System Frequency Response

In the time domain, a system is characterized by an impulse response $h[n]$ which is the system output if a unit impulse signal is given at its input. In the frequency domain, it’s the frequency response that gives us insights into system behavior. There are two methods that lead to the same result.

Method 1

Frequency response is defined as the Fourier transform of its impulse response $h[n]$.

$$H[k]=\sum_{n=0}^{N-1}h[n]e^{-j2\pi\frac{k}{N}n}$$ ...