A qeustion about "mixing down" a freqency

Hi Skfir,

Multiplying two signals to mix down the frequency is right and proper, and it should work fine for you. To provide a more complete answer, let's assume that your incoming 50 KHz signal has some additional frequency components. For example, if it were amplitude modulated with an audio signal at telephone quality (about 3KHz bandwidth), it would have frequency components from 47KHz to 53KHz. Multiplying this with a 50KHz sine wave, the output includes your desired result centered at the difference frequency of 5KHz. It also has a sum component centered at 95KHz, as shown in the "spectral diagram" below:

With the signals you're handling, likely you're running at 192KHz (the fastest a -1701 can do). The corresponding Nyquist frequency is 96KHz -- as you know, above that aliasing (frequency folding) occurs. In the above example with the three KHz baseband limit, the mixed output centered at 95KHz extends to 98KHz, exceeding the Nyquist limit. Base-band components above 1KHz, after mixing, run above 96KHz and are mirrored to the 94-96KHz region, where they compete with the direcly-mixed 95KHz signal. If you needed the 95-KHz signal the aliasing would cause trouble, but since you're only interested in the 5KHz signal, you can filter out the higher-frequency one. Thus, no problem.

To be sure your mixing process works well, you may wish to bandpass filter the incoming 50KHz signal so it contains only the frequency components you're interested in. Low-pass filter the baseband result to eliminate the unwanted sum components. If your output has no useful components below a certain frequency, you can high-pass filter it as well.

Best regards.

Bob

Yes, understand, Thank you Bob!!!

Hi Skfir,

I neglected to describe how multiplying two signals "mixes down" (or up) in frequency. Starting with the two input sinusoidal waves of frequency F1 and F2 respectively:

Wave1 = cos (2 * pi * F1) and

Wave2 = cos (2 * pi * F2)

Multiplying them together, we get:

Wave1 * Wave2 = cos (2 * pi * F1) * cos (2 * pi * F2)

Apply the trigonometric identity: cos (A) * cos (B) = 0.5 * [cos (A-B) + cos (A+B)]

to get:

Wave1 * Wave2 = 0.5 * [cos (2 * pi * (F1 - F2)) + cos (2 * pi * (F1 + F2))]

We recognize the two output terms as sinusoids: one of frequency (F1-F2) -- "the difference frequency", and another of (F1+F2) -- "the sum frequency". Thus, multiplying two waveforms exactly performs the "mix-up" and "mix-down" functions.

Best regards,

Bob

Great! Now I understand completely. Thank you Bob!!