The Role of Complex Sinusoids in System Characterization

Investigate the role of complex sinusoids to determine the frequency and impulse response of a system.

Complex sinusoids are disproportionately emphasized among all signals in DSP formulations. Why? This is what we are going to investigate now.

System input

Let’s probe a system that has an impulse response h[n]h[n] with a complex sinusoid x[n]=ejω0nx[n]=e^{j\omega_0 n} as shown in the figure below:

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