E(f) = |X(f)|^2
The gradient of the cost function is:
1.1 : Prove that the Fourier transform of a rectangular pulse is a sinc function. E(f) = |X(f)|^2 The gradient of the cost function is: 1
X(f) = e^-π^2f^2σ^2
2.1 : Find the impulse response of a system with a transfer function H(z) = 1 / (1 - 0.5z^-1). E(f) = |X(f)|^2 The gradient of the cost function is: 1
4.1 : Minimize the cost function J(x) = x^2 + 2x + 1 using gradient descent.
The energy spectral density is then:
X(f) = T * sinc(πfT)