3.5. fmas.analytic_signal¶
Implements class AnalyticSignal, which uses the frequncy-domain algorithm detailed in [M1999] to compute the complex-valued analytic signal for a real-valued discrete-time field.
- M1999(1,2,3,4)
S. L. Marple, Computing the Discrete-Time Analytic signal via FFT, IEEE Transactions on Signal Processing, 47 (1999) 2600.
-
fmas.analytic_signal.
AS
¶ alias of
fmas.analytic_signal.AnalyticSignal
-
class
fmas.analytic_signal.
AnalyticSignal
(x)¶ Class converting real-valued field to analytic signal.
Implements methods that take a real-valued \(N\)-point discrete-time field \(E\) and provide access to the complex-valued discrete-time analytic signal \(\mathcal{E}\), both in time-domain and Fourier-domain.
Note
The class implements the frequency-domain algorithm specified in [M1999], given by the three-step procedure
1. Compute \(E_\omega\), i.e. the \(N\)-point discrete Fourier-trasform (DFT) of the real-valued discrete-time field \(E\).
2. Compute the \(N\)-point discrete-time analytic signal in the Fourier-domain, given by
\[\begin{split}\mathcal{E}_\omega[m] = \begin{cases} E_\omega[0], & m=0,\\ 2E_\omega[m], & 1\leq m \leq N/2-1,\\ E_\omega[N/2], & m = N/2,\\ 0, & N/2+1 \leq m \leq N - 1. \end{cases}\end{split}\]3. Compute the complex-valued \(N\)-point discrete-time analytic signal \(\mathcal{E}\) using an inverse DFT.
- Parameters
x (
numpy.ndarray
) – Real-valued field \(E\).
-
x
¶ Real-valued field \(E\).
- Type
numpy.ndarray
-
num
¶ Number \(N\) of field points.
- Type
int
-
property
t_rep
¶ Time-domain representation \(\mathcal{E}\) of the analytic signal.
- Type
numpy.ndarray
-
test_orthogonality
()¶ Check if real and imaginary parts are orthogonal.
Real and imaginary parts of the analytic signal must be orthogonal, i.e.
\[\sum_{n=0}^{N-1} \mathsf{Re}(\mathcal{E}[n])\,\mathsf{Im}(\mathcal{E}[n]) = 0,\]see Eq. (7) of [M1999].
-
test_recover_original_field
()¶ Check if real part of analytic signal equals original field.
Real part of the discrete-time analytic signal must be equal to the original field, i.e.
\[\mathsf{Re}(\mathcal{E}[n]) = E[n], \quad 0\leq n\leq N-1,\]see Eq. (6) of [M1999].
-
property
w_rep
¶ Frequency-domain representation \(\mathcal{E}_\omega\) of the analytic signal.
- Type
numpy.ndarray