Any methods to compress frequency/bandwidth?

[kel8157]

Assume a wifi signal with bw of 20MHz, after RF mixer and LPF, you get an intermediate signal from o to 20MHz..
Is it possible to compress that 20MHz BW signal into a 10MHz BW.. (I dont mean half band filtering with 10MHz)..
And how?

And is it a very stupid question?

 

[Ow@i$]

No question is stupid!!!
BTW why you need to compress??

 

[kel8157]

When one compresses the bandwidth, one can reduce sampling rate and processing speed I assume.
I used Wifi as an example.

 

[Mityan]

I think you cant do that. Your signal band depends on channel symbol rate but not on sampling rate of your ADC.
When you reduce channel symbol rate twice you get a halfband signal.
To preserve initial data rate you may increase your signal constellation dimension (e.g. 16QAM instead of QPSK) but this requires greate SNR.
Or use an input data compression, but you cant perform a lossless compression on a random bit stream.

 

[kel8157]

I think you cant do that. Your signal band depends on channel symbol rate but not on sampling rate of your ADC.
When you reduce channel symbol rate twice you get a halfband signal.
To preserve initial data rate you may increase your signal constellation dimension (e.g. 16QAM instead of QPSK) but this requires greate SNR.
Or use an input data compression, but you cant perform a lossless compression on a random bit stream.

I understand there are different bit rates for Wifi.
Maybe I should not have mentioned Wifi as example, rephrase my question.

Assume that I sample a downconverted/bandlimited RF from ADC, and it contains 5MHz, 8MHz, 9MHz.
Are there any digital operation which can convert them into 2.5MHz, 4MHz and 4.5MHz?
Are there any analog circuit which can do the conversion before ADC?

 

[Mityan]

Assume that I sample a downconverted/bandlimited RF from ADC, and it contains 5MHz, 8MHz, 9MHz.
Are there any digital operation which can convert them into 2.5MHz, 4MHz and 4.5MHz?
Are there any analog circuit which can do the conversion before ADC?

If you mean 5,8 and 9 are bandwidths - the answer was NOT.
The spectrum and time series are just two sides, two representations of one process.
You cant compress or expand the signal in frequency domain without influencing time domain and vice-versa.

 

[kel8157]

If you mean 5,8 and 9 are bandwidths - the answer was NOT.
The spectrum and time series are just two sides, two representations of one process.You cant compress or expand the signal in frequency domain without influencing time domain and vice-versa.

I see. Assume there are 3 tones of that frequency.
As for the two representations of one process, that is the answer I believe.

 

[Mityan]

For the purpose to reduce sampling rate that you claimed above you may take the band from 5 to 9 MHz, not from 0 to 9 and that will give the reduction of processing speed. For 3-tone signal you cant shift that frequencies the way you wish.

 

[W_Heisenberg]

compress the BW means you need to think this in freq domain.

that is you first need to do a fourier transform, x(t) -> X(jw)

now you will have a X(jw), now you want half of the bandwidth of this thing. That means you want to compress the w by a factor of 2, this can be done by downsampling in freq domain by 2. In such way, you will obtain a uniformly modified signal. Then you can inverst FT to get the signal in time domain, say x'(t).

You do not need to shift the freq in this situation, since since after all you will inverst FT it.

 

[kel8157]

For the purpose to reduce sampling rate that you claimed above you may take the band from 5 to 9 MHz, not from 0 to 9 and that will give the reduction of processing speed. For 3-tone signal you cant shift that frequencies the way you wish.

compress the BW means you need to think this in freq domain.

that is you first need to do a fourier transform, x(t) -> X(jw)

now you will have a X(jw), now you want half of the bandwidth of this thing. That means you want to compress the w by a factor of 2, this can be done by downsampling in freq domain by 2. In such way, you will obtain a uniformly modified signal. Then you can inverst FT to get the signal in time domain, say x'(t).

You do not need to shift the freq in this situation, since since after all you will inverst FT it.

Thanks.
Are there any analog circuit which can do the trick?

 

[Mityan]

Just provide the band of interest to fit the nyquist zone (any, not the 1st exactly) and provide an analog antialiasing filter at ADC input

 

[W_Heisenberg]

Just provide the band of interest to fit the nyquist zone (any, not the 1st exactly) and provide an analog antialiasing filter at ADC input

i am not sure whether we can do anolog downsampling thing, usually we have to do this in digital field. Like first ADC it, and then DAC back.

The reason behind this I think is that anolog is more like time domain thing, thus to build a anolog circuit for the purpose of downsampling seems not reasonable.

Obviously all digital circuits built from analog, thus finally I think we can still say it is a analog circuit. However, it is not the pure analog, which means discrete value for voltage but not quantized ones.

In such way, there is really not meaningful to build such "analog" circuit. It is reconmended you buy the ADC and DAC, or even a PIC to do such job.

I am not sure whether my statement make any sense here. Yet hope it could help a bit.

 

[FvM]

Downsampling is a method to reduce signal bandwidth by discarding part of the total information in the in put signal, preferably the unwanted part or just noise. If the bandwitdh of the original is significant, there's no way to keep the signal information during downsampling.

Generally, bandwidth of a modulated signal can be traded against signal-to-noise ratio. In most cases, this requires demodulation and re-modulation. In a few special cases, it might be possible to strip of redundant bandwidth. E.g. one side band of DSB AM, at cost of more demodulation effort. But similar options don't exist for optomized digital modulation schemes.

 

[Mityan]

i am not sure whether we can do anolog downsampling thing, usually we have to do this in digital field. Like first ADC it, and then DAC back.

The reason behind this I think is that anolog is more like time domain thing, thus to build a anolog circuit for the purpose of downsampling seems not reasonable.

Obviously all digital circuits built from analog, thus finally I think we can still say it is a analog circuit. However, it is not the pure analog, which means discrete value for voltage but not quantized ones.

In such way, there is really not meaningful to build such "analog" circuit. It is reconmended you buy the ADC and DAC, or even a PIC to do such job.

I am not sure whether my statement make any sense here. Yet hope it could help a bit.

I'm not sure that I understood a single word from your post, sorry.
Sampling is a digitizing process. After sampling there is a digital domain. And antialiasing fiter at the ADC input is always analog.
If kel8157 has a strong wish to reduce sample rate he can do it by narrowing the band of interest (by the way this leads to the adequate losses in SNR (i.e. processing gain)).
For example having the upper tone of 9 MHz one should sample at 18 MHz at least (even more in practice). But for a set of known frequencies of 5,7 and 9 MHz - they all get into 2nd nyquist zone for 9.5 MHz sample rate (band from 4.75 to 9.5). This is the sample rate reduction - this three tone signal may be sampled at 9.5 instead of 18.

 

[W_Heisenberg]

I'm not sure that I understood a single word from your post, sorry.
Sampling is a digitizing process. After sampling there is a digital domain. And antialiasing fiter at the ADC input is always analog.
If kel8157 has a strong wish to reduce sample rate he can do it by narrowing the band of interest (by the way this leads to the adequate losses in SNR (i.e. processing gain)).
For example having the upper tone of 9 MHz one should sample at 18 MHz at least (even more in practice). But for a set of known frequencies of 5,7 and 9 MHz - they all get into 2nd nyquist zone for 9.5 MHz sample rate (band from 4.75 to 9.5). This is the sample rate reduction - this three tone signal may be sampled at 9.5 instead of 18.

He wants an analog circuit to do the sampling, if you know, plz tell us the circuit then.

How to exactly build one? i.e. with input and output?

 

[FvM]

I see two problems with the thread
- the question is still vague
- we have to distinguish between the principle feasibility to perform analog pre-processing and an implementation with reasonable effort

Referring to this problem "specification"

Assume that I sample a downconverted/bandlimited RF from ADC, and it contains 5MHz, 8MHz, 9MHz.

And supplementing this clarification

Assume there are 3 tones of that frequency.

You can e.g. downconvert it with 6 MHz LO to 1,2 and 3 MHz signals. Presuming a high-level mixer, there won't be considerable second order IM products. So you can reduce the sample rate respectively. The problem is that there must be no interfering signal that alias to the signal frequencies during down convert. If you can't guarantee this without analog filtering, the "reasonable effort" point can't be achieved.

Another option is to run an overampling ADC at 6 MS/s.