Abstract
Digital signal processing (DSP) is an area of engineering that “has seen explosive growth during the past three decades” (Mitra, 2005). Its rapid development is a result of significant advances in digital computer technology and integrated circuit fabrication (Jovanovic Dolecek, 2002; Smith, 2002). Diniz, da Silva, and Netto (2002) state that “the main advantages of digital systems relative to analog systems are high reliability, suitability for modifying the system’s characteristics, and low cost”. The main DSP operation is digital signal filtering, that is, the change of the characteristics of an input digital signal into an output digital signal with more desirable properties. The systems that perform this task are called digital filters. The applications of digital filters include the removal of the noise or interference, passing of certain frequency components and rejection of others, shaping of the signal spectrum, and so forth (Ifeachor & Jervis, 2001; Lyons, 2004; White, 2000). Digital filters are divided into finite impulse response (FIR) and infinite impulse response (IIR) filters. FIR digital filters are often preferred over IIR filters because of their attractive properties, such as linear phase, stability, and the absence of the limit cycle (Diniz, da Silva & Netto, 2002; Mitra, 2005). The main disadvantage of FIR filters is that they involve a higher degree of computational complexity compared to IIR filters with equivalent magnitude response (Mitra, 2005; Stein, 2000).
TopIntroduction
Digital signal processing (DSP) is an area of engineering that “has seen explosive growth during the past three decades” (Mitra, 2005). Its rapid development is a result of significant advances in digital computer technology and integrated circuit fabrication (Jovanovic Dolecek, 2002; Smith, 2002). Diniz, da Silva, and Netto (2002) state that “the main advantages of digital systems relative to analog systems are high reliability, suitability for modifying the system’s characteristics, and low cost”.
The main DSP operation is digital signal filtering, that is, the change of the characteristics of an input digital signal into an output digital signal with more desirable properties. The systems that perform this task are called digital filters. The applications of digital filters include the removal of the noise or interference, passing of certain frequency components and rejection of others, shaping of the signal spectrum, and so forth (Ifeachor & Jervis, 2001; Lyons, 2004; White, 2000).
Digital filters are divided into finite impulse response (FIR) and infinite impulse response (IIR) filters. FIR digital filters are often preferred over IIR filters because of their attractive properties, such as linear phase, stability, and the absence of the limit cycle (Diniz, da Silva & Netto, 2002; Mitra, 2005). The main disadvantage of FIR filters is that they involve a higher degree of computational complexity compared to IIR filters with equivalent magnitude response (Mitra, 2005; Stein, 2000).
For example let us consider an FIR filter of length N = 11 with impulse response
,
(1)as shown in Figure 1a.
Figure 1. Impulse responses of FIR and IIR filters
In Figure 1b the initial 20 samples of the impulse response of an IIR filter
.
(2)are plotted.
(3) Key Terms in this Chapter
Impulse Response: h ( n ): The response of a digital filter to a unit sample sequence, which consists of a single sample at index n = 0 with unit amplitude.
System Function: Z-transform of the impulse response of the filter. FIR filters has only the nominator, while an IIR filter has denominator or both nominator and denominator.
Magnitude Response: Absolute value of the complex frequency response.
Singularities: Poles and zeros of system function. Poles of system function are zeros of its denominator while zeros are zeros of its nominator.
Phase Response: Phase of the complex frequency response.
Difference Equation: Time domain relation between the output and the input of digital filter in terms of coefficients which are characteristics of the filter. Generally contains recursive and nonrecursive parts.
Convolution: y(n)=x(n)*h(n): Time domain operation which relate the output of the digital filter y(n) with the input signal x(n) and the impulse response of the filter h(n).