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If I have a signal that looks like v(t) in the image. The signal is a high frequency noise at frequency f1, that repeats with a a lower frequency of f2.

If a low pass filter is applied that attenuates only f1, how can I predict what the output of the filter will look like without simulating?

enter image description here

From a frequency perspective, this is basically a sinusoid of f1 frequency, multiplied by a square wave of f2 frequency. Sinusoid appears as a fixed frequency in the FFT at f1, square wave appears at f2, 3f2, 5f2 harmonics (only fundamental shown)

Is it correct to apply superposition and LTI system theory and consider each frequency independently entering the filter or do I mix the two frequencies (f1* f2, f1* 3f2, etc.) and then enter the filter?

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    \$\begingroup\$ Your FFT graph has f1 and f2 in the wrong positions. Why can't you use a simulator? What order of filter? How can f2 be a square wave? From your images it must have a low duty cycle = not a square wave (strictly speaking). \$\endgroup\$
    – Andy aka
    Commented Jun 22 at 15:27
  • \$\begingroup\$ Note also that f1 is modulated by f2. So, add f1-f2 and f1+f2 at least in the spectrum ... \$\endgroup\$
    – Antonio51
    Commented Jun 22 at 16:10
  • \$\begingroup\$ And if the duty cycle is low ... then you should add f1-n * f2 and f1+n * f2 ... n=1 ... 10 or more ... \$\endgroup\$
    – Antonio51
    Commented Jun 22 at 16:36

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Is it correct to apply superposition and LTI system theory and consider each frequency independently entering the filter or do I mix the two frequencies (f1 f2, f1* 3f2, etc.) and then enter the filter?*

That latter is the correct way. For instance, if we look at a 1 MHz sinewave multiplied by a 100 kHz squarewave that has a duty of 20% we get this: -

enter image description here

And, if you look at its spectrum you will see that sum and differences are produced ranging all the way up to infinity: -

enter image description here

how can I predict what the output of the filter will look like without simulating?

Just to be clear about this, I have used a simulator to show you the input to the filter. I can't simulate the output of the filter because (a) you banned that action and, (b) I don't know what the filter is hence, I can't simulate it.

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