Digital Signal Processing Reference
In-Depth Information
9.5 CONCLUSION
This completes our chapter on the FFT and its application to linear filtering. The
FFT is a valuable function that provides a link from the time domain to the
frequency domain. We have found that FFT will find application to linear filtering
when the number of coefficients is large enough to warrant the more complex
computations.
This is also the conclusion for the text. Along the way, we have developed
some of the most time-honored methods used in analog and digital filter design.
By no means have we explored every nuance of filter design, and we see new
techniques being developed every day. However, we have developed the key
approximation techniques used today. The methods used can serve as a template
in the development of other approximations. We have been able to adjust
normalized functions for use in a variety of selectivities. We have shown one
method of implementing analog filters and discussed some of the potential pitfalls
that must be considered.
After the introduction of some principles of discrete-time theory, we learned
how to design both FIR and IIR digital filters using two entirely different
techniques. C code for the implementation of these filter types was developed and
analyzed. And finally, we finished with the discussion of the FFT in filtering
applications. I hope this text and the accompanying software disc will serve as a
starting point for your journey into the exciting field of filter design.
