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### How to create a "tone" with wider bandwidth

Posted: **Wed Mar 18, 2015 9:10 pm**

by **irmurray**

Hi folks,

In the Expression Evaluator, I can create a single-frequency tone using an expression such as:

sin(2*pi*f*t)

The spectrum of this would be a peak at a single frequency (left diagram below).

My question is how to create a signal like that on the

*right *- still a single peak but with a

**spread** of frequency components.

I want to create this peak formulaicly, I don't want to filter it from white noise.

Thanks for any suggestions.

Regards,

Iain.

### Re: How to create a "tone" with wider bandwidth

Posted: **Thu Mar 19, 2015 1:17 am**

by **DougDbug**

I think it depends on what you really want... Maybe frequency modulation (under effects in the expression evaluator).

Maybe several tones very-close to the close to the center-frequency with the center-frequency the strongest and the other tones tapering-off as they get farther away.

If you generate multiple frequencies and add them (add the amplitudes, not the frequencies) you'll need to scale-down the amplitudes so they don't sum into clipping (overload distortion).

### Re: How to create a "tone" with wider bandwidth

Posted: **Thu Mar 19, 2015 7:01 am**

by **irmurray**

Hi Doug,

Thanks for your reply.

Maybe several tones very-close to the close to the center-frequency with the center-frequency the strongest and the other tones tapering-off as they get farther away.

Yes, that was my 2nd thought, my first being "is there a simple way to do it with some sort of bandwidth variable" ... I toyed around with random numbers trying to create these other frequency components, but just ended up with a noisy signal. My suspicion is that I'll have to create a lot of side frequency components, but I'll give it a go and see what happens.

Thanks again,

Iain.

### Re: How to create a "tone" with wider bandwidth

Posted: **Thu Mar 19, 2015 3:12 pm**

by **DougDbug**

I don't have much experience with the Expression Evaluator... I'm mostly just used the canned presets.

Random may not work since it's generating the data sample-by-sample... It's not generating "frequencies". so I guess you are just adding randomness (noise) to each sample.

I'm sure it can be done, but I can't "visualize" the math in my head. And I'm too lazy, and my math is too rusty for for me to do it on paper.

### Re: How to create a "tone" with wider bandwidth

Posted: **Thu Mar 19, 2015 3:32 pm**

by **irmurray**

And I'm too lazy, and my math is too rusty for for me to do it on paper.

With you on that one!

Regards,

Iain.

### Re: How to create a "tone" with wider bandwidth

Posted: **Sat Mar 21, 2015 5:28 am**

by **Moonmist**

irmurray wrote:Hi folks,

In the Expression Evaluator, I can create a single-frequency tone using an expression such as:

sin(2*pi*f*t)

The spectrum of this would be a peak at a single frequency (left diagram below).

My question is how to create a signal like that on the

*right *- still a single peak but with a

**spread** of frequency components.

I want to create this peak formulaicly, I don't want to filter it from white noise.

Thanks for any suggestions.

Regards,

Iain.

Code: Select all

`y^cos(2*pi*(f/x)*t)*sin(2*pi*f*t)/y`

f = Frequency (make sure to pay attention to what I said below about x if you want this to be the center frequency.)

y = Amplitude (1 = single frequency tone. numbers above 1 = the higher the number, the louder the spread of frequency components.)

x = Bandwidth (1 = f becomes the fundamental as opposed to the center, and all frequency components are multiples of f. numbers above 1 = the higher the number, the closer the frequency components are together with f. Also the higher y is, the higher x needs to be in order to create symmetry of the frequency components on either side of f. The higher y becomes without raising x, the more lopsided the frequency components will be above f.)

Here are some values to start you out with something, enter the equation I posted above into the Expression Evaluator and enter the variables I'm about to put below. After that check out the Spectrum Visual and see if it looks like what you had in mind (make sure to have the FFT Size high enough to see the peaks good). Here are the variables:

f = 1000

y = 1.5

x = 50

The best way to understand what values are going to do what is to just try different values and observe how it changes the spectrum after each change. I'm no math wiz, I just figured out everything I said above by tinkering around with the variables, so hopefully you'll figure it out as well! Have fun.