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How do you represent a signal in terms of Fourier series?
Fourier Series Representation of Continuous Time Periodic Signals. A signal is said to be periodic if it satisfies the condition x (t) = x (t + T) or x (n) = x (n + N). These two signals are periodic with period T=2π/ω0. Where ak= Fourier coefficient = coefficient of approximation.
What does Fourier series represented?
A Fourier series is a way of representing a periodic function as a (possibly infinite) sum of sine and cosine functions. It is analogous to a Taylor series, which represents functions as possibly infinite sums of monomial terms.
Why is Fourier series representation used for periodic signals?
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.
Can two different signals have same Fourier transform?
Of course they can. Simply imagine that a signal is composed by two sine waves with different frequencies. The magnitude of the Fourier-transform of both signals will be identical.
Can two functions have the same Fourier transform?
In particular, taking differences, if two functions have the same Fourier coefficients, then they are the same (except on a set of measure zero).
Are Fourier transforms unique?
It is unique. If the function f(t) is piecewise continious and square integrable the fourier coffiecients are unique.
What is the function of a Fourier series?
A Fourier series is a way of representing a periodic function as a (possibly infinite) sum of sine and cosine functions. It is analogous to a Taylor series, which represents functions as possibly infinite sums of monomial terms. For functions that are not periodic, the Fourier series is replaced by the Fourier transform.
Why to use the Fourier series?
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.
Why do we use the Fourier series?
Fourier series make use of the orthogonality relationships of the sine and cosine functions. The computation and study of Fourier series is known as harmonic analysis and is extremely useful as a way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually,…
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.