I am having trouble grasping some of the fundamental concepts of multirate filtering. I see from various sources that the basic building blocks of a multirate filter are the dyadic analysis and synthesis blocks.

Question 1:

The analysis block structure looks like the following, where the wide band signal is split into lowpass and highpass bands, each with a cutoff of FS/4 (Nyquist/2). Each band is then decimated by a factor of 2.

How can you accurately represent the signal in the high frequency band when it contains frequency information above the Nyquist limit of the new decimated sample rate?

Question 2:

The analysis block structure looks like the following, where the sub-band signal is interpolated, re-filtered and then summed.

What is the purpose of the second filtering?

I am having trouble grasping some of the fundamental concepts of multirate filtering. I see from various sources that the basic building blocks of a multirate filter are the dyadic analysis and synthesis blocks.

• Question 1:

The analysis block structure looks like the following, where the wide band signal is split into lowpass and highpass bands, each with a cutoff of FS/4 (Nyquist/2). Each band is then decimated by a factor of 2.

How can you accurately represent the signal in the high frequency band when it contains frequency information above the Nyquist limit of the new decimated sample rate?

• Question 2:

The analysis block structure looks like the following, where the sub-band signal is interpolated, re-filtered and then summed.

What is the purpose of the second filtering?