Conversion of data to complex numbers??

Hi,

I have a question regarding complex numbers in FFT.

I used an ADC to convert an analogue signal to a digital signal and
send it to the computer through the parallel port. It is a 8-bit ADC.

When i got the data inside the computer, how do I change it into a
complex number? Can anyone advise me on how to deal with this problem?

Another thing is about the N-points. How do i determine the N-points of
a signal? Is it N=8 because the input signal is a 8-bit signal?

Please advise and guide me. Thanks

"ooi_yw" <yuwei_1712@hotmail.com> wrote in message
news:1136309904.904078.6310@g49g2000cwa.googlegroups.com...
> Hi,
>
> I have a question regarding complex numbers in FFT.
>
> I used an ADC to convert an analogue signal to a digital signal and
> send it to the computer through the parallel port. It is a 8-bit ADC.
>
> When i got the data inside the computer, how do I change it into a
> complex number? Can anyone advise me on how to deal with this problem?

Hi yuwei

Changing your data into a complex number depends on what kind of data you
have sampled using your ADC.
Based on your question, it appears that you are confused on how to perform
an FFT on the sampled data. With this in mind, your data can be considered
the real part of a complex number x = a + ib where a is the real part and b
is the imaginary part.
So you can create complex numbers x(n) = a(n) + i*b(n) where all the b(n)=0
and a(n) is your data.

Most fft routines should be able to directly deal with real data as input
and output a complex number in the frequency domain. But if you'd rather
keep things straight forward, you can use my suggestions of setting your
imaginary numbers to 0 and creating the complex values.

> Another thing is about the N-points. How do i determine the N-points of
> a signal? Is it N=8 because the input signal is a 8-bit signal?

No, the bit width (in your case 8) has nothing to do with the length of your
FFT (N).
You have to decide the size/length of your FFT based on how much frequency
resolution you need. The frequency resolution will be fs/N where fs is the
sampling frequency of your data.

There are plenty of tutorials on the web on FFTs which you can find by
googling. I highly recommend that you study some of these tutorials to
understand what you are doing a little better.

Cheers
Bhaskar

"ooi_yw" <yuwei_1712@hotmail.com> wrote in message
news:1136309904.904078.6310@g49g2000cwa.googlegroups.com...
> Hi,
>
> I have a question regarding complex numbers in FFT.
>
> I used an ADC to convert an analogue signal to a digital signal and
> send it to the computer through the parallel port. It is a 8-bit ADC.
>
> When i got the data inside the computer, how do I change it into a
> complex number? Can anyone advise me on how to deal with this problem?

Hi yuwei

Changing your data into a complex number depends on what kind of data you
have sampled using your ADC.
Based on your question, it appears that you are confused on how to perform
an FFT on the sampled data. With this in mind, your data can be considered
the real part of a complex number x = a + ib where a is the real part and b
is the imaginary part.
So you can create complex numbers x(n) = a(n) + i*b(n) where all the b(n)=0
and a(n) is your data.

Most fft routines should be able to directly deal with real data as input
and output a complex number in the frequency domain. But if you'd rather
keep things straight forward, you can use my suggestions of setting your
imaginary numbers to 0 and creating the complex values.

> Another thing is about the N-points. How do i determine the N-points of
> a signal? Is it N=8 because the input signal is a 8-bit signal?

No, the bit width (in your case 8) has nothing to do with the length of your
FFT (N).
You have to decide the size/length of your FFT based on how much frequency
resolution you need. The frequency resolution will be fs/N where fs is the
sampling frequency of your data.

There are plenty of tutorials on the web on FFTs which you can find by
googling. I highly recommend that you study some of these tutorials to
understand what you are doing a little better.

Cheers
Bhaskar

"ooi_yw" <yuwei_1712@hotmail.com> wrote in message
news:1136309904.904078.6310@g49g2000cwa.googlegroups.com...
> Hi,
>
> I have a question regarding complex numbers in FFT.
>
> I used an ADC to convert an analogue signal to a digital signal and
> send it to the computer through the parallel port. It is a 8-bit ADC.
>
> When i got the data inside the computer, how do I change it into a
> complex number? Can anyone advise me on how to deal with this problem?

Hi yuwei

Changing your data into a complex number depends on what kind of data you
have sampled using your ADC.
Based on your question, it appears that you are confused on how to perform
an FFT on the sampled data. With this in mind, your data can be considered
the real part of a complex number x = a + ib where a is the real part and b
is the imaginary part.
So you can create complex numbers x(n) = a(n) + i*b(n) where all the b(n)=0
and a(n) is your data.

Most fft routines should be able to directly deal with real data as input
and output a complex number in the frequency domain. But if you'd rather
keep things straight forward, you can use my suggestions of setting your
imaginary numbers to 0 and creating the complex values.

> Another thing is about the N-points. How do i determine the N-points of
> a signal? Is it N=8 because the input signal is a 8-bit signal?

No, the bit width (in your case 8) has nothing to do with the length of your
FFT (N).
You have to decide the size/length of your FFT based on how much frequency
resolution you need. The frequency resolution will be fs/N where fs is the
sampling frequency of your data.

There are plenty of tutorials on the web on FFTs which you can find by
googling. I highly recommend that you study some of these tutorials to
understand what you are doing a little better.

Cheers
Bhaskar

"Bhaskar Thiagarajan" <bhaskart@deja.com> wrote in message 
news:43bab8ef$0$15791$14726298@news.sunsite.dk...
> "ooi_yw" <yuwei_1712@hotmail.com> wrote in message
> news:1136309904.904078.6310@g49g2000cwa.googlegroups.com...
...........

> You have to decide the size/length of your FFT based on how much frequency
> resolution you need. The frequency resolution will be fs/N where fs is the
> sampling frequency of your data.
>

Or, similarly, the resolution may be based on how many samples you have 
available.

As Bhaskar said, the frequency resolution will be fs/N where fs is the 
sampling frequency of your data and N is the number of samples that you will 
transform .....

So, if all you have are K samples, the time epoch spanned by those samples 
is K*(1/fs) and the frequency resolution will be the reciprocal of the time 
epoch 1/[K*(1/fs)] = fs/K.
(and, of course, for the transform you compute, N=K)

Fred

Bhaskar Thiagarajan wrote:

> "ooi_yw" <yuwei_1712@hotmail.com> wrote in message
> news:1136309904.904078.6310@g49g2000cwa.googlegroups.com...
> 
>>Hi,
>>
>>I have a question regarding complex numbers in FFT.
>>
>>I used an ADC to convert an analogue signal to a digital signal and
>>send it to the computer through the parallel port. It is a 8-bit ADC.
>>
>>When i got the data inside the computer, how do I change it into a
>>complex number? Can anyone advise me on how to deal with this problem?
> 
> 
> Hi yuwei
> 
> Changing your data into a complex number depends on what kind of data you
> have sampled using your ADC.
> Based on your question, it appears that you are confused on how to perform
> an FFT on the sampled data. With this in mind, your data can be considered
> the real part of a complex number x = a + ib where a is the real part and b
> is the imaginary part.
> So you can create complex numbers x(n) = a(n) + i*b(n) where all the b(n)=0
> and a(n) is your data.
> 
> Most fft routines should be able to directly deal with real data as input
> and output a complex number in the frequency domain. But if you'd rather
> keep things straight forward, you can use my suggestions of setting your
> imaginary numbers to 0 and creating the complex values.
> 
> 
>>Another thing is about the N-points. How do i determine the N-points of
>>a signal? Is it N=8 because the input signal is a 8-bit signal?
> 
> 
> No, the bit width (in your case 8) has nothing to do with the length of your
> FFT (N).
> You have to decide the size/length of your FFT based on how much frequency
> resolution you need. The frequency resolution will be fs/N where fs is the
> sampling frequency of your data.
> 
> There are plenty of tutorials on the web on FFTs which you can find by
> googling. I highly recommend that you study some of these tutorials to
> understand what you are doing a little better.
> 
> Cheers
> Bhaskar


What is an "imaginary signal" in a "physical reality" context?

I'm of *PRAGMATIC* engineer mindset - if works then use ;)

I am reasonable comfortable representing a function as k*e^(jWt+phi) 
rather than (a*sin(wt+omega)).

But I'm sure I'm missing something in world of forward/inverse fouier 
transforms.

Get the idea I'm not sure even on how to form the question?
I'm missing something fundamental (and probably trivial).
[we *WILL* ignore question of what mathematician defines as trivial;]

Bhaskar Thiagarajan wrote:

> "ooi_yw" <yuwei_1712@hotmail.com> wrote in message
> news:1136309904.904078.6310@g49g2000cwa.googlegroups.com...
> 
>>Hi,
>>
>>I have a question regarding complex numbers in FFT.
>>
>>I used an ADC to convert an analogue signal to a digital signal and
>>send it to the computer through the parallel port. It is a 8-bit ADC.
>>
>>When i got the data inside the computer, how do I change it into a
>>complex number? Can anyone advise me on how to deal with this problem?
> 
> 
> Hi yuwei
> 
> Changing your data into a complex number depends on what kind of data you
> have sampled using your ADC.
> Based on your question, it appears that you are confused on how to perform
> an FFT on the sampled data. With this in mind, your data can be considered
> the real part of a complex number x = a + ib where a is the real part and b
> is the imaginary part.
> So you can create complex numbers x(n) = a(n) + i*b(n) where all the b(n)=0
> and a(n) is your data.
> 
> Most fft routines should be able to directly deal with real data as input
> and output a complex number in the frequency domain. But if you'd rather
> keep things straight forward, you can use my suggestions of setting your
> imaginary numbers to 0 and creating the complex values.
> 
> 
>>Another thing is about the N-points. How do i determine the N-points of
>>a signal? Is it N=8 because the input signal is a 8-bit signal?
> 
> 
> No, the bit width (in your case 8) has nothing to do with the length of your
> FFT (N).
> You have to decide the size/length of your FFT based on how much frequency
> resolution you need. The frequency resolution will be fs/N where fs is the
> sampling frequency of your data.
> 
> There are plenty of tutorials on the web on FFTs which you can find by
> googling. I highly recommend that you study some of these tutorials to
> understand what you are doing a little better.
> 
> Cheers
> Bhaskar


What is an "imaginary signal" in a "physical reality" context?

I'm of *PRAGMATIC* engineer mindset - if works then use ;)

I am reasonable comfortable representing a function as k*e^(jWt+phi) 
rather than (a*sin(wt+omega)).

But I'm sure I'm missing something in world of forward/inverse fouier 
transforms.

Get the idea I'm not sure even on how to form the question?
I'm missing something fundamental (and probably trivial).
[we *WILL* ignore question of what mathematician defines as trivial;]

Bhaskar Thiagarajan wrote:

> "ooi_yw" <yuwei_1712@hotmail.com> wrote in message
> news:1136309904.904078.6310@g49g2000cwa.googlegroups.com...
> 
>>Hi,
>>
>>I have a question regarding complex numbers in FFT.
>>
>>I used an ADC to convert an analogue signal to a digital signal and
>>send it to the computer through the parallel port. It is a 8-bit ADC.
>>
>>When i got the data inside the computer, how do I change it into a
>>complex number? Can anyone advise me on how to deal with this problem?
> 
> 
> Hi yuwei
> 
> Changing your data into a complex number depends on what kind of data you
> have sampled using your ADC.
> Based on your question, it appears that you are confused on how to perform
> an FFT on the sampled data. With this in mind, your data can be considered
> the real part of a complex number x = a + ib where a is the real part and b
> is the imaginary part.
> So you can create complex numbers x(n) = a(n) + i*b(n) where all the b(n)=0
> and a(n) is your data.
> 
> Most fft routines should be able to directly deal with real data as input
> and output a complex number in the frequency domain. But if you'd rather
> keep things straight forward, you can use my suggestions of setting your
> imaginary numbers to 0 and creating the complex values.
> 
> 
>>Another thing is about the N-points. How do i determine the N-points of
>>a signal? Is it N=8 because the input signal is a 8-bit signal?
> 
> 
> No, the bit width (in your case 8) has nothing to do with the length of your
> FFT (N).
> You have to decide the size/length of your FFT based on how much frequency
> resolution you need. The frequency resolution will be fs/N where fs is the
> sampling frequency of your data.
> 
> There are plenty of tutorials on the web on FFTs which you can find by
> googling. I highly recommend that you study some of these tutorials to
> understand what you are doing a little better.
> 
> Cheers
> Bhaskar


What is an "imaginary signal" in a "physical reality" context?

I'm of *PRAGMATIC* engineer mindset - if works then use ;)

I am reasonable comfortable representing a function as k*e^(jWt+phi) 
rather than (a*sin(wt+omega)).

But I'm sure I'm missing something in world of forward/inverse fouier 
transforms.

Get the idea I'm not sure even on how to form the question?
I'm missing something fundamental (and probably trivial).
[we *WILL* ignore question of what mathematician defines as trivial;]

Bhaskar Thiagarajan wrote:

> "ooi_yw" <yuwei_1712@hotmail.com> wrote in message
> news:1136309904.904078.6310@g49g2000cwa.googlegroups.com...
> 
>>Hi,
>>
>>I have a question regarding complex numbers in FFT.
>>
>>I used an ADC to convert an analogue signal to a digital signal and
>>send it to the computer through the parallel port. It is a 8-bit ADC.
>>
>>When i got the data inside the computer, how do I change it into a
>>complex number? Can anyone advise me on how to deal with this problem?
> 
> 
> Hi yuwei
> 
> Changing your data into a complex number depends on what kind of data you
> have sampled using your ADC.
> Based on your question, it appears that you are confused on how to perform
> an FFT on the sampled data. With this in mind, your data can be considered
> the real part of a complex number x = a + ib where a is the real part and b
> is the imaginary part.
> So you can create complex numbers x(n) = a(n) + i*b(n) where all the b(n)=0
> and a(n) is your data.
> 
> Most fft routines should be able to directly deal with real data as input
> and output a complex number in the frequency domain. But if you'd rather
> keep things straight forward, you can use my suggestions of setting your
> imaginary numbers to 0 and creating the complex values.
> 
> 
>>Another thing is about the N-points. How do i determine the N-points of
>>a signal? Is it N=8 because the input signal is a 8-bit signal?
> 
> 
> No, the bit width (in your case 8) has nothing to do with the length of your
> FFT (N).
> You have to decide the size/length of your FFT based on how much frequency
> resolution you need. The frequency resolution will be fs/N where fs is the
> sampling frequency of your data.
> 
> There are plenty of tutorials on the web on FFTs which you can find by
> googling. I highly recommend that you study some of these tutorials to
> understand what you are doing a little better.
> 
> Cheers
> Bhaskar


What is an "imaginary signal" in a "physical reality" context?

I'm of *PRAGMATIC* engineer mindset - if works then use ;)

I am reasonable comfortable representing a function as k*e^(jWt+phi) 
rather than (a*sin(wt+omega)).

But I'm sure I'm missing something in world of forward/inverse fouier 
transforms.

Get the idea I'm not sure even on how to form the question?
I'm missing something fundamental (and probably trivial).
[we *WILL* ignore question of what mathematician defines as trivial;]

Richard Owlett wrote:
> Bhaskar Thiagarajan wrote:
>
> > "ooi_yw" <yuwei_1712@hotmail.com> wrote in message
> > news:1136309904.904078.6310@g49g2000cwa.googlegroups.com...
> >
> >>Hi,
> >>
> >>I have a question regarding complex numbers in FFT.
> >>
> >>I used an ADC to convert an analogue signal to a digital signal and
> >>send it to the computer through the parallel port. It is a 8-bit ADC.
> >>
> >>When i got the data inside the computer, how do I change it into a
> >>complex number? Can anyone advise me on how to deal with this problem?
> >
> >
> > Hi yuwei
> >
> > Changing your data into a complex number depends on what kind of data you
> > have sampled using your ADC.
> > Based on your question, it appears that you are confused on how to perform
> > an FFT on the sampled data. With this in mind, your data can be considered
> > the real part of a complex number x = a + ib where a is the real part and b
> > is the imaginary part.
> > So you can create complex numbers x(n) = a(n) + i*b(n) where all the b(n)=0
> > and a(n) is your data.
> >
> > Most fft routines should be able to directly deal with real data as input
> > and output a complex number in the frequency domain. But if you'd rather
> > keep things straight forward, you can use my suggestions of setting your
> > imaginary numbers to 0 and creating the complex values.
> >
> >
> >>Another thing is about the N-points. How do i determine the N-points of
> >>a signal? Is it N=8 because the input signal is a 8-bit signal?
> >
> >
> > No, the bit width (in your case 8) has nothing to do with the length of your
> > FFT (N).
> > You have to decide the size/length of your FFT based on how much frequency
> > resolution you need. The frequency resolution will be fs/N where fs is the
> > sampling frequency of your data.
> >
> > There are plenty of tutorials on the web on FFTs which you can find by
> > googling. I highly recommend that you study some of these tutorials to
> > understand what you are doing a little better.
> >
> > Cheers
> > Bhaskar
>
>
> What is an "imaginary signal" in a "physical reality" context?
>
> I'm of *PRAGMATIC* engineer mindset - if works then use ;)
>
> I am reasonable comfortable representing a function as k*e^(jWt+phi)
> rather than (a*sin(wt+omega)).
>
> But I'm sure I'm missing something in world of forward/inverse fouier
> transforms.
>
> Get the idea I'm not sure even on how to form the question?
> I'm missing something fundamental (and probably trivial).
> [we *WILL* ignore question of what mathematician defines as trivial;]

The imaginary number system is, in the context of physics, convenient.
It is not necessarily "true" in any sense and the imaginary part does
not
necessaarily "mean" anything, but it does simplify the arithmetic.

To daw a parallel, the ancient Greeks and Romans lived in the same
physical world as we do, the same laws of both physics and maths
that are valid today were valid then. The Romans and Greeks did
discover lots of stuff relevant to modern day maths and physics, but
they
did not invent mathematical physics. Kepler and Gallileo did that.

Now, why did a society (well, two) that fostered an Archimedes, a
Pythagoras, a Ptolemaios,  that built tunnels through mountains and
aquaducts across valleys and so on, not come close to mathemathical
physics? Because they lacked the arithmetics. I don't know what number
system the Greeks used, but the Roman number system is all but
useless to do even the simplest arithmetics beyond trivial indexing.

The fact that the same number can be written in several ways, e.g.
MIM and MDCCCLXXXXIX are both representations of the same
number (if I got the L=50 and D=500 right...), 1999 in our notation.
Such a trivial detail makes it all but impossible to develop a
useful arithmetic.

So the complex numbers are useful arithmetical tools that make
life a lot easier. What mathemathical physics is concerned,
I believe it is best to leave the question there.

Rune