Operations on signals -Time Scaling, Down Sampling, Up Sampling, Decimation

Time Scaling
In the sequence x(n) if we replace n with lambda n or say Kn we get a time scaled version of x(n).
Consider K=2 in x(n) = {-4,-3,-2,-1,0,1,2,3,4}
like that we get y(n)={-4,-2,0,2,4}

This efect can be obtained by reducing the sampling rate while sampling from continuous signal x(t). This process of reducing sampling rate is called downsampling.

The other case up-sampling you can think on your own, up-sampling above x(n) with k=1/2 will produce a signal y(n)={-4,0,-3,0,-2,0,-1,0,0,0,1,0,2,0,3,0,4}

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