Suppose an investigator plans to collect a time series that can be modeled by a stationary process with SDF S(·). The sampling interval ∆t is set at 1/2 sec so the Nyquist frequency fN is 1 Hz....

Suppose an investigator plans to collect a time series that can be modeled by a stationary process with SDF S(·). The sampling interval ∆t is set at 1/2 sec so the Nyquist frequency fN is 1 Hz. Suppose that the rough shape of S(·) is known from either physical theory or previous experiments and is given by Figure 346. The investigator plans to use the Parzen lag window spectral estimator.

(a) What data taper would you recommend if the sample size N of the collected time series is 128? Would you change your recommendation if the sample size were increased to 1024? State the reasons for your recommendations.

(b) Would pre whitening be useful here? State the reasons for your answer.

(c) Determine the spectral bandwidth of S(·) by examining Figure 346. What does this imply about the size of the window bandwidth of the Parzen smoothing window? For the data taper(s) you selected in part (a) for sample sizes of N = 128 and 1024, determine what values of m (if any) achieve the desired window bandwidth. Determine the corresponding EDOFs ν.