S5-3.3 FIR Filter Design & Realization

Work through these

• Introduction to linear phase FIR filters

  The other filter family, and the reason it exists: exactly linear phase. Every frequency is delayed equally, so pulse shapes survive, which matters in data transmission and imaging.

• Types of linear phase FIR filters

  Four types, decided by symmetry and length. Knowing which types cannot realise which responses saves you designing something impossible.

• Magnitude and phase responses of linear phase FIR filters

  What the symmetry buys and what it costs, read off the response. This is the item that connects the classification above to a design you would actually choose.

• Windowing technique: rectangular and Bartlett windows

  The starting point, and the demonstration of the trade the whole topic turns on. The rectangular window has the narrowest main lobe and the worst side lobes, which is the compromise stated at its extremes.

• Hamming, Blackman and Kaiser windows

  The rest of the menu, ending with the one that lets you dial the compromise with a parameter. Kaiser is the practical choice once you understand the others.

• Frequency sampling technique

  A different route entirely: specify the response at points and transform back. Useful when the response you want is not a standard shape.

• Realization of FIR filters: direct form and linear phase structure

  Two structures again, and the second exploits coefficient symmetry to halve the multipliers. A nice case of mathematics buying hardware.

• Lab: FIR filter design using different windows in MATLAB

  The bench version of the window comparison. Plotting several windows for the same specification is the fastest way to internalise the trade above.

• Lab: implement an FIR filter on the DSK

  The same design on a real processor, where the multiplier count from the previous item stops being theoretical.