1 / 20

2. Multirate Signals

2. Multirate Signals. Content. Sampling of a continuous time signal Downsampling of a discrete time signal Upsampling (interpolation) of a discrete time signal. Sampling: Continuous Time to Discrete Time. Time Domain:. Frequency Domain:. Reason:. same. same. Antialiasing Filter.

sven
Download Presentation

2. Multirate Signals

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 2. Multirate Signals

  2. Content • Sampling of a continuous time signal • Downsampling of a discrete time signal • Upsampling (interpolation) of a discrete time signal

  3. Sampling: Continuous Time to Discrete Time Time Domain: Frequency Domain:

  4. Reason: same same

  5. Antialiasing Filter Anti-aliasing Filter sampled noise noise For large SNR, the noise can be aliased, … but we need to keep it away from the signal

  6. Example Anti-aliasing Filter 1. Signal with Bandwidth 2. Sampling Frequency 3. Attenuation in the Stopband Filter Order: slope

  7. Downsampling: Discrete Time to Discrete Time Keep only one every N samples:

  8. Effect of Downsampling on the Sampling Frequency The effect is resampling the signal at a lower sampling rate.

  9. Effect of Downsampling on the Frequency Spectrum We can look at this as a continuous time signal sampled at two different sampling frequencies:

  10. Effect of Downsampling on DTFT Y(f) can be represented as the following sum (take N=3 for example):

  11. Effect of Downsampling on DTFT Since we obtain:

  12. Downsampling with no Aliasing If bandwidth then Stretch!

  13. Antialiasing Filter In order to avoid aliasing we need to filter before sampling: LPF LPF noise aliased

  14. Example LPF Let be a signal with bandwidth sampled at Then Passband: Stopband: LPF

  15. See the Filter: Freq. Response… h=firpm(20,[0,1/22, 9/44, 1/2]*2, [1,1,0,0]); passband stopband 2f

  16. … and Impulse Response

  17. Upsampling: Discrete Time to Discrete Time it is like insertingN-1 zeros between samples

  18. Effect of Upsampling on the DTFT “ghost” freq. “ghost” freq. it “squeezes” the DTFT Reason:

  19. Interpolation by Upsampling and LPF LPF LPF

  20. SUMMARY: LPF LPF LPF LPF

More Related