Problem 5

The procedure for interpolation or upsampling by an integer factor N can be thought of as the cascade of two operations. The first operation, involving system A, corresponds to inserting N-1 zero-sequence values between each sequence value of , so that

For exact band-limited interpolation, is an ideal lowpass filter.

(a) Determine whether or not system A is linear.

(b) Determine whether or not system A is time variant.

(c) For as sketched in the figure and with N = 3, sketch.

(d) For N = 3, as in the figure, and appropriately chosen for exact band-limited interpolation, sketch .