0
What else can I help you with?
What is Trigonometric Fourier series for square?
The Trigonometric Fourier series for a square wave is a representation of the wave as an infinite sum of sine and cosine functions. For a square wave with period ( T ), the series consists only of odd harmonics, expressed as ( f(t) = \frac{4A}{\pi} \sum_{n=1,3,5,\ldots} \frac{\sin\left(\frac{2\pi nt}{T}\right)}{n} ), where ( A ) is the amplitude of the wave. This series converges to the square wave, exhibiting discontinuities at the edges of the wave, which leads to the Gibbs phenomenon, where overshoots occur near the discontinuities.
Is sine wave used in analog or digital?
No and yes. Digital signals are usually square or pulse waves. By Fourier analysis, however, every periodic wave, even a square wave, is the summation of some series (often infinite) of sine waves.
Why fourier series is used for frequency domain?
The fourier series relates the waveform of a periodic signal, in the time-domain, to its component sine/cosine frequency components in the frequency-domain. You can represent any periodic waverform as the infinite sum of sine waves. For instance, a square wave is the infinite sum of k * sin(k theta) / k, for all odd k, 1 to infinity. Using a Fourier Transformation, you take take a signal, convert it from time-domain to frequency-domain, apply some filtering or shifting, and convert it back to time-domain. Sometimes, this is easier than building an analog filter, even given that you need a digital signal processor to do it.
Discontinuous function in fourier series?
yes a discontinuous function can be developed in a fourier series
What is the Integration of sine wave?
cos wave
What is the Fourier transform of a sine wave?
The Fourier transform of a sine wave is a pair of delta functions located at the positive and negative frequencies of the sine wave.
Fourier analysis shows that the saw tooth wave consists of which type of wave?
Fourier analysis shows that the saw wave is constructed through manipulation of a sine wave, I can't remember the maths behind it but it's definitely a sine wave.
Can a discontinuous function can be developed in the Fourier series?
Yes. For example: A square wave has a Fourier series.
Why cannot aperiodic signal be represented using fourier series?
An aperiodic signal cannot be represented using fourier series because the definition of fourier series is the summation of one or more (possibly infinite) sine wave to represent a periodicsignal. Since an aperiodic signal is not periodic, the fourier series does not apply to it. You can come close, and you can even make the summation mostly indistinguishable from the aperiodic signal, but the math does not work.
What is Trigonometric Fourier series for square?
The Trigonometric Fourier series for a square wave is a representation of the wave as an infinite sum of sine and cosine functions. For a square wave with period ( T ), the series consists only of odd harmonics, expressed as ( f(t) = \frac{4A}{\pi} \sum_{n=1,3,5,\ldots} \frac{\sin\left(\frac{2\pi nt}{T}\right)}{n} ), where ( A ) is the amplitude of the wave. This series converges to the square wave, exhibiting discontinuities at the edges of the wave, which leads to the Gibbs phenomenon, where overshoots occur near the discontinuities.
In Mathematics what is meant by the Fourier series?
The Fourier series is a specific type of infinite mathematical series involving trigonometric functions that are used in applied mathematics. It makes use of the relationships of the sine and cosine functions.
Is sine wave used in analog or digital?
No and yes. Digital signals are usually square or pulse waves. By Fourier analysis, however, every periodic wave, even a square wave, is the summation of some series (often infinite) of sine waves.
What is the Fourier Series for x sinx from -pi to pi?
The word sine, not sinx is the trigonometric function of an angle. The answer to the math question what is the four series for x sine from -pi to pi, the answer is 24.3621.
What is the Fourier series of a triangular wave?
The Fourier series of a triangular wave is a sum of sine terms that converge to the triangular shape. It can be expressed as ( f(x) = \frac{8A}{\pi^2} \sum_{n=1,3,5,...} \frac{(-1)^{(n-1)/2}}{n^2} \sin(nx) ), where ( A ) is the amplitude of the wave, and the summation runs over odd integers ( n ). The coefficients decrease with the square of ( n ), leading to a rapid convergence of the series. This representation captures the essential harmonic content of the triangular wave.
How do you draw graph for Fourier series?
To draw a graph for a Fourier series, first, calculate the Fourier coefficients by integrating the function over one period. Then, construct the Fourier series by summing the sine and cosine terms using these coefficients. Plot the resulting function over the desired interval, ensuring to include enough terms in the series to capture the function's behavior accurately. Finally, compare the Fourier series graph against the original function to visualize the approximation.
Is the fnction in fourier series periodic?
Yes, a Fourier series represents a periodic function. It decomposes a periodic function into a sum of sine and cosine terms, each of which has a specific frequency. The resulting series will also be periodic, with the same period as the original function. If the original function is not periodic, it can still be approximated by a Fourier series over a finite interval, but the series itself will exhibit periodic behavior.
What is Fourier transformation?
Fourier transform. It is a calculation by which a periodic function is split up into sine waves.
