Derive Equation 4.698 for the cutoff frequency of the first-order low-pass digital filter with z-domain transfer function H(z)=(1−α)z/(z−α).
Q76; A notch filter is designed to attenuate input signals at one specific frequency called the notch frequency. The transfer function of a notch filter is
a. Find G(z), the z-domain transfer function of a digital filter obtained by approximation of G(s) using trapezoidal integration. Leave your answer in terms of ζ, ωn
and the integration step size T.
b. The digital filter is to be used to filter out the monthly lake temperature fluctuations in Example: Twenty-five years of end-of-month lake water temperature readings Tk, k = 0, 1, 2, 3, …, 300 months, are stored in MATLAB data file “Ch4_LakeTemp.mat.” Researchers would like to determine if the lake temperature, adjusted for monthly variations, has changed over that time. a. A moving average of the past 12 readings is used to smooth the seasonal temperature variations, that is
The notch frequency is ωn=π/6 rad/month and the sampling period is T=1 month. On the same graph, plot |G(ejωT)| vs. ω from zero to the Nyquist frequency for ζ=0.25, 0.5, 0.75.
c. Choose the value of ζ, which produces the largest attenuation at the notch frequency, and use the digital notch filter to filter out the monthly lake temperature fluctuations in the data. Prepare a graph similar to the ones in Figures.
