# Can a Fourier Transform be used to 'limit' the amplitude of a signal?

I never got a chance to study Fourier Transforms in school. What I do know about them (which isn't much) I have gleaned from the web. I understand that you can transform any periodic signal between the time domain and the frequency domain. So here's my question:

I have a periodic signal in the time domain:

$$f(t) = \\ \frac{6 (Sin[t] + 5/16 Sin[3 t] + 3/20 Sin[5 t] + 1/16 Sin[7 t])}{\pi} \\ + \frac{4 (Sin[2 t] + 5/16 Sin[6 t] + 3/20 Sin[10 t] + 1/16 Sin[14 t])}{\pi} \\ - 3/2$$

If you graph this function you can see it oscillates between a max value of about 1 to a min value of about -4.

Is there a way I can use a Fourier Transform to reduce or limit the amplitude of this signal between -1 and 1 ?

In my mind the steps of this may look something like:

• Step 1: Transform time-based signal f(t) to frequency-based signal $g(f)$.
• Step 2: apply some function to $g(f)$
• Step 3: use inverse transform of $g(f)$ (that has had limiter function applied) to get $f'(t)$

Now all $f'(t)$ values are between -1 and 1 (for example).

Thanks a lot for any education/enlightenment you could pass along.

• But why not just multiply the function in the time domain by some function that limits the amplitude e.g 1/4? – Graham Hesketh Mar 26 '14 at 20:11
• You could use a filter in the frequency domain to cut off some harmonics ($\sin(m\phi)$ terms) if that is what you are thinking of but that wont directly correspond to a specific effect on the amplitude... – Graham Hesketh Mar 26 '14 at 20:13