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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
Determine second third and 12TH harmonic of a sine wave?
A sine wave has no harmonics. It only has a fundamental, so the value of the 2nd, 3rd, and 12th harmonics of a sine wave is zero.
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.
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.
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.
If the voltage applied across a capacitance is triangular in waveform then the waveform of the current?
Depend the value of capacitor. Capacitance in series act like a high pass filter, while in parallel act like low pass filter. By fourier series, triangular wave is combine of series of the sine or cosine waves. Therefore by certain capacitance, sine wave can preduce by applied a triangular signal through a capacitor. Current is just 90 degree shift from voltage, shape is same.
Why the basic building block of signal is sine wave?
Every periodic signal can be decomposed to a sum (finite or infinite) of sines and cosines according to fourier analysis.
