Frequency domain representation of reduced sampling

The frequency domain representation of the subtraction sample can be viewed from two angles:

1. Directly from the original signal point of view, this needless to say, according to the new sampling frequency of the original signal spectrum directly normalized to the digital domain on the line;

2. From the existing spectrum perspective, can be introduced (refer to discrete-time signal processing):

Xd (ejω) = (1/m) Sigma (i, 0:m-1) X (EJ (ω/m-2πi/m))

Xd (ejω) is the new spectrum.

Suppose m=2,

Then the formula is: Xd (ejω) = (a) [X (EJΩ/2) + x (EJ (ω-2π)/2)]

X (EJΩ/2) will be originally in 0,2pi,4pi ... The periodic Spectrum x (ejω) expands and moves to the 0,4pi,8pi ...

X (EJ (ω-2π)/2) will be originally in 0,2pi,4pi ... The periodic Spectrum x (ejω) expands and moves to the 2pi,6pi,10pi ...

So the overall effect is that the original spectrum in 0,2pi,4pi ... Expanded at the same place. This is consistent with angle 1.

Frequency domain representation of reduced sampling