Signal Processing: Solution Manual Mathematical Methods And Algorithms For

2.1 : Find the impulse response of a system with a transfer function H(z) = 1 / (1 - 0.5z^-1).

: The FIR filter design involves selecting a window function and a filter length. Using the Hamming window, we can design a FIR filter with a cutoff frequency of 0.2π:

4.1 : Minimize the cost function J(x) = x^2 + 2x + 1 using gradient descent.

The impulse response is then:

where M is the filter length.

X(f) = T * sinc(πfT)