Sampling & Reconstruction of Sparse Multiband Signals

1. Sampling & Reconstructionof Sparse Multiband Signals Performed by: Eli Sorin Zvika Shirazi Supervisor: Michael Yampolsky Characterization Presentation Spring 2009

2. Background • As technology advances, processing of wider band signals is required. • The Bad News: Sampling the signals at Nyquist rate is impractical even by the best existing ADCs. • The Good News: Manmade radio signals are often sparse (multiband model).

3. Let’s see more specifically what the problems are: • There are techniques for sampling wide band sparse signals but … • Non uniform sampling (multi-coset) • Non blind signal • Time shifts are used in the algorithms • All existing ADCs have built in LPFs

4. A research of Prof. Yonina C.Eldar and Mr. Moshe Mishali proposes a solution to the problem…

5. The system Sampling Block Reconstruction Block Mathematical Algorithm Sampling Block h(t) . . . . . . x(t) x(t) y(t) h(t) h(t)

6. System components • pi(t) - random periodic mixing functions. • h(t) - Low Pass Filter • Low rate samplers (ADCs). • Reconstruction Algorithm

7. The Idea In General • The sampling block constructs a matrix A that operates on the signal: y(t)=Ax(t) • The reconstruction block - • Reconstructs the support S of x out of A and y. • Now, Using S, A can be inverted and x reconstructedas in the non-blind case.

8. Does it work ?

9. So far, algorithm’s correctness was proven by numerical experiments

10. What is the next step?

11. Implement the system: • Prove Practicability • Hardware Acceleration

12. Mathematical Algorithm Our project goal Analog Block Sampling & Reconstruction device Sampling Block h(t) . . . . . . x(t) x(t) h(t) h(t)

13. Our project goal Implement the reconstruction algorithm: • Phase 1: by software (C++) • Phase 2: by hardware

14. Schedule

15. Good Luck!