Contents
What is the correct representation of Fourier Transform?
The discrete-time Fourier transform (DTFT) or the Fourier transform of a discrete–time sequence x[n] is a representation of the sequence in terms of the complex exponential sequence ejωn. Where Xre(ω), Ximg(ω) are real and imaginary parts of X(ω) respectively.
How do you represent Fourier series?
Fourier Series Representation of Continuous Time Periodic Signals
- x(t)=cosω0t (sinusoidal) &
- x(t)=ejω0t (complex exponential)
- These two signals are periodic with period T=2π/ω0.
- A set of harmonically related complex exponentials can be represented as {ϕk(t)}
- Where ak= Fourier coefficient = coefficient of approximation.
Why do we use Fourier series of representation?
We use Fourier series to write a function as a trigonometric polynomial. Control Theory. The Fourier series of functions in the differential equation often gives some prediction about the behavior of the solution of a differential equation. They are useful to find out the dynamics of the solution.
What is Fourier series and why it is used?
Fourier series is just a means to represent a periodic signal as an infinite sum of sine wave components. A periodic signal is just a signal that repeats its pattern at some period. The primary reason that we use Fourier series is that we can better analyze a signal in another domain rather in the original domain.
What is the purpose of the Fourier series?
fourier series is broadly used in telecommunications system, for modulation and demodulation of voice signals, also the input,output and calculation of pulse and their sine or cosine graph.
What is a discrete time series?
A discrete signal or discrete-time signal is a time series consisting of a sequence of quantities. Unlike a continuous-time signal, a discrete-time signal is not a function of a continuous argument; however, it may have been obtained by sampling from a continuous-time signal.
What is the limitation of Fourier series?
Limitations of Fourier series: · It can be used only for periodic inputs and thus not applicable for aperiodic one. · It cannot be used for unstable or even marginally stable systems.