2. Multirate Signals

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 N3 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
hfirpm(20,0,1/22, 9/44, 1/22, 1,1,0,0)
passband
stopband
2f
16
and Impulse Response
17
Upsampling Discrete Time to Discrete Time
it is like inserting N-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