Exercise · ZW-SHORT-TIME-FOURIER-TRANSFORM-003 · ★☆☆ Basic
Is the STFT a linear operation with respect to the signal \( x[n] \)?
Choose one option.
Show answer
- C. Yes, because it is a weighted sum of samples of \( x[n] \)
Explanation
Each coefficient is a linear weighted sum of samples of \( x[n] \), so the STFT is linear in the signal. Dependence on the window does not break linearity.
Review the concept: Short-time Fourier transform
The short-time Fourier transform (STFT, \( X(\tau,\omega) \)) describes how the frequency content of a signal varies over time using a sliding window.
\[X(\tau,\omega)=\sum_{n} x[n]\,w[n-\tau]\,e^{-j\omega n}\]
More practice problems: short-time fourier transform
- ZW-SHORT-TIME-FOURIER-TRANSFORM-001 What does the squared magnitude of the STFT represent?
- ZW-SHORT-TIME-FOURIER-TRANSFORM-002 Which variable does the window w[n] shift over in the STFT definition?
- ZW-SHORT-TIME-FOURIER-TRANSFORM-004 What type of window is w[n] when it equals 1 on a finite interval and 0 outside?
- ZW-SHORT-TIME-FOURIER-TRANSFORM-005 What is the name of the condition that allows reconstructing the signal from the STFT with adequate…
- ZW-SHORT-TIME-FOURIER-TRANSFORM-006 A signal equals x[n]=cos (2π 0.25 n) for all time. At what normalized frequency does the peak of it…
- ZW-SHORT-TIME-FOURIER-TRANSFORM-007 A window of length L=64 is shifted by hop R=16 . What is the overlap in samples between consecutive…
- ZW-SHORT-TIME-FOURIER-TRANSFORM-008 If the STFT is computed with L=256 and R=128 , what is the approximate redundancy factor relative t…
- ZW-SHORT-TIME-FOURIER-TRANSFORM-009 A 1024-sample signal is analyzed with an STFT of window L=128 and hop R=64 , with no padding. How m…
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