discrete frequency domain sample

When a 4 point DFT of a time domain signal x(n) is calculated,

1) I am assuming that each sample represents equivalent value (probably
called spectrum) in frequency domain
2) As the sample value increases, the frequency it represents also
increases

I have one question though - a sample in frequency domain basically implies
a single point in a complex plane (as specified by magnitude and angle).
So, I am confused as to how this translates (or represents) into frequency
of any sort. Somehow, I am not getting a complete picture.

On Mon, 08 Aug 2011 08:52:34 -0500, "manishp"
<manishp.p18@n_o_s_p_a_m.gmail.com> wrote:

>When a 4 point DFT of a time domain signal x(n) is calculated,
>
>1) I am assuming that each sample represents equivalent value (probably
>called spectrum) in frequency domain
>2) As the sample value increases, the frequency it represents also
>increases
>
>I have one question though - a sample in frequency domain basically implies
>a single point in a complex plane (as specified by magnitude and angle).
>So, I am confused as to how this translates (or represents) into frequency
>of any sort. Somehow, I am not getting a complete picture.


The phase of the frequency coefficient is with respect to the basis
function for that coefficient (i.e., in the case of a DFT it is a
complex exponential/sinusoid).   If you shift the window of the DFT in
time a little bit, or shift the phase of the basis function, the phase
of the frequency coefficient will shift accordingly.


Eric Jacobsen
http://www.ericjacobsen.org
http://www.dsprelated.com/blogs-1//Eric_Jacobsen.php

On Mon, 08 Aug 2011 08:52:34 -0500, manishp wrote:

> When a 4 point DFT of a time domain signal x(n) is calculated,
> 
> 1) I am assuming that each sample represents equivalent value (probably
> called spectrum) in frequency domain
> 2) As the sample value increases, the frequency it represents also
> increases
> 
> I have one question though - a sample in frequency domain basically
> implies a single point in a complex plane (as specified by magnitude and
> angle). So, I am confused as to how this translates (or represents) into
> frequency of any sort. Somehow, I am not getting a complete picture.

A four-point DFT isn't going to give you a very rich "frequency domain" 
representation.  You're getting DC, half Nyquist, and Nyquist.  That's 
hardly "frequency domain" at all.

What are you really trying to do, and why -- perhaps we can suggest a 
method that will get you there.

-- 
www.wescottdesign.com

manishp wrote:

> When a 4 point DFT of a time domain signal x(n) is calculated,
> 
> 1) I am assuming that each sample represents equivalent value (probably
> called spectrum) in frequency domain
> 2) As the sample value increases, the frequency it represents also
> increases
> 
> I have one question though - a sample in frequency domain basically implies
> a single point in a complex plane (as specified by magnitude and angle).
> So, I am confused as to how this translates (or represents) into frequency
> of any sort. Somehow, I am not getting a complete picture.

manishp <manishp.p18@n_o_s_p_a_m.gmail.com> wrote:

> When a 4 point DFT of a time domain signal x(n) is calculated,

> 1) I am assuming that each sample represents equivalent value (probably
> called spectrum) in frequency domain
> 2) As the sample value increases, the frequency it represents also
> increases

> I have one question though - a sample in frequency domain basically 
> implies a single point in a complex plane (as specified by 
> magnitude and angle).   So, I am confused as to how this translates 
> (or represents) into frequency of any sort. Somehow, I am not 
> getting a complete picture.

It is hard to see with only four points, but not so hard at 128,
or even down to 32.

Sample a sine wave with a period of 32 at points from 0 to 31.
You can even draw one on graph paper, and connect the dots.

Now, graph a sine wave with a period of 32/33.  That is, 33
cycles over the interval of 0 to 32, at the same points,
and plot it on the same graph.

It still works at four, though harder to see.

-- glen

On Mon, 08 Aug 2011 08:52:34 -0500, "manishp"
<manishp.p18@n_o_s_p_a_m.gmail.com> wrote:

Hi,

>When a 4 point DFT of a time domain signal x(n) is calculated,
>
>1) I am assuming that each sample represents equivalent value (probably
>called spectrum) in frequency domain

What does the phrase 'equivalent value mean'? 

>2) As the sample value increases, the frequency it represents also
>increases

What do you mean by 'sample value'?

>I have one question though - a sample in frequency domain basically implies
>a single point in a complex plane (as specified by magnitude and angle).
>So, I am confused as to how this translates (or represents) into frequency
>of any sort. Somehow, I am not getting a complete picture.

Do *NOT* think of frequency-domain samples as 
points on a complex plane, or else you will 
confuse yourself

There must be a hundred web sites that provide 
tutorial information regarding the discrete 
Fourier transform (DFT).  Start visiting those 
web sites.  

By the way, 4-point DFTs are interesting in the 
sense that they can be performed without the need 
for multiplication.

[-Rick-]

Rick Lyons <R.Lyons@_bogus_ieee.org> wrote:
(snip)
> Do *NOT* think of frequency-domain samples as 
> points on a complex plane, or else you will 
> confuse yourself

(snip)
> By the way, 4-point DFTs are interesting in the 
> sense that they can be performed without the need 
> for multiplication.

If you are interested in minimizing multiplication,
look at the ICT.  (Integer Cosine Transform) 
It was designed to run on the CDP1802 processor.
(The inverse transform is more complicated.)

-- glen

On 8/8/2011 6:52 AM, manishp wrote:
> When a 4 point DFT of a time domain signal x(n) is calculated,
>
> 1) I am assuming that each sample represents equivalent value (probably
> called spectrum) in frequency domain
> 2) As the sample value increases, the frequency it represents also
> increases
>

Why when the amplitude increases, the frequency increases?

Thank you all once again for the comments and the feedback.
I have put few clarification below ...

>On 8/8/2011 6:52 AM, manishp wrote:
>> When a 4 point DFT of a time domain signal x(n) is calculated,
>>
>> 1) I am assuming that each sample represents equivalent value (probably
>> called spectrum) in frequency domain
>> 2) As the sample value increases, the frequency it represents also
>> increases
>>
>
>Why when the amplitude increases, the frequency increases?

[Tim Wescott]
A four-point DFT isn't going to give you a very rich "frequency domain" 
representation.  You're getting DC, half Nyquist, and Nyquist.  That's 
hardly "frequency domain" at all.

What are you really trying to do, and why -- perhaps we can suggest a 
method that will get you there.
[manishp] I am mainly trying to understand the basics of frequency domain
representations. I saw this particular example (4-point DTFT) in Proakis
book and hence my question.

[Rick Lyons ]
What do you mean by 'sample value'?
[manishp] Maybe I am not using the right formal terms but what I meant is
that each sample in frequency domain represents a particular frequency
component that makes up the time domain behavior.

[Nasser M. Abbasi ]
Why when the amplitude increases, the frequency increases?
[manishp] No. What I meant is that as the frequency domain sample increases
X(1) compared to X(0), it represents a higher frequency (compared to X(0))

On 8/8/2011 9:30 AM, Tim Wescott wrote:
> On Mon, 08 Aug 2011 08:52:34 -0500, manishp wrote:
>
>> When a 4 point DFT of a time domain signal x(n) is calculated,
>>
>> 1) I am assuming that each sample represents equivalent value (probably
>> called spectrum) in frequency domain
>> 2) As the sample value increases, the frequency it represents also
>> increases
>>
>> I have one question though - a sample in frequency domain basically
>> implies a single point in a complex plane (as specified by magnitude and
>> angle). So, I am confused as to how this translates (or represents) into
>> frequency of any sort. Somehow, I am not getting a complete picture.
>
> A four-point DFT isn't going to give you a very rich "frequency domain"
> representation.  You're getting DC, half Nyquist, and Nyquist.  That's
> hardly "frequency domain" at all.
>
> What are you really trying to do, and why -- perhaps we can suggest a
> method that will get you there.
>

Tim,

I would have said:

DC, fs/4 fs/2 and 3fs/4 'cause I don't know what "Nyquist" means in this 
context and yet I'm sure it doesn't mean 3fs/4!

Fred