Implementing waveform shaping filters to pre-equalize gain and phase distortion of the analog signal processing path in DSP based modems

The shaping filter in a DSP based transmitter must perform a number of simultaneous signal processing tasks prior to delivering digital samples to its digital-to-analog converter (DAC) and analog smoothing filter. The primary task is spectral shaping with a specified up-sampling rate (to permit large transition bandwidth in the analog smoothing filter following the DAC). A secondary task is compensation for spectral gain and phase distortion introduced in the analog signal processing chain following the digital shaping filter. Distortion effects include the DAC´s sin(x)/(x) spectral response and the non-uniform gain and phase response of the analog smoothing filter following the DAC. This paper presents a technique for incorporating arbitrary gain and phase corrections in the digital shaping filter