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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.

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2. Multirate Signals

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  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

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