Spectral Analysis
DFT · frequency resolution · windowing
Physics: DFT: X[k] = Σ x[n]·e^(-i2πkn/N); frequency resolution Δf = f_s/N. Nyquist theorem: must sample at >2f_max to avoid aliasing. Windowing reduces spectral leakage from non-integer cycles within the analysis window. Rectangular window: -13 dB sidelobe (worst leakage); Hann window: -31 dB; Blackman: -58 dB at cost of wider main lobe. FFT (Cooley-Tukey, 1965): O(N log N) vs direct O(N²). Spectral leakage: when signal frequency isn't an exact integer multiple of bin spacing, energy spreads across adjacent bins.