Exercise · ZW-SHORT-TIME-FOURIER-TRANSFORM-002 · ★☆☆ Basic
Which variable does the window \( w[n] \) shift over in the STFT definition?
Choose one option.
Show answer
- D. The time \( \tau \)
Explanation
The window shifts in time \( \tau \), which is why the STFT depends on two variables. Shifting in frequency is not what the window does.
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-003 Is the STFT a linear operation with respect to the signal x[n] ?
- 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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