Mathematically based method to increase bandwidth of ADC

That's just what LeCroy is doing, but with a separate ADC (actually, a bank of interleaved ADCs) per band.

John

I'm going to explain it in a practical way so some of you understand.

Lets suppose you have a signal s(t),

you apply a LP filter on s(t) to get s_0(t) = LP(s(t))

You construct another signal s_1(t) = BP(s(t) - s_0(t)).

The idea is that we now have subtracted those frequencies that are in s_0(t) out of s_1(t) since they are already in s_0(t). This is true because the fourier transform is linear. (BP = Band pass and means to filter the signal appropriately)

In general,

s_k(t) = BP(s(t) - s_(k-1)(t))

The problem is that each s_k(t) has higher and higher frequency bands... but each of them is disjoint..

| |---|---|---| | 1 | 2 | 3 |... | | | | |---------------

The numbers represent the bands and the frequency range of the function s_k. Each band is disjoint from any others(just show here all together).

so the bandwidth of s_(k+1) is disjoint from s_k but right next to it but in higher frequency.

This is in effect exactly what I've done. Nothing special.

Now, the "trick" is to use the fact that we can shift the bands all into the lowest frequency range(or any range we want)..

so we have the frequencies for s_k,

| |---| | k | | | |---------------

(but notices this doesn't mean s_k = s_(k+1) but just that they both have the same bandwidth)

Now we can use ADC(s)'s that have the bandwidth to sample the s_k's. Once we do this we will have there "digital" versions and we can then "unshift" the functions back to there original locations, i.e.,

| |---|---|---| | 1 | 2 | 3 |... | | | | |---------------

and then just sum all the functions back up to get the original s(t).

------ I just made this up at the moment so I'm not sure if its mathematically solid. The above equations seem to work but are not like the original convolution I had before. (although I think it might be the same but is simplified).

------

I wrote a new post that explains my method in terms like this(its very similar)... I'm not sure if they are doing what I said or not but it sounds similar.

yeah, I think the interleaved method is the same. By delaying the signal slightly you are, in effect, picking up higher frequencies(relative to the first)... the longer the delay the lower the frequencies you get. Because a "low frequency" won't be able to change fast enough between two consecutive samples as it would in 3. I'm not sure the math behind it but I think its very similar to what I'm doing if one were able to represent it mathematically(basicaly instead of shifting the frequency spectrums you are shifting the clock... but they are equivilent mathematically)

There are two methods currently in use - one is old and the other is new.

The old method is temporal (or time) interleaving in which multiple digitizers are "interleaved". This method is utilized to increase the effective sample rate of the digitizer and often can increase the memory length in a scope (since usually an individual digitizer drives its own memory). The amount of interleaving ranges from 160 digitizers running at 125 Ms/s to

12 in Agilent scopes to 16 digitizers running at 1.25 Gs/s in Tek Scopes. You will not find individual digitizing elements running much above 1.5 Gs/s, so anything faster is time interleaved (this is for real-time digitizers - don't get confused with equivalent time or sampling scopes which behave completely differently). While interleaving seems easy, it is very difficult in that that the frequency response of each digitizer must be matched precisely.

The new method is one which shifts frequencies. This method has the added advantage of increasing bandwidth. The following white paper explains this for the layman.

The frequency shifting method has been used successfully in the development of an 11 GHz, 40 Gs/s scope (the LeCroy SDA 11000) and an 18 GHz, 60 Gs/s scope (the LeCroy SDA 18000) which is the fastest real-time waveform digitizer on the planet.

There are many issues with the development of such an instrument. No one would attempt such a design without the DSP capability to recover and "fix" the waveform after running the gauntlet of the microwave circuitry required to separate, downconvert and acquire the waveforms. LeCroy has this expertise and is the world expert in waveform processing and analysis.

The phase is affected by the local oscillator used for the mixing action and the phase of the local oscillator must be known or recovered in order to accomplish the desired result - something you might not have considered. Additionally, the sharp filters utilized create quite a bit of phase distortion at the band edges that must be corrected.

search the patent and publication database at

for more details.

P.S. Don't believe all of the Tek stories - they'll tell you they invented everything - especially if you're in the market for a scope :)

Pete Pupalaikis