[hpsdr] FFT latency

[Roger Rehr W3SZ]

Acquisition time and frequency bin width of the FFT'd signal have a 
simple theoretical relationship.  Its determined by Math/Physics. [Those 
of us with Physics degrees would say it comes out of the math that 
describes the physical reality.  Those with Math degrees might say it 
comes out of the math, period].

In any event, acquisition time is simply the inverse of the FFT's 
signal's bin width in Hz:

T = 1 / df
where T is acquisition time and df is bin width of the FFT'd signal in Hz.

Because

df = fs / N
where N = number of bins [number of sample points] and fs = sampling 
frequency,

this can also be expressed as

T = N / fs

This doesn't account for processing time of course; it just accounts for 
the laws of nature.  So no matter how fast your computer, you have a 
minimum necessary delay.  For example:

FFT bin size 1 Hz --> 1 second delay
FFT bin size 10 Hz --> 0.1 second delay
etc.

Faster sampling rates lead to a smaller delay for a given frequency bin 
width.  Processing delay would be added to this theoretical minimum.  
For those of us doing weak signal work with FFT bin widths of less than 
one Hz, our minimum delay is thus a bit more than 1 second.  For those 
of us operating in the weak signal world, this is not a problem;  even 
with non-SDR equipment we use sequencers to go from transmit to receive 
and back that introduce delays typically on the order of 200-500 msec.  
VOX and break-in CW are verboten in our world.

73,

Roger
W3SZ

On 4/5/2015 6:54 AM, G3XJP wrote:
> ***** High Performance Software Defined Radio Discussion List *****
>
> I need your collective wisdom!  Is it not an inescapable fact that any 
> serious FFT in the real-time path between your antenna and your ears 
> must introduce an inherent and inevitable delay that will preclude a 
> conversational VOX/QSK QSO?  I can see that it would not preclude 
> listening to a monologue - or to watching spectral pictures on a 
> display.  But anything more than about 1/5 sec is doomed to feel like 
> Skype on a bad day - where you often end up having to say "over".  As 
> a generality, am I missing something fundamental here?  Peter G3XJP


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