User manual

Code: ENIGMA III User Manual
Edition: 1 Revision: 4
Date: 19/12/2008
Page: 53/97
performs undersampling of the IF signal. Please refer to common literature for further
explanations about bandpass theory and band limited signals.
2. Assuming a IF frequency of 30 MHz the IF sampling frequency (76.8 MHz) fulfills the Nyquist
criterion and there is no frequency folding. The lowpass filter needs to be mixed up to the IF
frequency of 30 MHz.
6.6.3 Computation of a real lowpass filter
The are several methods for the computation of the filter coefficients like for example inverse FFT or the
well known Remez algorithm. We recommend the Remez algorithm which is an iterative optimization
algorithm for the computation of real FIR filter coefficients.
6.6.4 Mixing of the real lowpass filter to a linear phase complex bandpass
filter
coeff
bandpass
 x=coeff
lowpass
 x∗cos 2π
f
center
f
sample
x j sin 2π
f
center
f
sample
x
Example code for the mixing procedure:
centerFreq /= samplingFreq;
for (int i=0; i<numtap; ++i)
{
Complex cFreq( cos( 2.0*M_PI*centerFreq*(i-numtap/2+0.5) ),
sin( 2.0*M_PI*centerFreq*(i-numtap/2+0.5) ));
coeff[i] *= cFreq;
}
with
numtapNumber of coefficients
centerFreq Center frequency (16.8MHz or 30MHz)
SamplingFreq Sampling frequency (76.8MHz)
coeff[] Lowpass filter coefficients
The number of coeffients must fulfill some constrains.
1. It must be a multiple of the given decimation factor. The decimation factor
can be any number in the range [3...32].
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