I am learning about image processing. Currently, I am reading about upsampling and down sampling. 

Here is some background what I am reading:

I was wondering if someone show me a proof of how equation (70) is true. It simply says "It can be shown that".

Thanks!

3.2 Introduction to Multirate Signal Processing 3.2.1 Definition Consider a discrete-time signal z[n], = 0, 1, 1, . . . , its z-transform is given by Co -CO and its discrete-time Fourier transform (DTFT) is given by Co (65) The quantities Kelu) | and (w) spectrums. are(X(el w)) are called its mangnitude and phase In the time domain, we can perform down-sampling and up-sampling of a discrete- time signal. In down-sampling with a sampling rate of M, we take every -th sample of the input sequence to generate the output sequence, as illustrated in Fig. 10(a). More specifically, the output sequence, denoted bv unl, is given bv (66)