Answer

Frequency-domain representation shows signal spectral content via Fourier.

Transform

$X(f)=\int_{-\infty}^{\infty}x(t)e^{-j2\pi ft}dt$.

• Periodic: Fourier Series → line spectrum at $nf_0$.
• Aperiodic: Continuous $X(f)$.
• AM: $s(t)=A_c[1+\mu m(t)]\cos\omega_c t$ → impulses at $\pm f_c$ plus sidebands $M(f\pm f_c)$.
• FM: Bessel sidebands $J_n(\beta)$.

Importance

Reveals bandwidth, filter design, modulation analysis.

Final: Time → frequency via Fourier series/transform.