Abstract
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 201T1 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 reponse. The lowpass filter, while of relative limited use, is presented to compare it with a popular elementary ‘smoothing’ filter.
Similar content being viewed by others
References
Andrews HC, Hunt BR (1977) Digital image restoration. Prentice-Hall, Englewood Cliffs, New Jersey, pp 21–22, 91–101, 147–148
Cappellini V, Constantinides AG, Emiliani P (1978) Digital filters and their applications. Academic Press, New York, pp 53–104
Hamming RW (1977) Digital filters. Prentice-Hall, Englewood Cliffs, New Jersey, pp 27–54, 134–137
Kuhl DE, Sanders TD, Edwards RQ, Makler PT (1972) Failure to improve observer performance with scan smoothing. J Nucl Med 13:752–757
Lo CM, Sawchuk AA (1979) Nonlinear restoration of filtered images with Poisson noise. SPIE 207:84–95
McClellan JH, Parks TW, Rabiner LR (1973) A computer program for designing optimum FIR linear phase digital filters. IEEE Trans Audio Electroacoustics AU-21:506–526
McClellan JH (1977) A 2-D FIR filter structure derived from the Chebyshev recursion. IEEE Trans Circuits Systems CAS-24:372–378
Metz CE, Goodenough DJ (1973) Letter to the editor. J Nucl Med 14:873–876
Miller TR, Sampathkumaran K, Biello DR, Vannier MW (1981) Evaluation of computer display systems using digital test patterns. J Nucl Med 22:264–268
Oppenheim AV, Schafer RW (1975) Digital signal processing. Prentice-Hall, Englewood Cliffs, New Jersey, pp 26–29, 237–239
Pizer SN, Todd-Pokropek AE (1978) Improvement of scintigrams by computer processing. Semin Nucl Med 8:125–146
Pratt WK (1978) Digital image processing. John Wiley and Sons, New York, pp 381–383
Rabiner LR, Kaiser JF, Schafer RW (1974) Some considerations in the design of multiband finite-impulse-response digital filters. IEEE Trans Acoust, Speech, Signal Processing ASSP-22:462–472
Rabiner LR, McClellan JH, Parks TW (1975) FIR digital filter design techniques using weighted Chebyshev approximation. Proc IEEE 63:595–610
Rollo FD, (ed) (1977) Nuclear medicine physics, instrumentation, and agents. CV Mosby, St. Louis, Missouri, pp 442–445
Shannon CE, Weaver W (1949) The mathematical theory of communication. Univ. of Illinois Press, Urbana, Illinois, pp 31–125
Todd-Pokropek A (1980) Image processing in nuclear medicine. IEEE Trans Nucl Sci NS-17:1080–1094
Twogood RE (1980) 2-D digital signal processing with an array processor. IEEE International Conference on Acoustics, Speech and Signal Processing, Denver, Colorado, pp 426–429
Author information
Authors and Affiliations
Additional information
This study was supported in part by National Institutes of Health Grants No. HL17646 and HL13851.
Rights and permissions
About this article
Cite this article
Miller, T.R., Sampathkumaran, K.S. Design and application of finite impulse response digital filters. Eur J Nucl Med 7, 22–27 (1982). https://doi.org/10.1007/BF00275240
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00275240