Overview | momoiot

Signal Analysis Overview

Radar signal analysis can be categorized into two main types:

time-frequency transform-based methods and time-alignment-based similarity analysis.

The former includes FFT, STFT, and Wavelet, while the latter includes DTW.

1. FFT, STFT and Wavelet Transform

FFT, STFT, and Wavelet Transform are methods that analyze signals by extracting components using basis functions.

FFT uses sinusoidal bases, STFT uses time-localized sinusoids with a window, and Wavelet uses scalable, shifted waveforms.

Aspect	FT(FFT)	STFT	Wavelet Transform
Basis Function	e−jωt	g(t−τ)e−jωt	ψ(at−b)
Varying Parameters	Frequency ω	Time τ, Frequency ω	Time b, Scale a
Meaning	Extract frequency components over the entire signal	Extract frequency components within a local time window	Extract time-scale components at a specific time and scale

Aspect

FT(FFT)

STFT

Wavelet Transform

Basis Function

e−jωt

g(t−τ)e−jωt

ψ(at−b)

Varying Parameters

Frequency ω

Time τ, Frequency ω

Time b, Scale a

Meaning

Extract frequency components

over the entire signal

Extract frequency components

within a local time window

Extract time-scale components

at a specific time and scale

2. DTW

DTW (Dynamic Time Warping) is an algorithm that measures similarity between two signals even when their time axes are nonlinearly distorted.

It finds an optimal alignment path by stretching or compressing the time axis to minimize the overall difference.

Input	Two signals
Core Concept	Time alignment (warping)
Varying Parameter	Time index (nonlinear mapping)
Mathematical Operation	Distance minimization with dynamic programming
Meaning	Measure similarity by aligning signals in time
Output	Alignment path and distance