Complex Number Fundamentals Representations A complex number $z$ admits three canonical forms: Cartesian: $z = a + bi$, where $i^2 = -1$ Polar: $z = r(\cos\theta + i\sin\theta)$, with $r = |z|$ and $\theta = \arg(z)$ Euler: $z = re^{i\theta}$ via Taylor expansion equivalence De Moivre's Theorem For...
Signal Analysis Parameters To analyze a signal using FFT, several key parameters must be defined: Target signal frequency: f Target signal period: T = 1/f Sampling frequency: fs Sampling period: Ts = 1/fs Total sample points: NPT Total sampling time: t = NPT × Ts Frequency resolution: f0 = fs/NPT Ca...
Polynomial Representations A polynomial $A(x) = \sum_{i=0}^{n-1} a_i x^i$ of degree $n-1$ admits two canonical representations. The coefficient representation stores the vector $[a_0, a_1, \ldots, a_{n-1}]$. Alternatively, the point-value representation consists of $n$ distinct evaluation pairs ${(x...