To implement a smoothing operation using a Parzen window of width 0.1 Hz on the Fourier Amplitude Spectrum (FAS) of a signal, the parzenwin function can be of help.
First, we need to compute the Fourier Transform of the given signal. This can be done using the fft function available in MATLAB. Then, we apply the Parzen window for smoothing.
Here's how you can find the Fourier Transform:
fs = 200; % Sampling frequency
N = length(signal); % Number of points in the signal
f = fs * (0:(N/2)) / N; % Frequency vector
signal_fft = fft(signal);
signal_fft_amplitude = abs(signal_fft / N); % Amplitude spectrum
Here's how you can create a Parzen window:
window_width_Parzen = 0.1; % Hz
w_Parzen = (1 / window_width_Parzen) * fs;
w_Parzen = round(w_Parzen, 0); % Ensure it's an integer
parzen_window = parzenwin(w_Parzen * 2 + 1); % The Parzen window function requires an odd length
parzen_window = parzen_window / sum(parzen_window); % Normalize
Moreover, during the smoothing of any curve, there will be an alteration in the amplitude. We can use Root Mean Square Error (RMSE) to find the difference between the original and smoothed signal amplitudes. To minimize this alteration, you might need to adjust the window width. We can iteratively try to find the window width that minimizes the RMSE.
You can refer the following MathWorks documentation for more information:
