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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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Presentation Transcript
slide2

Content

  • Sampling of a continuous time signal
  • Downsampling of a discrete time signal
  • Upsampling (interpolation) of a discrete time signal
slide3

Sampling: Continuous Time to Discrete Time

Time Domain:

Frequency Domain:

slide4

Reason:

same

same

slide5

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

slide6

Example

Anti-aliasing Filter

1. Signal with Bandwidth

2. Sampling Frequency

3. Attenuation in the Stopband

Filter Order:

slope

slide7

Downsampling: Discrete Time to Discrete Time

Keep only one every N samples:

slide8

Effect of Downsampling on the Sampling Frequency

The effect is resampling the signal at a lower sampling rate.

slide9

Effect of Downsampling on the Frequency Spectrum

We can look at this as a continuous time signal sampled at two different sampling frequencies:

slide10

Effect of Downsampling on DTFT

Y(f) can be represented as the following sum (take N=3 for example):

slide12

Downsampling with no Aliasing

If bandwidth then

Stretch!

slide13

Antialiasing Filter

In order to avoid aliasing we need to filter before sampling:

LPF

LPF

noise

aliased

slide14

Example

LPF

Let be a signal with bandwidth

sampled at

Then Passband:

Stopband:

LPF

slide15

See the Filter: Freq. Response…

h=firpm(20,[0,1/22, 9/44, 1/2]*2, [1,1,0,0]);

passband

stopband

2f

slide17

Upsampling: Discrete Time to Discrete Time

it is like insertingN-1 zeros between samples

slide18

Effect of Upsampling on the DTFT

“ghost” freq.

“ghost” freq.

it “squeezes” the DTFT

Reason:

slide20

SUMMARY:

LPF

LPF

LPF

LPF