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*Subject*: Re: [linrad] DSP Question*From*: Alberto di Bene <dibene@xxxxxxxxxxx*Date*: Thu, 29 Apr 2004 14:35:42 +0200

Mark Erbaugh wrote:

Mark,In my case, the IF that I am sampling is at12 kHz. Since this is a real signal the frequencies range from 0 on up.

if the signal is real, it has both the positive and the negative spectrum components.

For an explanation look here :

http://ptolemy.eecs.berkeley.edu/eecs20/week10/negativefreqs.html

or here, starting at mid page :

http://www.qsl.net/dl6iak/projects/iqmodulator.htm

Don't forget that when sampling you have the spectrum cyclically repeated at all the positive and negativeSo now, I have these samples that represent 0 to 24 kHz, and a mirror image at -24 kHz to 0. I digitally mix this with a complex 12 kHz signal. This shifts everything up by 12 kHz so, if I understand it the signal that was at -12 kHz is now at 0 Hz, the signal that was at 12 kHz is now at 24 kHz. My question is what happened to the signal that was at 18 kHz. Adding 12 kHz to it puts it at 30 kHz out of the range of my samples. Also since there was no input signal at - 30 kHz what is now at -18 kHz? I realize that the original 18 kHz signal had a mirror image at -18 kHz that is now shifted up to -6 kHz.

multiples (zero included) of the sampling frequency. I think that, instead of giving a lengthy explanation

in words, it is much more useful if you look at these two pages that I have scanned from the Frerking book

that I mentioned in a previous message. They should clarify the issue.

http://images.i2phd.com/page131.gif

http://images.i2phd.com/page132.gif

However, generating a 12 kHz complex signal for a 48 kHz sample rate wasTo generate a complex NCO signal with millihertz resolution, you can use the routine that you can find

very simple and precise. Since 12 kHz is exactly 1/4 of the sample rate, all

the sin and cos terms became -1, 0 or +1. This wasn't the case with the

10.75 or 13.25 kHz rates.

I'm wondering if (or how) I can simply mix with the 12 kHz signal, do a

complex FFT on the resulting I and Q signals and then somehow "rotate" the

FFT bins to bring the desired signal to 0 Hz? Then could I apply your

technique below of taking the complex conjugate of the signals near zero and

mirroring them to the opposite end (24 kHz)?

in the SDRadio source I sent you.

The technique of shifting the FFT spectrum is much more simple, but has the drawback that the minimum

step is the FFT bin size. which not always is fine enough. Doing a complex mixing requires certainly more

computational resources, but allows arbitrary shift amounts. That NCO routine can easily generate the sin

and cos components of the 10.75 or 13.25 kHz signals that you give as examples.

73 Alberto I2PHD

LINRADDARNIL