Signals: Time, Frequency, and the Digital World
Prof. Dr. Alessandro Del Vecchio · 7 concepts · 5 questions
Concept 1 / 7
Signals as Functions — 1D, 2D, and 3D Arrays
A signal is any quantity that depends on another variable — most often time: y(t). The dimensionality of a signal describes the number of independent variables it depends on.
| Dimensionality | Description | Biomedical example | NumPy shape |
|---|---|---|---|
| 1D | Depends on time only | Single EMG channel voltage(t), elbow angle θ(t) | (T,) |
| 2D | Depends on two variables (space × space, or space × time snapshot) | EMG electrode-grid frame at one instant; greyscale image | (rows, cols) |
| 3D | Depends on three variables | MUAP propagation movie (rows × cols × time); fMRI volume | (rows, cols, T) |
In Python, a signal is an np.ndarray plus metadata: the sampling rate fs [Hz] and the physical unit (mV, deg, N). Without metadata, the array is just numbers — always document what the axes represent.
import numpy as np
fs = 2000 # 2000 samples per second
t = np.linspace(0, 1, fs) # 1-second time axis, shape (2000,)
emg = np.random.randn(fs) # placeholder 1D signal, shape (2000,)