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Why a sine wave is a simple vertical line in a frequency domain?
A sine wave is a simple vertical line in the frequency domain because the horizontal axis of the frequency domain is frequency, and there is only one frequency, i.e. no harmonics, in a pure sine wave.
What is the difference between transfer function and frequency transfer function?
frequency transfer function deals with transfer in frequency domain, transfer function alone can be referring to any type of transfer in different domain e.g time domain
What is the element law of a capacitor in frequency domain?
The element law of a capacitor in frequency domain is based on Ohm's Law, which is capacitance times voltage is equal to current. The higher frequency, the lower the capacitance and vice versa.
What is the Time domain analysis of control system?
Time domain basically means plotting a curve of amplitude over thr time axis. A given function or signal can be converted between the time and frequency domains with a pair of mathematical operators called a transform. An example is the Fourier transform, which decomposes a function into the sum of a (potentially infinite) number of sine wave frequency components. The 'spectrum' of frequency components is the frequency domain representation of the signal. The inverse Fourier transform converts the frequency domain function back to a time function.
Why you do convolution instead of multiplication?
Convolution is particularly useful in signal analysis. See related link.
What is frequency counterpart of convolution?
Convolution in the time domain is equivalent to multiplication in the frequency domain.
State and prove convolution theorem for fourier transform?
Convolution TheoremsThe convolution theorem states that convolution in time domain corresponds to multiplication in frequency domain and vice versa:Proof of (a):Proof of (b):
What is the need for convolution in digital signal processing?
If we need to add two signals in time domain, we perform convolution. A better way, is to convert the two signals from time domain to frequency domain. This can be achieved by FAST FOURIER TRANFORM. Once both the signals have been converted to frequency domain, they can simply be multiplied. Since Convolution in time domain is similar to multiplying in Frequency domain. Once both the signals have been multiplied, they can be converted back to time domain by Inverse Fourier Transform method. Thus achieving accurate results.
How can you prove that convolution in time domain is equal to multiplication in frequency domain Mathematically with the help of Laplace transform?
Check this : https://ccrma.stanford.edu/~jos/sasp/img2442.png
To find inverse Fourier transform using convolution?
The inverse Fourier transform can be computed using convolution by utilizing the property that the inverse transform of a product of two Fourier transforms corresponds to the convolution of their respective time-domain functions. Specifically, if ( F(\omega) ) is the Fourier transform of ( f(t) ), then the inverse Fourier transform is given by ( f(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} F(\omega) e^{i\omega t} d\omega ). This integral can be interpreted as a convolution with the Dirac delta function, effectively allowing for the reconstruction of the original function from its frequency components. Thus, the convolution theorem links multiplication in the frequency domain to convolution in the time domain, facilitating the computation of the inverse transform.
What are the Differences between Convolution and correlation?
A convolution is an integral that expresses the amount of overlap of one function as it is shifted over another function.You can use correlation to compare the similarity of two sets of data. Correlation computes a measure of similarity of two input signals as they are shifted by one another. The correlation result reaches a maximum at the time when the two signals match bestThe difference between convolution and correlation is that convolution is a filtering operation and correlation is a measure of relatedness of two signalsYou can use convolution to compute the response of a linear system to an input signal. Convolution is also the time-domain equivalent of filtering in the frequency domain.
What is convolution of a signal?
the convolution of a signal is to filter the components of the signal. The convolution does not mean the masking. Masking means it is going to remove all the masked components(both high and low frequency components).But convolution is going to remove any one (either low r high frequency) depending upon the filter response.
Definition of Time domain and frequency domain in data communication?
time domain is respected to the time and frequency domain is respected to the frequency
How do you represent the discrete hilbert transform?
The discrete Hilbert transform can be represented using the convolution of a discrete signal with the kernel ( h[n] = \frac{1}{\pi n} ), where the convolution is defined for all integer ( n ). It can also be computed using the Fast Fourier Transform (FFT) by multiplying the frequency components of the signal by ( -i , \text{sgn}(f) ), where ( \text{sgn}(f) ) is the sign function. This approach efficiently computes the transform in the frequency domain and then transforms it back to the time domain using the inverse FFT.
What is the solution to the Heat equation using fourier transform?
The solution to the Heat equation using Fourier transform is given by the convolution of the initial condition with the fundamental solution of the heat equation, which is the Gaussian function. The Fourier transform helps in solving the heat equation by transforming the problem from the spatial domain to the frequency domain, simplifying the calculations.
Why a sine wave is a simple vertical line in a frequency domain?
A sine wave is a simple vertical line in the frequency domain because the horizontal axis of the frequency domain is frequency, and there is only one frequency, i.e. no harmonics, in a pure sine wave.
What is the need of conversion from time to frequency domain?
Design of filtering and control systems is usually easier in the frequency domain than in the time domain.
