# Signal frequency

signal frequency!!!

suppose we have a signal varying randomly in amplitude with time...when we plot the frequency responce of this signal , we get a bandwidth of frequencies...My question is ' are all these frequencies present at all times??', or 'at any time , say t=to , only one of these frequencies is present??'...

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I'm not sure how you would quantify the randomness of the amplitude. You can't really throw random numbers in for amplitude or you would get junk. You would need to increase or decrease the amplitude with a "random walk" like process to have anything that looks remotely periodic.

chroot
Staff Emeritus
Gold Member

My question is ' are all these frequencies present at all times??', or 'at any time , say t=to , only one of these frequencies is present??'...
Well, the very concept of frequency is meaningless for intervals of zero time. If all you're considering is a single point in time, an infinity of different signals (with different frequency content) could result in the point you're seeing.

The best you can do is to study a signal over some interval of time, and describe what frequency content is present in that interval. The next interval of time, however, could include totally different frequencies.

- Warren

minger

In my area we deal with discrete functions. Applying the same thinking, I would say that the signal or function can be thought of as an infinte series of sine waves with varying frequencies and amplitudes. While the direct contribution of low or high order sine functions may not be directly prevalent at a specific point in time, t; the function does exist from t0 to t_inf.

Do you have additional information regarding a specific problem?

If your signal is a constant-frequency signal with varying amplitudes (AM modulation), the observed bandwidth is sidebands due to the amplitude modulation. The frequency spread of the sidebands is due to the frequency of the amplitude modulation.

It doesn't seem clear whether the time-varying amplitude varies over the period of the waveform or over the time the signal is produced. If it's over the period of the waveform, the signal can be expressed as a sum of sinusoidal signals, each having amplitudes that do not change with time. If the main signal varies over the time the signal is produced, all of the sinusoidal components will likely all still be present but their amplitudes will change over time.