for (j=2;j | 558 Chapter 13. Fourier and Spectral Applications for j 2 j m j j2 j j p j SQR w1 j2 SQR w1 j2-1 SQR w1 m44-j2 SQR w1 m43-j2 den sumw den m4 Correct normalization. for j 1 j m j p j den Normalize the output. free_vector w2 1 m free_vector w1 1 m4 CITED REFERENCES AND FURTHER READING Oppenheim . and Schafer . 1989 Discrete-Time Signal Processing Englewood Cliffs NJ Prentice-Hall . 1 Harris . 1978 Proceedings of the IEEE vol. 66 pp. 51-83. 2 Childers . ed. 1978 Modern Spectrum Analysis New York IEEE Press paper by . Welch. 3 Champeney . 1973 Fourier Transforms and Their Physical Applications New York Academic Press . Elliott . and Rao . 1982 Fast Transforms Algorithms Analyses Applications New York Academic Press . Bloomfield P. 1976 Fourier Analysis of Time Series - An Introduction New York Wiley . Rabiner . and Gold B. 1975 TheoryandApplication of Digital SignalProcessing Englewood Cliffs NJ Prentice-Hall . Digital Filtering in the Time Domain Suppose that you have a signal that you want to filter digitally. For example perhaps you want to apply high-pass or low-pass filtering to eliminate noise at low or high frequencies respectively or perhaps the interesting part of your signal lies only in a certain frequency band so that you need a bandpass filter. Or if your measurements are contaminated by 60 Hz power-line interference you may need a notch filter to remove only a narrow band around that frequency. This section speaks particularly about the case in which you have chosen to do such filtering in the time domain. Before continuing we hope you will reconsider this choice. Remember how convenient it is to filter in the Fourier domain. You just take your whole data record FFT it multiply the FFT output by a filter function H f and then do an inverse FFT to get back a filtered data set in time domain. Here is some additional background on the Fourier technique that you will want to take into account. Remember that you must define your
