[hpsdr] Call for Comments and Discussion - OzyII

[jeff millar]

Alberto I2PHD wrote:
> ***** High Performance Software Defined Radio Discussion List *****
>
> jeff millar wrote:
>>
>> Linrad uses a series of FFT's to break down a 96 KHz sample stream 
>> into SSB or CW bandwidths. The size of the FFTs depends the bandwidth 
>> of the incoming sample stream. For a wide band SDR, the size of the 
>> FFT will grow and the processing power also grows by what's called "N 
>> log(N)".
>
> You don't need a series of FFTs to reduce the bandwidth....
> You can just do a downconversion (lowpass filtering + decimation)
> on the time domain signal. Using FFTs to do that is not much
> computationally efficient.
>
> This is how it is done in Winrad, and it works. In Winrad the FFTs
> are used only for the visual aspects of the program (apart from the
> final bandpass filtering, done with the overlap-and-save technique).
Certainly FIR filters work. But FFT based filters have an advantage over 
FIR filters when the number of FIR coefficients becomes large. Two 
filter requirement drive the number of taps required, the skirt 
selectivity and the stop band attenuation. Skirt selectivity is 
expressed as a fraction of the sample rate, so the required number of 
taps rises with the sample rate through the filter. This mean that FIR 
computational load grows as N squared because both the rate of 
multiplications and the quantity of multiplications grows linearly with 
sample rate. FFT based filters only grow a N log2(N) vs sample rate.

If we design an SDR with high bandwidth between the SDR and the PC, then 
it more likely that an FFT based filtering scheme will have better 
performance than an FIR based approach.

FFTs have a number of practical advantages as well. Since it's a common 
algorithm, the code becomes highly optimized. New technologies focus on 
the FFT as a core building block. The new 4G wireless networks will all 
use OFDMA modulation protocol based on FFTs. The new OpenCL (and similar 
computational accelerators) have the FFT as the baseline implemetation
http://en.wikipedia.org/wiki/OpenCL

Another problem with FIR and decimation based filtering approaches turns 
up in practical implementations of DSP for high dynamic range radios. 
Each decimation looks like another mixer with opposite sideband 
rejection to worry about. That means that each of the decimation filters 
needs about 100 dB of stop band attenuation to keep up with the rest of 
the high dynamic range radio. High stop band attenuation requires more 
taps or cascading of several filters. It also require more numerical 
precision...making fixed point implementations less practical. FFT based 
algorithms can work on the entire bandwidth without decimation.

As an aside, an interesting alternative to FFT based filters for narrow 
band signals seems to be Frequency Sampling Filters described in Richard 
Lyons book, "Understanding Digital Signal Processing", Chapter 7. Those 
filters can provide excellent skirt selectivity and full tunability in 
frequency and bandwidth for signals much narrower than the sampled 
bandwidth.

jeff, wa1hco

> 73 Alberto I2PHD


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