Abstract—This paper introduces a new algorithm to transform a digital low-pass filter into a digital low-pass, high-pass, band-pass, band-stop and narrow-band filter in the digital domain. The technique of this method is based on bilinear and inverse bilinear z-transformation with pre-warping frequency and the support of Pascal’s triangle. From this, a matrix equation is derived, called ‘Digital low-pass to digital filter Pascal matrix equation’. This equation will make it easier for hand calculations and programming when transformations are made from a digital low-pass filter to another digital filter in the digital domain.
 

Index Terms—frequency transformation, bilinear z-transformation, digital filters, analog filters, pre-warping frequency, Pascal’s triangle

Cite: Phuoc S. Nguyen, "Frequency Transformation in Digital Domain," International Journal of Signal Processing Systems, Vol. 4, No. 5, pp. 389-393, October 2016. doi: 10.18178/ijsps.4.5.389-393