Design and application of finite impulse response digital filters

The finite impulse response (FIR) digital filter is a spatial domain filter with a frequency domain representation. The theory of the FIR filter is presented and techniques are described for designing FIR filters with known frequency response characteristics. Rational design principles are emphasized based on characterization of the imaging system using the modulation transfer function and physical properties of the imaged objects. Bandpass, Wiener, and low-pass filters were designed and applied to 201Tl myocardial images. The bandpass filter eliminates low-frequency image components that represent background activity and high-frequency components due to noise. The Wiener, or minimum mean square error filter 'sharpens' the image while also reducing noise. The Wiener filter illustrates the power of the FIR technique to design filters with any desired frequency response. The low-pass filter, while of relative limited use, is presented to compare it with a popular elementary 'smoothing' filter.