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# Discussion Groups | Comp.DSP | Fractional Fourier Transform

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# Fractional Fourier Transform - calimero - 2012-07-19 08:33:00

```Hi all,

In FrFT module in c++, the input signal have real samples and the output
has complex samples. But I need real output samples. Therefore either I can
take the magnitude of samples or take the real part of the complex output.
But with both ways, I loose the sign of samples or loss on the power of the
signal. I stuck at this point how I can obtain again the input signal after
taking FrFT and inverse FrFT operations?

y= FrFT(input, alpha);
input= IFrFT(y, -alpha);

```
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# Re: Fractional Fourier Transform - Dave - 2012-07-19 09:00:00

```On Jul 19, 8:33 am, "calimero" <1@dsprelated> wrote:
> Hi all,
>
> In FrFT module in c++, the input signal have real samples and the output
> has complex samples. But I need real output samples. Therefore either I can
> take the magnitude of samples or take the real part of the complex output.
> But with both ways, I loose the sign of samples or loss on the power of the
> signal. I stuck at this point how I can obtain again the input signal after
> taking FrFT and inverse FrFT operations?
>
>   y= FrFT(input, alpha);
>   input= IFrFT(y, -alpha);
>

If everything has been coded properly then when you take the IFrFT,
the imaginary components should be negligible and you can just use the
real portion.

Cheers,
Dave
```
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# Re: Fractional Fourier Transform - calimero - 2012-07-19 22:12:00

```Thanks Dave.But why do you think that the imaginary output of inverse FrFT
is negligible (close to zero)? In my case the real and imaginary output
values are close to each other.
```
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# Re: Fractional Fourier Transform - Dave - 2012-07-20 10:44:00

```On Thursday, July 19, 2012 10:12:54 PM UTC-4, calimero wrote:
> Thanks Dave.But why do you think that the imaginary output of inverse FrFT
> is negligible (close to zero)? In my case the real and imaginary output
> values are close to each other.

If you do an operation and then the inverse of that operation, you should get back what you put
in. A simple case is the Fourier Transform.

You said you were after the input signal. If the parameters alpha and -alpha are set correctly
then you will get back pretty much exactly what you put in (except for numerical precision).

However, if you are just choosing the alpha parameters randomly between FrFT and IFrFT then
you'll need both the real and complex part.

You haven't stated what it is you're doing - why do you need only real output samples. The
output of arbitrary FrFT and IFrFt operations is normally going to give you a complex output.

Cheers,
Dave
```
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# Re: Fractional Fourier Transform - Dave - 2012-07-20 11:27:00

```On Friday, July 20, 2012 10:44:23 AM UTC-4, Dave wrote:
> On Thursday, July 19, 2012 10:12:54 PM UTC-4, calimero wrote:
> &gt; Thanks Dave.But why do you think that the imaginary output of inverse FrFT
> &gt; is negligible (close to zero)? In my case the real and imaginary output
> &gt; values are close to each other.
>
> If you do an operation and then the inverse of that operation, you should get back what you
put in. A simple case is the Fourier Transform.
>
> You said you were after the input signal. If the parameters alpha and -alpha are set
correctly then you will get back pretty much exactly what you put in (except for numerical
precision).
>
> However, if you are just choosing the alpha parameters randomly between FrFT and IFrFT then
you&#39;ll need both the real and complex part.
>
> You haven&#39;t stated what it is you&#39;re doing - why do you need only real
output samples. The output of arbitrary FrFT and IFrFt operations is normally going to give you
a complex output.
>
> Cheers,
> Dave

God-damn, I hate the new google groups.
Cheers,
Dave
```
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# Re: Fractional Fourier Transform - Fred Marshall - 2012-07-21 13:56:00

```On 7/19/2012 5:33 AM, calimero wrote:
> Hi all,
>
> In FrFT module in c++, the input signal have real samples and the output
> has complex samples. But I need real output samples. Therefore either I can
> take the magnitude of samples or take the real part of the complex output.
> But with both ways, I loose the sign of samples or loss on the power of the
> signal. I stuck at this point how I can obtain again the input signal after
> taking FrFT and inverse FrFT operations?
>
>    y= FrFT(input, alpha);
>    input= IFrFT(y, -alpha);
>
>
>

Well, without analyzing the heck out of it, I think it's OK to say that
the normal identities apply:

Real input <> complex output

Real, even input <> real, (and even) output.

You didn't say:
"...how I can obtain again the input signal after taking FrFT *then
doing something to get Real numbers* and inverse FrFT operations?"

The one operation is nonlinear .. so you can't.

If you need real output and want to be able to inverse the transform in
the normal way with the normal output result then you have to start with
a Real, Even input.  At least that's the normal case.  I'd not state
that so strongly for the FrFT but I suspect it holds.

After all the transform of a real even transform is also real and even.

Fred

```
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