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This video investigates discrete-time signal time scaling which includes downsampling and upsampling operations.
The time scaled signal y[k] = x[ak] is created by replaced the discrete-time variable k with ak. If a is greater than 1 we downsample the discrete-time signal x[k]. If a is between 0 and 1 we upsample (or expand) the discrete-time signal x[k].
Two different specific examples are worked. We show a downsampling example for the case of a = 2, and we show an upsampling example for the case of a = 1/2. In the upsampling case we also show two different options; either zero-insertion or linear interpolation can be used for the expanded signal values.
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