Down sampling, bandpass sampling theorem, downconversion

In summary, the conversation involves the use of bandpass sampling theorem to demodulate AM signals using an ADC. The theorem allows for the reproduction of a bandpass signal with a much lower sampling frequency as long as the sampling frequency is greater than twice the bandwidth. The bandwidth of the ADC must also be at least equal to the frequency of the signal being sampled. Further explanation and understanding of bandpass sampling and DSP may be necessary for a deeper understanding of the topic.
  • #1
FrankJ777
140
6
I'm trying to demodulate simple AM by using an ADC and the bandpass sampling theorem (as I understand it.) The way I understand the theorem is that by sampling a bandpass signal of frequency f[itex]_{0}[/itex] and bandwidth B, where f[itex]_{0}[/itex] >> B, as long as I use a sampling frequency of >2B I can reproduce the signal even though the sampling frequency is much less than f[itex]_{0}[/itex].
From what I've read, to accomplish the bandwidth of the ADC must be at least f[itex]_{0}[/itex]. I'm not sure exactly what this means. Does it only mean the input to the ADC must not attenuate a signal of f[itex]_{0}[/itex]? Or are they referring to the sampling aperture. I see the formula use to demonstrate the concept is m[n] = M(t)δ (t-nTs). But i realize that δ is instantaneous where as a ADC is not, so I'm wondering if the width of my sample needs to be around 1/f[itex]_{0}[/itex]?

If anyone can lend some insight I'd appreciate the help.
Thanks
 
Engineering news on Phys.org
  • #2
FrankJ777 said:
I'm trying to demodulate simple AM by using an ADC and the bandpass sampling theorem (as I understand it.) The way I understand the theorem is that by sampling a bandpass signal of frequency f[itex]_{0}[/itex] and bandwidth B, where f[itex]_{0}[/itex] >> B, as long as I use a sampling frequency of >2B I can reproduce the signal even though the sampling frequency is much less than f[itex]_{0}[/itex].
From what I've read, to accomplish the bandwidth of the ADC must be at least f[itex]_{0}[/itex]. I'm not sure exactly what this means. Does it only mean the input to the ADC must not attenuate a signal of f[itex]_{0}[/itex]?
Yes, that is correct.
FrankJ777 said:
Or are they referring to the sampling aperture. I see the formula use to demonstrate the concept is m[n] = M(t)δ (t-nTs). But i realize that δ is instantaneous where as a ADC is not, so I'm wondering if the width of my sample needs to be around 1/f[itex]_{0}[/itex]?
I don't understand your question.

Bandpass sampling is somewhat sophisticated, and requires different filtration than regular baseband sampling to achieve a good SNR. I fear that a couple of short answers on this forum won't give you a deep enough understanding of sampling, filtration and DSP. Have you had a course in DSP? Do you have a DSP text to read?
 
Last edited:

1. What is down sampling?

Down sampling is the process of reducing the sampling rate of a signal by removing some of the samples. This is commonly done to reduce the amount of data needed for storage or transmission.

2. What is the bandpass sampling theorem?

The bandpass sampling theorem states that in order to accurately reconstruct a signal that has been bandpass sampled (sampled at a rate lower than the Nyquist rate), the signal must be band-limited to less than half of the sampling rate.

3. Why is down sampling necessary?

Down sampling is necessary to reduce the data size of a signal, making it easier to store and transmit. It can also be used to reduce the computational complexity of signal processing algorithms.

4. What is downconversion?

Downconversion is the process of converting a high frequency signal into a lower frequency signal. This is commonly used in radio communication systems to reduce the frequency of the signal for easier transmission and processing.

5. How does down sampling affect signal quality?

Down sampling can reduce the quality of a signal if not done properly. If the sampling rate is too low, important information in the signal may be lost, leading to distortion or loss of fidelity. However, if done correctly, down sampling can have minimal impact on signal quality.

Similar threads

  • Electrical Engineering
Replies
4
Views
708
  • Electrical Engineering
Replies
24
Views
2K
Replies
7
Views
3K
  • Electrical Engineering
Replies
8
Views
12K
  • Electrical Engineering
Replies
6
Views
2K
Replies
9
Views
1K
  • Electrical Engineering
Replies
1
Views
3K
  • Electrical Engineering
Replies
1
Views
4K
  • Electrical Engineering
Replies
1
Views
10K
Replies
6
Views
4K
Back
Top