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I am getting a bit confused about fps (frame rate) in a video.

I build a video (using python and opencv) using 600 frames and I specify 10 fps.

However I want to also record the timestamps for each frame in a text file. If the time for the first frame is 0 ns what would be the time stamp for the second frame provided the values I gave above?

EDIT:

About my confusion. If we have 10 frames with 0.1 difference we have

|     |   |    |    |    |    |    |    |    |
-------------------------------------------------------------
0   0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9

As you can see the time for the 10 frames is not one second but less so fps would not be 10 fps

|      |     |     |    |     |     |    |     |    |
-------------------------------------------------------------
0   0.11  0.22  0.33  0.44  0.56  0.67  0.78  0.89  1

Wouldn't this be the correct calculation?

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  • $\begingroup$ Given the frame-rate FPS, then the duration between the frames is: $\Delta T = 1/FPS$ and the n-th frame is at time $t_n = (n-1)*\Delta T$, where $n = 1,2,...,N$ having $N = 600$ total frames $\endgroup$
    – Fat32
    Commented May 10, 2022 at 11:49
  • $\begingroup$ I get very confused by this. Shouldn't it be 1/(FPS-1)? Because if not the N frames will have a difference less than FPS $\endgroup$
    – KansaiRobot
    Commented May 11, 2022 at 7:37
  • $\begingroup$ For your convenience, if you have 10 frames at 10 FPS, then the 10th frame will be at: $t_{10} = (n-1) \times \Delta T = (10-1) \times (1/10) = 0.9 $ s, where $\Delta T = 1/FPS = 1/10 = 0.1 s$.. And if there would be any 11th frame, it would be at 1.0 s... So if there are N frames in the interval [ 0 , T ] s , then your frame rate is FPS = (N-1)/T . (your first figure is correct) $\endgroup$
    – Fat32
    Commented May 11, 2022 at 11:07

1 Answer 1

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Python implementation:

import numpy as np

frames = 600
# frames per seconds
fps = 10 
# sampling time in seconds
t_s = np.arange(600) / fps
# sampling time in nano-seconds
t_ns = t_s * (10**9)

Regarding the confusion related to the duration, the problem is that the sampling does not start at $t=0$, where the first sample takes place. If you consider that the sampling starts at $t=-\frac{1}{F_s}$ then it would all make sense.

Please do not neglect the integration time, which is part of the sampling process. For example, in the attached figure the sampling starts at $t=0$ but the first sample is at $t=\frac{1}{F_s}$. enter image description here

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  • $\begingroup$ that 600 should be frames right? (in t_s calculation) $\endgroup$
    – KansaiRobot
    Commented May 11, 2022 at 6:55
  • $\begingroup$ I run this script. My only doubt is that if I substact t_ns[599] from t_ns[0] it gives me 59900000000.0 which divided by 10**9 gives me 59.9. Shouldn't it be 60? $\endgroup$
    – KansaiRobot
    Commented May 11, 2022 at 7:02

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