Therefore, any other frequency, no matter the amplitude, won't interfere or degrade original wave in the DSP frequency domain systems?

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    $\begingroup$ I'm voting to close this question as off-topic because because this is physics or electrical engineering, not signal processing. $\endgroup$ – Marcus Müller Feb 23 '17 at 14:59
  • $\begingroup$ Also, you already got an answer to the underlying physical question on electronics.stackexchange.com/questions/286185/…. DSP is really just Math. You can write down any equation involving a discrete signal and call it DSP, including an equation that breaks or upholds a non-interfering condition. $\endgroup$ – Marcus Müller Feb 23 '17 at 15:01

This is a question where theory and practice will diverge somewhat.


I assume that by "frequencies" you mean sinusoids of varying frequency. In that case, yes, you're correct, for any amplitudes $a_1$ and $a_2$ and frequencies $f_1$ and $f_2$ (where $f_1 \ne f_2$), the signals

$$ x_1(t) = a_1e^{j2\pi f_1 t} \\ x_2(t) = a_2e^{j2\pi f_2 t} $$

are orthogonal to one another. The exact meaning of orthogonal varies from context to context, but in this sense, you can take it to mean that you could isolate the two signals from one another. If you had infinite time and infinite resources (and perhaps the ability to bend physics to your will if you want to realize it in hardware), you could build a filter that would pass $x_1(t)$ and eliminate $x_2(t)$, or vice versa. In theory.

In our theoretical utopia, the relative amplitudes of $x_1(t)$ and $x_2(t)$ don't matter either. Your theoretical processor can have unlimited dynamic range and/or numeric precision, so having one really large and one really small sinusoid isn't a problem.


Practical systems are hamstrung by several limitations that can invalidate the above claims. Among them:

  • If $f_1$ is really close to $f_2$, it can be difficult to resolve them as two separate sinusoidal components. If you were trying to do so digitally using short-time Fourier analysis, for example, you need a longer observation time in order to properly separate the two frequencies in your spectral estimate.

    Another similar way of looking at it: if $f_1$ and $f_2$ are close to one another, and you wanted to build a filter that would pass one and eliminate the other, you would need a filter with a very sharp transition band. It can be shown that, qualitatively, the width of a filter's transition band is inversely proportional to its overall delay. So, as your transition band gets smaller and smaller, the delay required to implement the filter gets larger and larger. Furthermore, such a sharp transition band would require higher- and higher-order filters, possibly beyond the point of being practically realizable.

  • Practical systems do not have unlimited dynamic range. There will be some finite ratio between the maximum and minimum amplitudes that a system can reliably measure. This can limit your ability to resolve sinusoids that have widely-varying amplitudes, even if their frequencies are far apart. A very strong signal can desensitize your observer to the point where you can't see smaller signals.

    Try shining a bright flashlight and a small LED at your face at the same time. Even if they are comfortably spread apart in space, you'll have a hard time seeing the LED due to the bright flashlight; your visual system has limited dynamic range.

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  • $\begingroup$ Aha, this is where I get confused. Because I'm trying to marry the theory with real life practice, and although I do get the typical answer of "no" interference, research shows, there are issues which still cause problems, and are outside the frequency match!. Thank you for this explanation $\endgroup$ – Rain Feb 23 '17 at 15:08

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