An analysis on the calculation of the inverse discrete Fourier transform (IDFT) of passband frequency response measurements in terms of lowpass equivalent responses is shown, in order to specify the differences in the results given from different common algorithms; differences with respect to the calculation of the IDFT for true lowpass responses are remarked. It is shown how the basic sequence has to be represented in time domain by invoking the causality, which is supported by results. Results are corroborated by an application on measured data in a reverberation chamber. The present analysis helps readers understand different IDFT algorithms used by Manufacturers and make their own codes whenever desirable.
2. Hines, M. E. and H. E. Stinehelfer, "Time-domain oscillographic microwave network analysis using frequency-domain data," IEEE Trans. on Microw. Theory and Techniques, Vol. 22, No. 3, 276-282, Mar. 1974.
3. Ulriksson, B., "Conversion of frequency-domain data to the time domain," Proc. of the IEEE, Vol. 74, 74-77, 1986.
4. Papoulis, A., The Fourier Integral and Its Applications, Prentice-Hall, New Jersey, 1974.
5. Bracewell, R. M., The Fourier Transform and Its Applications, Prentice-Hall, New Jersey, 1974.
6. Carlson, A. B., Communication Systems: An Introduction to Signal and Noise in Electrical Communication, McGraw-Hill, New York, 1986.
7. Brigham, E. O., The Fast Fourier Transform, McGraw-Hill, New York, 1986.
8. Smith III, J. O., Mathematics of the DFT with Audio Applications, W3K Publishing, Standford University, ISBN 978-0-97456007-4-8, Copyright 2014-04-21, 2007.
9. Holloway, C. L., H. A. Shah, R. J. Pirkl, K. A. Remely, D. A. Hill, and J. M. Ladbury, "Early time behaviour in reverberation chamber and its effect on the relationships between coherence bandwidth, channel decay time, RMS delay spred, and the chamber buildup time," IEEE Trans. Electromagn. Compat., Vol. 54, 714-725, Aug. 2012.
10. Esposito, G., G. Gradoni, F. Moglie, and V. M. Primiani, "Stirrer performance of reverberation chambers evaluated by time domain fidelity," IEEE Intern. Symp. on EMC, 207-212, Denver, CO, USA, 2013, DOI: 10.1109/ISEMC.2013.6670410.
11. Zhang, X., M. Robinson, and I. D. Flintoft, "On measurement of reverberation chamber time constant and related curve fitting techniques," IEEE Intern. Symp. on EMC, 406-411, Dresden, Germany, 2015, DOI: 10.1109/ISEMC.2015.7256196.
12. Agilent Technologies, "Time domain analyzer using a network analyzer," Application note 1287-12, Literature number 5989-5723EN, Published in USA, May 2, 2012.
13. Hiebel, M., Fundamentals of Vector Network Analysis, Rhode & Schwarz, Munchen, 2014, ISBN 978-3- 939837-06-0.
14. Keysight Technologies, "Time domain analyzer using a network analyzer," Application note 1287-12, Literature number 5989-5723EN, Published in USA, Aug. 2, 2014.
15. Anritsu, "Time domain measurements using network analyzers," Application note No. 11410-00206, Rev. D, Printed in USA, 2009-03.
16. Campagnaro, G., Private communication,, Keysight Technologies, Italy, Mar. 2017.
17. Vaughan, R. G., N. L. Scott, and D. R. White, "The theory of bandpass sampling," IEEE Trans. on Signal Processing, Vol. 39, No. 9, 1973-1984, Sep. 1991.
18. Gifuni, A., A. Sorrentino, A. Fanti, G. Ferrara, M. Migliaccio, G. Mazzarella, and F. Corona, "On the evaluation of the shielding effectiveness of an electrically large enclosure," Advanced Electromagnetics, Vol. 1, No. 1, 84-91, May 2012, DOI: http://dx.doi.org/10.7716/aem.v1i1.44.
19. Gifuni, A., G. Ferrara, M. Migliaccio, and A. Sorrentino, "Estimate of the shielding effectiveness of an electrically large enclosure made with pierced metallic plate in a well-stirred reverberation chamber," Progress In Electromagnetics Research C, Vol. 44, 133-144, 2013.
20. Migliaccio, M., G. Ferrara, A. Gifuni, A. Sorrentino, F. Colangelo, C. Ferone, R. Cioffi, and F. Messina, "Shielding effectiveness tests of low-cost civil engineering materials in a reverberating chamber," Progress In Electromagnetics Research B, Vol. 54, 227-243, 2013.