Best Answer

A Fourier series is a series of sine and cosine harmonics of a particular frequency.

For example sinf+icosf + 3 sin2f+ 5icos2f... where the successive terms are multiples of the fundamental frequency f. It is typical ( but as far as I know not required) that complex numbers are used.

A Fourier transform converts a time domain wave form (like a sound wave) into the coefficients of the corresponding Fourier series.

A DFT is a digital approximation to a Fourier transform, usually using something like the Cooley-Tuckey Fast Fourier Transform (FFT) for efficiency.

The underlying Fourier theorem is something like: Every bounded periodic continuous (needed to avoid Gibbs) function , or wave form, can be written as the sum of its Fourier series. i.e. It is a sum of sines and cosines

In otherwords, you take a wave form in the time domain like a sound wave and break it into its components (various frequencies) by the Fourier Transform. The results of the Transform are the coefficients of the Fourier series. The wave form of a voice converted to components (and perhaps a little more) is a voiceprint.

Study guides

☆☆

Q: Difference between fourier series fourier transform discrete time fourier transform and DFT?

Write your answer...

Submit

Still have questions?

Related questions

discrete fourier transformer uses digital signals whereas the fast fourier transform uses both analog and digital.

Fourier series is the sum of sinusoids representing the given function which has to be analysed whereas discrete fourier transform is a function which we get when summation is done.

They are similar. In many problems, both methods can be used. You can view Fourier transform is the Laplace transform on the circle, that is |z|=1. When you do Fourier transform, you don't need to worry about the convergence region. However, you need to find the convergence region for each Laplace transform. The discrete version of Fourier transform is discrete Fourier transform, and the discrete version of Laplace transform is Z-transform.

DTFT is the Fourier Transform of a Discrete Signal. DFT is the sampled version of DTFT

i want c code for fourier transform?

The fast fourier transform, which was invented by Tukey, significantly improves the speed of computation of discrete fourier transform.

Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.

z transform is related to discrete time signal while fourier series is related to continuous time signal. z transform=sigmalm -infinty to +infinity x(n)z-n

wavelet transform is located in space whereas fourier cosine and sine functions are not.:)

The Discrete Fourier Transform is used with digitized signals. This would be used if one was an engineer as they would use this to calculate measurements required.

fourier transform deals with continuous time non-periodic signals(if the input is continuous time periodic signal(time domain) then the output is continuous nonpeiodic signal (frequency domain)) DTFT-input-discrete time nonperoidic signal(time domain),output-continuous peroidic signal(frequency domain)

Density Functional Theory Discrete Fourier Transform

People also asked