# Time domain representation of colored noise

Started by December 21, 2012
```I understand that the time domain representation of white noise looks like impulses. How do colored noises like brown, pink etc. look like when we perform an inverse Fourier Transform on them ? What could be some sources of colored noise that may affect speech signals? I am currently working on a project that involved removing noise from speech signals. Any help would be greatly appreciated!

--
Prateek B.S
```
```On Fri, 21 Dec 2012 10:37:13 -0800, Prateek B S wrote:

> I understand that the time domain representation of white noise looks
> like impulses.

A flat power distribution doesn't have to look like impulses.  It could,
for example, look like a swept sine wave - which has rather different
time-domain characteristics.  Or any of a number of other waveforms.

If all you have is the power spectrum (which naturally excludes phase
information), you've lost so much that unless you can add some domain-
specific information you're not going to be able to say very much about
the time domain.

There's a classic paper that takes another kind of signal - the FT of a
couple of images, swaps the magnitude and phase information between the
two images (i.e. image A' gets magnitude from image A, but phase from
image B, etc.), and does the inverse FT.  The resulting images are
clearly distorted from the originals, but clearly resemble the image that
their phase information came from, not their magnitudes.

I've never heard of this being done for sound - surely someone must have
tried it.  Anyone know what happens?
```
```On 21/12/2012 19:33, Frank Miles wrote:
..
>
> There's a classic paper that takes another kind of signal - the FT of a
> couple of images, swaps the magnitude and phase information between the
> two images (i.e. image A' gets magnitude from image A, but phase from
> image B, etc.), and does the inverse FT.  The resulting images are
> clearly distorted from the originals, but clearly resemble the image that
> their phase information came from, not their magnitudes.
>
> I've never heard of this being done for sound - surely someone must have
> tried it.  Anyone know what happens?
>

It's a very well known process (indeed discussed in an earlier thread
about the phase vocoder). We usually call it "cross-synthesis", but it
is a form of vocoding using a large number of filters (via the FFT).
Because sound moves through time, we tend to use frequency rather than
phase values, but there are plenty of pvoc implementations that will
stick to using phases. One way of describing it is that the
(time-varying) spectral envelope (magnitudes) of one sound modifies or
fully replaces those of the other input. The effect can be applied with
a  time-varying percentage.

Richard Dobson
```
```On Saturday, December 22, 2012 1:03:54 AM UTC+5:30, cassiope wrote:
> On Fri, 21 Dec 2012 10:37:13 -0800, Prateek B S wrote:
>
>
>
> > I understand that the time domain representation of white noise looks
>
> > like impulses.
>
>
>
> A flat power distribution doesn't have to look like impulses.  It could,
>
> for example, look like a swept sine wave - which has rather different
>
> time-domain characteristics.  Or any of a number of other waveforms.
>
>
>
> If all you have is the power spectrum (which naturally excludes phase
>
> information), you've lost so much that unless you can add some domain-
>
> specific information you're not going to be able to say very much about
>
> the time domain.
>
I am sorry. I should have been a bit more specific in my query. I read an IEEE paper recently that described a technique to remove "impulsive colored noises" by using the Discrete Wavelet Transform. I wanted to know more about the sources of such noise that could affect speech signals and how these kind of noises look like in the time domain.
Thank you for mentioning that a flat power spectrum need not be caused due to impulsive kind of sources only.
```
```On Fri, 21 Dec 2012 19:33:54 +0000, Frank Miles wrote:

> On Fri, 21 Dec 2012 10:37:13 -0800, Prateek B S wrote:
>
>> I understand that the time domain representation of white noise looks
>> like impulses.
>
> A flat power distribution doesn't have to look like impulses.  It could,
> for example, look like a swept sine wave - which has rather different
> time-domain characteristics.  Or any of a number of other waveforms.
>
> If all you have is the power spectrum (which naturally excludes phase
> information), you've lost so much that unless you can add some domain-
> specific information you're not going to be able to say very much about
> the time domain.
>
> There's a classic paper that takes another kind of signal - the FT of a
> couple of images, swaps the magnitude and phase information between the
> two images (i.e. image A' gets magnitude from image A, but phase from
> image B, etc.), and does the inverse FT.  The resulting images are
> clearly distorted from the originals, but clearly resemble the image
> that their phase information came from, not their magnitudes.
>
> I've never heard of this being done for sound - surely someone must have
> tried it.  Anyone know what happens?

If you do it with speech, it sounds like heavily distorted, but
recognizable speech.  In fact, the technique is used in AM and AM-like
(i.e., SSB) transmitters to more effectively communicate with the
available power, at the expense of sounding like a duck with laryngitis.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
```
```Prateek B S <bs.prateek@gmail.com> wrote:

(snip)

> I am sorry. I should have been a bit more specific in my query.
> I read an IEEE paper recently that described a technique to
> remove "impulsive colored noises" by using the Discrete
> Wavelet Transform. I wanted to know more about the sources
> of such noise that could affect speech signals and how
> these kind of noises look like in the time domain.

Hmm. In the pre-CD days, there used to be devices that would
remove the pop noise from vinyl (analog) records. Mostly from
dust and scratches on the surface.

The spectrum is, apparently unique enough to separate from the
rest of the signal.

> Thank you for mentioning that a flat power spectrum need not
> be caused due to impulsive kind of sources only.

-- glen
```
```On Sat, 22 Dec 2012 06:43:49 +0000, glen herrmannsfeldt wrote:

> Prateek B S <bs.prateek@gmail.com> wrote:
>
> (snip)
>
>> I am sorry. I should have been a bit more specific in my query. I read
>> an IEEE paper recently that described a technique to remove "impulsive
>> colored noises" by using the Discrete Wavelet Transform. I wanted to
>> know more about the sources of such noise that could affect speech
>> signals and how these kind of noises look like in the time domain.
>
> Hmm. In the pre-CD days, there used to be devices that would remove the
> pop noise from vinyl (analog) records. Mostly from dust and scratches on
> the surface.
>
> The spectrum is, apparently unique enough to separate from the rest of
> the signal.
>
>> Thank you for mentioning that a flat power spectrum need not be caused
>> due to impulsive kind of sources only.
>
> -- glen

Does it sound like an impulse going through an RIAA filter?

--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com
```
```On Fri, 21 Dec 2012 19:47:48 -0800, Prateek B S wrote:

> On Saturday, December 22, 2012 1:03:54 AM UTC+5:30, cassiope wrote:
>> On Fri, 21 Dec 2012 10:37:13 -0800, Prateek B S wrote:
>>
>>
>>
>> > I understand that the time domain representation of white noise looks
>>
>> > like impulses.
>>
>>
>>
>> A flat power distribution doesn't have to look like impulses.  It
>> could,
>>
>> for example, look like a swept sine wave - which has rather different
>>
>> time-domain characteristics.  Or any of a number of other waveforms.
>>
>>
>>
>> If all you have is the power spectrum (which naturally excludes phase
>>
>> information), you've lost so much that unless you can add some domain-
>>
>> specific information you're not going to be able to say very much about
>>
>> the time domain.
>>
> I am sorry. I should have been a bit more specific in my query. I read
> an IEEE paper recently that described a technique to remove "impulsive
> colored noises" by using the Discrete Wavelet Transform. I wanted to
> know more about the sources of such noise that could affect speech
> signals and how these kind of noises look like in the time domain. Thank
> you for mentioning that a flat power spectrum need not be caused due to
> impulsive kind of sources only.

In general I would expect that something that could be fairly described
as an "impulsive colored noise" would have a sharp rise time to a high
peak, probably a rounded-off tip to the peak, followed by a fall back to
nothing, perhaps with ringing.

BUT

You really should dig into the paper and see if they describe the noise.
Best would be a graph, but a spectrum or (better yet) a Fourier or
Laplace transform of the impulse would be pretty good, and the best you
could do in text rather than graphics.

--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com
```
```Thanks a lot for all the help. Unfortunately the paper does not delve into describing the noise. I hope I get a response when I email the authors.
Thanks again.

--
Prateek B.S
```
```Tim Wescott <tim@seemywebsite.com> wrote:

(snip, I wrote)
>> Hmm. In the pre-CD days, there used to be devices that would remove the
>> pop noise from vinyl (analog) records. Mostly from dust and scratches on
>> the surface.

>> The spectrum is, apparently unique enough to separate from the rest of
>> the signal.

>>> Thank you for mentioning that a flat power spectrum need not be caused
>>> due to impulsive kind of sources only.

> Does it sound like an impulse going through an RIAA filter?

I never bought one, they were pretty expensive for college students.

I think it came between the phone cartridge and preemp, maybe
line level output. So it gets it before the RIAA filter.
But I might have forgotten. It also used to be popular to put
devices in the tape loop. That is, between tape out and tape in.

-- glen
```