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Is the infinite sum of continuous function continuous?
An infinite sum of continuous functions does not have to be continuous. For example, you should be able to construct a Fourier series that converges to a discontinuous function.
What is the difference between fourier series and fourier transform with real life example please?
A Fourier series is a set of harmonics at frequencies f, 2f, 3f etc. that represents a repetitive function of time that has a period of 1/f. A Fourier transform is a continuous linear function. The spectrum of a signal is the Fourier transform of its waveform. The waveform and spectrum are a Fourier transform pair.
How does the graph of Fourier Series differ to the graph of Fourier Transform?
You can graph both with Energy on the y-axis and frequency on the x. Such a frequency domain graph of a fourier series will be discrete with a finite number of values corresponding to the coefficients a0, a1, a2, ...., b1, b2,... Also, the fourier series will have a limited domain corresponding to the longest period of your original function. A fourier transforms turns a sum into an integral and as such is a continuous function (with uncountably many values) over the entire domain (-inf,inf). Because the frequency domain is unrestricted, fourier transforms can be used to model nonperiodic functions as well while fourier series only work on periodic ones. Series: discrete, limited domain Transform: continuous, infinite domain.
What are the limitation of fourier series?
what are the limitations of forier series over fourier transform
Can a discontinuous function can be developed in the Fourier series?
Yes. For example: A square wave has a Fourier series.
What does the Fourier time series analysis help with in signal processing?
It is difficult to describe how Fourier time series analysis helps with signal processing without going into deep detail. Basically, it helps to manipulate the data to be understood in a simpler way. For the complete detailed explanation one can view Wikipedia "Fourier Analysis".
Is the infinite sum of continuous function continuous?
An infinite sum of continuous functions does not have to be continuous. For example, you should be able to construct a Fourier series that converges to a discontinuous function.
What is the difference between fourier series and fourier transform with real life example please?
A Fourier series is a set of harmonics at frequencies f, 2f, 3f etc. that represents a repetitive function of time that has a period of 1/f. A Fourier transform is a continuous linear function. The spectrum of a signal is the Fourier transform of its waveform. The waveform and spectrum are a Fourier transform pair.
How does the graph of Fourier Series differ to the graph of Fourier Transform?
You can graph both with Energy on the y-axis and frequency on the x. Such a frequency domain graph of a fourier series will be discrete with a finite number of values corresponding to the coefficients a0, a1, a2, ...., b1, b2,... Also, the fourier series will have a limited domain corresponding to the longest period of your original function. A fourier transforms turns a sum into an integral and as such is a continuous function (with uncountably many values) over the entire domain (-inf,inf). Because the frequency domain is unrestricted, fourier transforms can be used to model nonperiodic functions as well while fourier series only work on periodic ones. Series: discrete, limited domain Transform: continuous, infinite domain.
What are Joseph Fourier's works?
Fourier series and the Fourier transform
What are the limitation of fourier series?
what are the limitations of forier series over fourier transform
What has the author F de Meyer written?
F. de Meyer has written: 'The sampling of a continuous function' -- subject(s): Continuous Functions, Fourier series, Spectral theory (Mathematics)
Discontinuous function in fourier series?
yes a discontinuous function can be developed in a fourier series
How do you find the inverse Fourier transform from Fourier series coefficients?
no
Can a discontinuous function can be developed in the Fourier series?
Yes. For example: A square wave has a Fourier series.
What is physical significance of Fourier series?
Fourier series is series which help us to solve certain physical equations effectively
What is the difference between fourier series and discrete fourier transform?
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.
