Linear vs. circular time delay: The DTFT vs. the DFT viewpoint
Delay d (samples)
Window N
Animate
Reset
Signal
Exponential decay
Short pulse
Ramp
Cosine on bin 2
Outside the window
Periodic extension (the DFT view)
Zeros outside the window (the DTFT view: usual linear delay)
Analysis window after the substitution
Samples that wrap round
Magnitudes |Y
k
| vs |X
k
|
Phase change per bin
Space: animate / pause. Left and right arrows: d − 1 / d + 1.