# Bandwidth and frequency domain Hello. I have one question to solve, but I have no idea about calculating bandwidth and converting time domain into frequency domain.

Can you give me a hint?

• Decompose the pictured signal into sinusoids, for a start. Jun 19, 2017 at 1:20
• You should be able to rule out one of the options for (b) immediately. If not, you have quite a bit of studying to do. Jun 19, 2017 at 2:22
• the correct one in b) should jump right out of the picture by counting humps although none of the graphs are exactly to any correct scale. Although we often describe filters by -3dB BW with some slope beyond this but it with appears this waveform and spectrum have limited harmonics so it must have a brick slope cuttoff LP filter which must be the answer expected Jun 19, 2017 at 2:57

You have to think about what sine waves would make that waveform, if combined with the right amplitude and phase.

Assuming f0 is the fundamental signal frequency of 1kHz (1ms period) if it had no harmonics it would look like this:- Now add 3f0 (3kHz) with the same phase but 30% amplitude, and you get this:- Notice how the humps are going up and down at 3f0. Still not there yet...

Finally, add 5f0 (5kHz) at 30% amplitude:- Bingo! We have a match. The correct answer must be the middle graph because it is the only one with f0, 3f0, and 5f0.

The bandwidth is the range from lowest to highest frequency which is present in the signal, in this case 1kHz to 5kHz = 4kHz.

Bandwidth is simply the frequency range of your signal.

Look at the time domain signal, you can easily see that it contains signal that is summation of signals of at-least 2 frequencies.If your signal has some Dc component (avg value =/= 0), then you will have some magnitude at 0 Hz frequency as well. That's all for a hint ;).

Signal Chain Explorer produces this with this harmonic-level setup 