X( f ) centered at origin.
An ideal lowpass filter with unity gain over
-0.5 fs ≤ f
≤ 0.5 fs recovers the distorted signal.
To recover X( f ) with no amplitude distortion, we must use a compensating filter that negates the effects of the Sinc distortion by profiling a concave shaped magnitude spectrum corresponding to the reciprocal of the Sinc function over the principal period
| f | ≤
0.5 fs
Figure : Spectrum of a filter that compensates for Sinc distortion
The magnitude spectrum of the compensating filter is given by
