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Unformatted text preview: Ve451 Lecture Notes Dianguang Ma Summer 2010 Chapter 10 Design of Digital Filters Introduction In the design of frequencyselective filters, the desired filter characteristics are specified in terms of the desired frequency response of the filter. In the filter design process, we determine the coefficients of a causal FIR or IIR filter that closely approximates the desired frequency response specifications. The two main advantages of the FIR filters are their linear phase property and their guaranteed stability because of the absence of poles. Their potential disadvantage is that the requirement of sharp filter specifications can lead to long filter lengths, consequently increasing their computational cost. The two main advantages of the IIR filters are their low computational cost and their efficient implementation in cascade of secondorder sections. Their main disadvantage is the potential for instabilities introduced when the quantization of the coefficients pushes the poles outside the unit circle. For IIR filters, linear phase cannot be achieved exactly over the entire Nyquist interval, but it can be achieved approximately over the relevant passband of the filter. In practice, FIR filters are employed where there is a requirement for a linearphase characteristics within the passband of the filter. However, an IIR filter has lower sidelobes in the stopband than an FIR filter having the same number of parameters. For this reason, if some phase distortion is either tolerable or unimportant, an IIR filter is preferable. Today, FIR and IIR digital filter design is greatly facilitated by the availability of numerous computer software programs. In describing the various digital filter design methods in this chapter, the primary objective is to give the students the background necessary to select the filter best matches the application and satisfies the design requirements. Causality and Its Implication Let us consider the issue of causality in more detail by examing the impulse response ( ) of an ideal lowpass filter with frequency response 1, ( ) 0, The impulse response is sin( ( ) c c h n H h n = < = ) c n n A plot of ( ) for / 4 is illustrated in Figure 10.1.1. It is clear that the ideal lowpass filter is noncausal and hence it cannot be realized in practice. c h n = Although this discussion is limited to the realization of a lowpass filter, our conclusion hold, in general, for all the other ideal filter characteristics. A question that naturally arises at this point is the following: What are the conditions that a frequency response characteristic ( ) must satisfy in order for the resulting filter to be causal? The answer to this question is given by the Pal H eyWiener theorem. 2 . If ( ) has finite energy and ( ) 0 for 0, then ln ( ) Conversely, if ( ) and ln ( ) then we can associate with ( ) an argument ( ) so that the resu h n h n n H d H d H d H...
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This note was uploaded on 10/14/2011 for the course EE 451 taught by Professor Dianguangma during the Summer '10 term at Shanghai Jiao Tong University.
 Summer '10
 DianguangMa
 Frequency

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