Solution | Manual Mathematical Methods And Algorithms For Signal Processing

For a Gaussian distribution, the Fourier transform is also Gaussian:

2.1 : Find the impulse response of a system with a transfer function H(z) = 1 / (1 - 0.5z^-1). For a Gaussian distribution, the Fourier transform is

: The gradient descent algorithm updates the solution using: For a Gaussian distribution

5.1 : Find the maximum likelihood estimator of the mean of a Gaussian distribution. For a Gaussian distribution, the Fourier transform is

H(z) = 1 / (1 - 0.5z^-1) = 1 + 0.5z^-1 + 0.25z^-2 + ...