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Chapter 16

Digital Filtering

For example, for –0.02 dB passband ripple, the formula gives:

–0.02

= 20log

 

Ao( f)

------------

 

 

 

 

A

( f)

 

 

 

 

i

 

Ao( f)

10

–0.001

= 0.9977

------------ =

 

Ai( f)

 

 

 

 

 

which shows that the ratio of input and output amplitudes is close to unity.

You can view practical filter design as approximating the ideal desired magnitude response subject to certain constraints. The ideal passband and stopband are flat and constant. Practical filter passbands and stopbands may have ripples. Ideal filters have no transition region. Practical filters have transition regions. Practical filter design allows tradeoffs between these different components (passband ripple, stopband ripple, stopband attenuation, transition region width) subject to the filter structure (FIR or IIR) and the design algorithm.

FIR Filters

FIR filters have several different design methods. FIR filters have ripple in the magnitude response, so the design problem can be restated as how you can design a filter that has a magnitude response as close to the ideal as possible and distributes the ripple in a desired fashion. For example, a lowpass filter has an ideal characteristic magnitude response. A particular application may allow some ripple in the passband and more ripple in the stopband. The filter design algorithm should balance the relative ripple requirements while producing the sharpest transition region.

The simplest approach is the Windowed FIR design. The Windowed FIR design takes the inverse FFT of the desired magnitude response and applies a time domain window to the result. The advantages of this method are conceptual simplicity and ease of implementation. The disadvantages are the inefficiency and difficulty in specification. For a given number of taps, the Windowed FIR design does not distribute ripple equally and has a wider transition band than other designs. It also is difficult to specify a cut-off frequency that has a particular attenuation. To design a Windowed FIR filter, you must specify the ideal cut-off frequency, the sampling frequency, the number of taps, and the window type.

The other main FIR design approach uses the Parks-McClellan algorithm, also known as Remez Exchange. This is an iterative algorithm that

LabVIEW Measurements Manual

16-6

www.ni.com

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