# The Fourier spectrum of signals

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#### DrDolittle

##### Full Member level 3
fourier spectrum

Is fourier spectrum for aperiodic signals are discrete or continuous?

#### Ahmed Ragab

##### Full Member level 2
Re: fourier spectrum

The Fourier spectrum of signals fully can be summarized as follows:

for periodic signal..... the spectrum is discrete
for non-periodic signal ... spectrum is continuous
for discrete signals ... spectrum is periodic
for continuous signals ... spectrum is non-periodic

#### DrDolittle

##### Full Member level 3
Re: fourier spectrum

could you tell what is the thread connectiong the four classifications you have made.What i mean is to tell a general rule tersely between the between the sampled signal and it's spectrum.

Regards
drdolittle

#### ertug

##### Member level 1
Re: fourier spectrum

I want to explain this periodicity issue by giving some examples. A sine (or cosine) wave as everyone knows is formed by only one frequency (single period) component. So in the frequency domain it will be only one point showing the amplitude of the signal at that frequency. Shortly, the sine wave is continiuous and periodic but its spectrum is aperiodic and discrete.
With inverse Fourier transform you can generate the original signal easily by the parametres known by the spectrum: amplitude and frequency.
If you superpose a series of sines(or cosines) you have a periodic signal but the spectrum will be made of discrete points representing each of the component's amplitude and frequency points.

I hope this will be helpfull for you.

#### DrDolittle

##### Full Member level 3
Re: fourier spectrum

A simpler way of telling it goes like this.
The relation is : A time limited signal will be nonband limited and vice versa also holds good.I think this explains the entire thing.

Regards
drdolittle

##### Full Member level 3
Re: fourier spectrum

Is fourier spectrum for aperiodic signals are discrete or continuous?
and
A time limited signal will be nonband limited and vice versa also holds good.I think this explains the entire thing.

They are different stories. They are related but not the same.
You can have an infinite signal with finite band limit in frequency domain, yet imply nothing about periodic and discrete relationship.

#### cedance

Re: fourier spectrum

an infinite aperiodic signal.. its spectrum in the frequency domain.... u wouldnt know its infinite from lookin in the frequency domain....

/cedance

#### anto2

##### Member level 3
Re: fourier spectrum

the best thing to do is open a dsp book and look at the pictures,, they may be able to give you a clear visualisation,,

but to answer the original question aperiodic in time = continuous in frequency since such a wave consists of all fequencies.

#### Mina Ayman

##### Member level 2
fourier spectrum

This depends on the signal as other posts tell, You can skip your conflict and use the function fft and fftshift in MATLAB to get the fourier transform of the desired signal

#### Jackwang

##### Full Member level 2
fourier spectrum

In fact, if you are a beginner, if you want to understand the signal characteristics deeply.
you can use matlab to simulate them, so you can observe their output results.
through this method, you can find out many results that don't find in this book.

#### asymbian

##### Junior Member level 3
Re: fourier spectrum

The diagrams in DSP book by Proakis-Manolakis are perfect...
If you want to understand the underlying funda, you must try to visualise how sinusoids undergo superposition to form a particular signal, periodic or aperiodic. First try to visualise for periodic and then proceed towards aperiodic. As the signal becomes aperiodic, when you try to "construct" it using periodic sinusoids, you need to have infinite signals upto infinite frequency (there are exceptions!). Hope this will help you realise the beauty of the entire transform concept.

Regards,
asymbian

#### the_jackal

##### Member level 4
Re: fourier spectrum

Fourier Transform (CT-Aperiodic Signals)

Fourier series is used to represent a periodic signal as a linear comb. of harmincally related exponentials (from sophomore level course). As a result of periodicity these signals possess a line spectre with equidistant lines. Line spacing = fundamental frequency (1/T where T is the fundamental period). If we allow the period to increase without limit then the line spacing will tend to zero. In the limit when the period becomes infinite the signal becomes aperiodic and the spectrum becomes continuous.

#### nj_jack

##### Member level 5
fourier spectrum

that fourier spectrum for aperiodic signals are discrete or continuous depends on the form of input signal. you need to review the digital signal processing priciple.

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