Stearns and David (1996) states that “for many diverse applications, information is now most conveniently recorded, transmitted, and stored in digital form, and as a result, digital signal processing (DSP) has become an exceptionally important modern tool.” Typical operation in DSP is digital filtering. Frequency selective digital filter is used to pass desired frequency components in a signal without distortion and to attenuate other frequency components (Smith, 2002; White, 2000). The pass-band is defined as the frequency range allowed to pass through the filter. The frequency band that lies within the filter stop-band is blocked by the filter and therefore eliminated from the output signal. The range of frequencies between the pass-band and the stop-band is called the transition band and for this region no filter specification is given. Digital filters can be characterized either in terms of the frequency response or the impulse response (Diniz, da Silva & Netto, 2002). Depending on its frequency characteristic, a digital filter is either low-pass, high-pass, band-pass, or band-stop filters. A low-pass (LP) filter passes low frequency components to the output, while eliminating high-frequency components. Conversely, the high-pass (HP) filter passes all high-frequency components and rejects all low-frequency components. The band-pass (BP) filter blocks both low- and high-frequency components while passing the intermediate range. The band-stop (BS) filter eliminates the intermediate band of frequencies while passing both low- and high-frequency components. In terms of their impulse responses digital filters are either infinite impulse response (IIR) or finite impulse response (FIR) digital filters. Each of four types of filters (LP, HP, BP, and BS) can be designed as an FIR or an IIR filter (Ifeachor & Jervis, 2001; Mitra, 2005; Oppenheim & Schafer, 1999).
Frequency Transformation for Linear State-Space Systems and Its Application to High-Performance Analog/Digital Filters