Amitava, it is fantastic that you are contributing problems, but you really need to spend more time specifying what the solution should do. The person solving is left needing to guess too much.
Definitely Agree with the cyclist. W/o example it is impossible to understand the task to achieve.
The DC component of a signal is usually its mean. Now filter can have many meanings, but in this case, it means to remove the signal variation.
Which doors are open?
Duplicate each element of a vector.
Do Fast Fourier Transformation
02 - Vector Variables 3
area of an annulus
Multiply a column by a row
Distance walked 1D
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