[Python] optimal filter in fractional fourier domains [closed]

Is the code of optimal filter in fractional Fourier domains correct?

# Length of the exemplary signal
N = 256
t = linspace(-1, 1, N) # Time vector

# Original signal x(t)
x = exp(-t**2)

# Noise n(t)
n = 0.1 * randn(N) # Assuming you want a 1D noise array

# Observed signal y(t)
y = x + n

# Fractional order
a = 0.5

# Fractional Fourier Transform
X_a = frft(x, a)
Y_a = frft(y, a)

# Autocorrelation function
R_yy = Y_a * conj(Y_a)
R_xy = X_a * conj(Y_a)

# Optimal filter
G_a = R_xy / R_yy

# Applying the filter
X_hat_a = G_a * Y_a

# Inverse fractional Fourier transform
x_hat = frft(X_hat_a, -a)

# Plotting
figure()
subplot(3, 1, 1)
plot(t, x, 'b', t, y, 'r')
legend(['Original signal x(t)', 'Observed signal y(t)'])
title('Time-domain signals')
subplot(3, 1, 2)
plot(t, abs(X_a), 'b', t, abs(Y_a), 'r')
legend(['|X^{(a)}(u)|', '|Y^{(a)}(u)|'])
title('Magnitude in fractional Fourier domain')
subplot(3, 1, 3)
plot(t, x, 'b', t, real(x_hat), 'g')
legend(['Original signal x(t)', 'Estimated signal \hat{x}(t)'])
title('Filtering result')


paper

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