Not sure if this is the right forum for this kind of question.

I was looking at some of the SDR block diagrams out there, and I notice that some of the design, after the ADC, it uses Hilbert filter to perform the 90 degree phase shift, and at the same time, on the other branch it uses Delay 32 Tap to compensate for the delay incurred by the processing of the Hilbert filter.

Isn't phase shift 90 degrees the same thing as time delay by 1/4 cycle?

Since ADC samples not just a single frequency, but over a chunk of frequency, I am wondering, while at a single frequency, a phase shift and a time delay may not be different, but how is a phase shift over a wide range of frequency band, not have the same effect as a time delay?

Alas, I just don't get it, if anyone can shed some light on this or direct me to a link that talks about this, that'd be great appreciated.

 

Not sure if this is the right forum for this kind of question.

I was looking at some of the SDR block diagrams out there, and I notice that some of the design, after the ADC, it uses Hilbert filter to perform the 90 degree phase shift, and at the same time, on the other branch it uses Delay 32 Tap to compensate for the delay incurred by the processing of the Hilbert filter.

Isn't phase shift 90 degrees the same thing as time delay by 1/4 cycle?

Since ADC samples not just a single frequency, but over a chunk of frequency, I am wondering, while at a single frequency, a phase shift and a time delay may not be different, but how is a phase shift over a wide range of frequency band, not have the same effect as a time delay?

Alas, I just don't get it, if anyone can shed some light on this or direct me to a link that talks about this, that'd be great appreciated.

Delay and phase shift are definitely related. There are different types of delay. A simple transport delay has the same time delay for all frequencies and it equivalent to a phase shift that is linear with frequency.

Basically, time delay is measured in units of time, and phase shift is an angle, but if you are careful to specify either properly, they are basically giving the same information, in a slightly different form.

 

Thanks for the quick reply. But I am still a little confused. How can it be the same when we are dealing with quadrature modulation? where the I and Q branch out to be 90 degrees apart?

If Q branch is using Hilbert to perform the 90 degree shift, and the I has a time delay to compensate for process time done by the Hilbert transform, how do they keep 90 degrees apart?

 

Maybe I should try re-word my question.

In a quadrature modulation, if the Q branch is using Hilbert to perform the 90 degree shift, and the I has a time delay to compensate for process time done by the Hilbert transform, between the Hilbert transformation and the time delay, how do they keep 90 degrees apart?

Here's an example of SDR architecture I was looking at

http://www.simplecircuits.com/files/Download/SimpleSDR_Receiver_Manual.pdf

page 5 shows the block diagram of the RF receiver. On the second row is a Hilbert Transformer which is an All Pass Filter but shifts the phase by 90 degrees, and a delay block.

On page 10 second paragraph down it says the delay block is only there to compensate for the delays incurred by the processing of the Hilbert filter.

But how can it be the same when we are dealing with quadrature modulation? where the I and Q branch out to be 90 degrees apart?

If Q branch is using Hilbert to perform the 90 degree shift, and the I has a time delay to compensate for process time done by the Hilbert transform, how do they keep 90 degrees apart?

 

But how can it be the same

I didn't say they are the same. I'm saying that they are related and encode the same information.

If you consider linear systems, to keep in simple, then for every frequency component we can say that θ=ω δt, where θ is the phase shift (in radians), ω is the frequency in rad/s, and δt is the delay time.

Any real input signal to a system can be represented as an arbitrary sum of input sinusoids of various frequencies, and the system will operate on each frequency component to change the phase shift (or delay), and the amplitude.
Hence, to fully describe a system, you can either specify the frequency dependence of delay, or the frequency dependence of the phase shift. One also specifies the frequency dependence for the amplitude response, as well.

As I said, the simple case of a transport delay has constant time delay for all frequencies. Using the above formula, one can say that the phase shift is θ=ω δt where δt is a constant value (independent of frequency). Clearly, the phase shift is not a constant, but is instead a linear function of frequency. Hence, this proves that they are not the same thing at all, but it's clear that if you know one, you can determine the other.

If you still have questions about quadrature modulation, or the Hilbert transform, you might want to make a separate thread with a proper title for that. There are people here that know quite a bit about those subjects, and a separate thread will allow them to get drawn to help you.

 

Don't forget you can only phase shift by up to 2π at which point you get back to where you started.

You can introduce rather more time delay in the time domain.

So for instance a guitar phase shifter can delay the sound signal by a max λ/γ,
where is the sound wavelength and γ is the sound velocity

But a spring line or charge coupled unit can introduce as much delay as desired.

 

In a quadrature modulation, if the Q branch is using Hilbert to perform the 90 degree shift, and the I has a time delay to compensate for process time done by the Hilbert transform, between the Hilbert transformation and the time delay, how do they keep 90 degrees apart?

Well, the 90 degree phase shift is different than the time delay for process time compensation.

The time delay is the same time delay for all frequencies (to a good approximation in your bandwidth).

The Hilbert transform is the same 90 degree phase shift for all frequencies (to a good approximation in your bandwidth).

Clearly, the time delay has linear phase shift with frequency, and the Hilbert transform has inverse 1/w time delay with frequency.

I'm not sure what your question is exactly. Hopefully you can see that the Hilbert transform is a mathematical computation that takes time to execute by a processor. If this time is not compensated for, then the phase shift will not be 90 degrees, as desired.

 

It's really just a matter of time. If two signals are less than a wavelength different in time, it's easier to measure the phase shift. If you have two signals separated by long delays...such as radar pulses, the time delay is more relevant.

Hope this helps a bit.

Eric

 

Phase shift is any change that occurs in the phase of one quantity, or in the phase difference between two or more quantities.

A time delay relay is a relay that stays on for a certain amount of time once activated. This time delay relay is made up of a simple adjustable timer circuit which controls the actual relay. The time is adjustable from 0 to about 20 seconds with the parts specified. The current capacity of the circuit is only limited by what kind of relay you decide to use.
http://en.wikipedia.org/wiki/Phase_(waves)#cite_note-Ballou2005-0

 

Let's look at some sinewaves.

At 1MHz,a time delay of 250nS is equivalent to a phase delay of 90 degrees.

At 2MHz the same delay is equivalent to a phase delay of 180 degrees.

At 4MHz.it is equivalent to a phase delay of 360 degrees----but wait! that takes us back to the beginning of the measurement at 0 degrees.

All of the above sinewaves are delayed by the same time interval,but it may be seen that the phase delay increases with frequency,until 360 degrees is reached for any particular frequency.

Time delay is absolute,phase delay is relative.