2. Signal Processing

Mathematically, the inner product measures the similarity between two waveforms.

The FFT calculates this similarity between the input signal and frequency-specific basis functions,

thereby decomposing and quantifying the signal’s frequency components.

 

 

 

 

 

 

3. Representation and Interpretation

The FFT result provides a visual mapping of the frequency components that constitute an arbitrary time-domain signal.

Based on the principle of similarity, the spectrum identifies dominant frequencies through the following interpretations:

 

 

1) Component Identification:

High-amplitude peaks pinpoint the dominant frequency components

where the signal most closely matches the sinusoidal basis, with each peak’s height quantifying that component’s strength.

2) Signal Environment Analysis:

Beyond individual peaks, the overall distribution reveals the signal’s distinct characteristics and noise floor,

providing a comprehensive profile of the signal’s quality and its operational environment.

3) Phase Information:

The FFT result contains both magnitude and phase information.

While the spectrum focuses on magnitude to show frequency strength,

the phase components are vital for Doppler analysis and will be covered in detail in later sections.

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4. Radar Application

In radar systems, the FFT is the core engine used to extract vital physical information.

While Range FFT identifies a target’s range and Doppler FFT estimates its velocity.

As the most fundamental signal processing framework, its principles are inherited by and integrated into nearly all advanced radar algorithms.