Thread Subject: trying to understand the frequency plot ...

Hi,

Based on a textbook example on DFT, I have plotted magnitude vs frequency response plot. The plot shows bigger magnitude at lower frequency and exponentially decreases as frequency increases.
The time domain equation is: x(n)=(0.5)**n u(n)
This clearly tell me that as time increases, the amplitude decreases. But I am not able to appreciate what the frequency plot of this (exponentially decaying plot) conveys.

Thanks in advance ...

Regards,

sbr487 <sharan.basappa@gmail.com> wrote in message <658738066.3252.1258644775618.JavaMail.root@gallium.mathforum.org>...
> Hi,
>
> Based on a textbook example on DFT, I have plotted magnitude vs frequency response plot. The plot shows bigger magnitude at lower frequency and exponentially decreases as frequency increases.
> The time domain equation is: x(n)=(0.5)**n u(n)
> This clearly tell me that as time increases, the amplitude decreases. But I am not able to appreciate what the frequency plot of this (exponentially decaying plot) conveys.
>
> Thanks in advance ...
>
> Regards,

Can you clarify the time domain equation, I am not sure what the ** means. Do you mean the exponent. Also is there a summation involved here or is it just the single term. Regards Matt

On Nov 20, 4:32 am, sbr487 <sharan.basa...@gmail.com> wrote:
> Hi,
>
> Based on a textbook example on DFT, I have plotted magnitude vs frequency response plot. The plot shows bigger magnitude at lower frequency and exponentially decreases as frequency increases.
> The time domain equation is: x(n)=(0.5)**n u(n)
> This clearly tell me that as time increases, the amplitude decreases. But I am not able to appreciate what the frequency plot of this (exponentially decaying plot) conveys.
>
> Thanks in advance ...
>
> Regards,

What it conveys is that as frequency increases the energy decreases.
In other words, the high frequency components in the DFT become less
and less important, as would be expected for a smoothly decaying
function in the time domain. If the decay in the frequency domain is
linear in log-log space, S ~ f^-k, then you may have a fractal signal,
depending on what the slope k is.

Sorry if my question sounds very basic. But what frequency does the term "frequency domain" refers to is still not clear to me. I am taking one step back and using a simple example ...

* Assume I have a digital waveform spanning from time unit t0-t99 (for example).
* Assume that the amplitude is A units

I convert this to frequency domain. Most likely I am going to end up with a power concentrated at DC and zero elsewhere.

Now what does the frequency refer to in this case:
Is it the frequency of sampling the digital waveform?
Is it the frequency of amplitude variation?

When I deep dive into this topic, I get a feeling that it is the second item that the frequency refers to. But still I dont get a bigger picture ...

Regards,

On Nov 20, 2:57 am, sbr487 <sharan.basa...@gmail.com> wrote:
> Sorry if my question sounds very basic. But what frequency does the term "frequency domain" refers to is still not clear to me. I am taking one step back and using a simple > example ...

The time function can be approximated, over a finite interval,
by a sum of weighted sines and cosines (or, equivalently,
complex exponentials).

The frequency domain contains the information that yields
the corresponding amplitudes and phases.

Hope this helps.

Greg



> * Assume I have a digital waveform spanning from time unit t0-t99 (for example).
> * Assume that the amplitude is A units

You don't specify the shape of the waveform. However, I'm guessing
that it is a constant.

> I convert this to frequency domain. Most likely I am going to end up with a power concentrated at DC and zero elsewhere.

OK

> Now what does the frequency refer to in this case:

The frequency where the power is concentrared.

> Is it the frequency of sampling the digital waveform?

No.

> Is it the frequency of amplitude variation?

No. How can it be if the amplitude doesn't vary?

>
> When I deep dive into this topic, I get a feeling that it is the second item that the frequency refers to. But still I dont get a bigger picture ...

Try

N = 32, T = 2*pi, dt = T/N, t = dt*(0:N-1);
x1 = cos(t) + sin(2*t);

Hope this helps.

Greg

Greg Heath <heath@alumni.brown.edu> wrote in message <45b3f51b-9df6-401d-b74f-11992f6e11a8@h10g2000vbm.googlegroups.com>...
> On Nov 20, 2:57?am, sbr487 <sharan.basa...@gmail.com> wrote:
> > Sorry if my question sounds very basic. But what frequency does the term "frequency domain" refers to is still not clear to me. I am taking one step back and using a simple > example ...
>
> The time function can be approximated, over a finite interval,
> by a sum of weighted sines and cosines (or, equivalently,
> complex exponentials).
>
> The frequency domain contains the information that yields
> the corresponding amplitudes and phases.
>
> Hope this helps.
>
> Greg
>
>
>
> > * Assume I have a digital waveform spanning from time unit t0-t99 (for example).
> > * Assume that the amplitude is A units
>
> You don't specify the shape of the waveform. However, I'm guessing
> that it is a constant.
>
> > I convert this to frequency domain. Most likely I am going to end up with a power concentrated at DC and zero elsewhere.
>
> OK
>
> > Now what does the frequency refer to in this case:
>
> The frequency where the power is concentrared.
>
> > Is it the frequency of sampling the digital waveform?
>
> No.
>
> > Is it the frequency of amplitude variation?
>
> No. How can it be if the amplitude doesn't vary?
>
> >
> > When I deep dive into this topic, I get a feeling that it is the second item that the frequency refers to. But still I dont get a bigger picture ...
>
> Try
>
> N = 32, T = 2*pi, dt = T/N, t = dt*(0:N-1);
> x1 = cos(t) + sin(2*t);
>
> Hope this helps.
>
> Greg

U might pick up a book on Fourier Transform or do a google search for Fourier Transform tutorial. Or frequency analysis tutorial....

Thanks. That helped.

One more question ...

If I want to visualize the fourier tranform, would the following method be (nearly) correct?

* Get frequency component, one by one
* For each frequency component, imagine spatial domain response
* Below the spatial domain response draw sines and cosines waveforms of same frequency but different phases
* The number of sine and cosine is same as the N-point in the spatial domain
* Now at each discrete time step in spatial domain, multiply the amplitude with the corresponding sine and cosine
* Repeat this for next frequency component and with different sine and cosine frequency

Regards,