Which of the following Cannot be Fourier series of periodic signal?

Which of the following Cannot be Fourier series of periodic signal?

Which of the following cannot be the Fourier series expansion of a periodic signal? Explanation: x1(t) = 2 cost + 3 cost is periodic signal with fundamental frequency w0 = 1. x2(t) = 2 cos πt + 7 cos t The frequency of first term w1 = π frequency of 2nd term is w2 = 1. Since, \frac{ω_1}{ω_2} = π, which is not rational.

What kind of signals can be represented with a Fourier series?

The Fourier series represents periodic, continuous-time signals as a weighted sum of continuous-time sinusoids. It is widely used to analyze and synthesize periodic signals.

Can we apply Fourier series to all periodic signals?

A Fourier series is only defined for functions defined on an interval of finite length, including periodic signals, as you can see from the definition of the Fourier coefficients (in the basis {einx}n∈Z) an=12π∫π−πf(x)e−inx dx.

Which of the following function Cannot be expressed as Fourier series?

Yes. In fact, almost all periodic functions cannot be expressed as Fourier series. Nevertheless, if you consider the L^2 space, then all L^2 functions can be expressed as Fourier series in the L^2 sense.

How do you know if a function can be represented by a Fourier series?

Well there are 3 conditions for a Fourier Series of a function to be exist: 1. It has to be periodic. 2. It must be single valued, continuous.it can have finite number of finite discontinuities.

Is the Fourier series always used for periodic signals and?

Fourier Series (FS) exists only for periodic signals. Fourier Transform (FT) is derived from FS, i.e. FT is the envelope of the FS. Thus as the frequency domain became more finer, time domain enlarges making it a aperiodic signal.

What is the equation for the Fourier series?

Where a k = Fourier coefficient = coefficient of approximation. This signal x (t) is also periodic with period T. Equation 2 represents Fourier series representation of periodic signal x (t). The term k = 0 is constant. The term k = ± 1 having fundamental frequency ω 0, is called as 1 st harmonics.

How is a Fourier transform derived from a FS?

Fourier Transform (FT) is derived from FS, i.e. FT is the envelope of the FS. Thus as the frequency domain became more finer, time domain enlarges making it a aperiodic signal. So when FT is applied on a periodic signal, the result is just, T*X (k) where T is the time period of the signal and X (k) is the FS of the signal. Fourier is just awesome!

What happens when ft is applied to a periodic signal?

Thus as the frequency domain became more finer, time domain enlarges making it a aperiodic signal. So when FT is applied on a periodic signal, the result is just, T*X (k) where T is the time period of the signal and X (k) is the FS of the signal.