Downsapling and Upsampling of the DTS

[Eshal]

Hello experts!

I was studying Digital Signal Processing and got confused how the x was downsampled to x(2n) i.e. by factor of 2.

Here is the image of the original and downsampled signal. Kindly tell me how does x(2n) created from x


Also kindly tell me how to get the upsampled signal as shown in the figure below.


And what is meant by this? See below image (red boxed)


Thank you all.

 

[FvM]

It's created by applying the scaling function in the red box.

Or visually:





In other words dropping each second sample in downsampling, inserting zero samples in upsampling.