Spectrum analyzer block in Simulink - Time & Space Complexity

Time Complexity: Spectrum analyzer block

O(n)

Understanding Time Complexity

We want to understand how the time needed to analyze a signal changes as the signal size grows when using the Spectrum analyzer block.

How does the processing time grow when the input signal gets longer or more detailed?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

% Simulink Spectrum Analyzer block setup
spectrumAnalyzer = dsp.SpectrumAnalyzer('SampleRate', Fs, 'SpectrumType', 'Power density');

for k = 1:numFrames
    frame = inputSignal((k-1)*frameSize+1 : k*frameSize);
    spectrumAnalyzer(frame);
end
    

This code sends frames of the input signal to the Spectrum analyzer block to compute and display the power spectrum for each frame.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Computing the spectrum for each frame of the input signal.
• How many times: Once per frame, so the number of frames depends on the input signal length divided by frame size.

How Execution Grows With Input

As the input signal gets longer, the number of frames increases, so the Spectrum analyzer runs more computations.

Input Size (n)	Approx. Operations
10,000 samples	About 100 frames (if frame size is 100), so 100 spectrum computations
100,000 samples	About 1,000 frames, so 1,000 spectrum computations
1,000,000 samples	About 10,000 frames, so 10,000 spectrum computations

Pattern observation: The total work grows roughly in direct proportion to the input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to analyze the signal grows linearly as the input size increases.

Common Mistake

[X] Wrong: "The Spectrum analyzer processes the entire signal all at once, so time does not depend on input size."

[OK] Correct: The analyzer processes the signal frame by frame, so more input means more frames and more processing time.

Interview Connect

Understanding how processing time grows with input size helps you explain performance in real signal processing tasks confidently and clearly.

Self-Check

"What if we changed the frame size to be twice as large? How would the time complexity change?"