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The fractiona lFourier transform (FRFT) is a potent tool to analyze the chirp signal. However,it failsin locating the fractional Fourier domain (FRFD)-frequency contents which is requiredin some applications. The short-time fractional Fourier
transform (STFRFT) is proposed to solve this problem
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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.
Why short time Fourier transform is necessary?
The Short-Time Fourier Transform (STFT) is necessary because it allows for the analysis of non-stationary signals, where the frequency content changes over time. By dividing a signal into shorter segments and applying the Fourier Transform to each segment, STFT provides a time-frequency representation that captures how the frequency characteristics evolve. This is crucial in applications like speech processing, music analysis, and biomedical signal analysis, where understanding the time-varying nature of signals is essential for accurate interpretation and processing.
What is the difference between Discrete-time Fourier transform and Discrete Fourier transform?
The Discrete Fourier Transform (DFT) is a specific mathematical algorithm used to compute the frequency spectrum of a finite sequence of discrete samples. In contrast, the Discrete-time Fourier Transform (DTFT) represents a continuous function of frequency for a discrete-time signal, allowing for the analysis of signals in the frequency domain over an infinite range. Essentially, the DFT is a sampled version of the DTFT, applied to a finite number of samples, whereas the DTFT provides a broader, continuous frequency representation of the signal.
What is the need for fourier transform in analog signal processing?
The fourier transform is used in analog signal processing in order to convert from time domain to frequency domain and back. By doing this, it is easier to implement filters, shifters, compression, etc.
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.
Application of fourier transform?
the main application of fourier transform is the changing a function from frequency domain to time domain, laplaxe transform is the general form of fourier transform .
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.
Why short time Fourier transform is necessary?
The Short-Time Fourier Transform (STFT) is necessary because it allows for the analysis of non-stationary signals, where the frequency content changes over time. By dividing a signal into shorter segments and applying the Fourier Transform to each segment, STFT provides a time-frequency representation that captures how the frequency characteristics evolve. This is crucial in applications like speech processing, music analysis, and biomedical signal analysis, where understanding the time-varying nature of signals is essential for accurate interpretation and processing.
What is the Fourier Transform?
The Fourier transform is a mathematical transformation used to transform signals between time or spatial domain and frequency domain. It is reversible. It refers to both the transform operation and to the function it produces.
How can a composite signal be decomposed?
Spectral analysis of a repetitive waveform into a harmonic series can be done by Fourier analyis. This idea is generalised in the Fourier transform which converts any function of time expressed as a into a transform function of frequency. The time function is generally real while the transform function, also known as a the spectrum, is generally complex. A function and its Fourier transform are known as a Fourier transform pair, and the original function is the inverse transform of the spectrum.
What type of algorithm is fast fourier transform?
A fast fourier transform is an algorithm that converts time or space to frequency, or vice versa. They are mainly used in engineering, math and sciences.
How do you find the inverse Fourier transform from Fourier series coefficients?
To find the inverse Fourier transform from Fourier series coefficients, you first need to express the Fourier series coefficients in terms of the complex exponential form. Then, you can use the inverse Fourier transform formula, which involves integrating the product of the Fourier series coefficients and the complex exponential function with respect to the frequency variable. This process allows you to reconstruct the original time-domain signal from its frequency-domain representation.
What is the difference between Fourier transform and Wavelet transform?
Fourier transform analyzes signals in the frequency domain, representing the signal as a sum of sinusoidal functions. Wavelet transform decomposes signals into different frequency components using wavelet functions that are localized in time and frequency, allowing for analysis of both high and low frequencies simultaneously. Wavelet transform is more suitable than Fourier transform for analyzing non-stationary signals with localized features.
What is the difference between Discrete-time Fourier transform and Discrete Fourier transform?
The Discrete Fourier Transform (DFT) is a specific mathematical algorithm used to compute the frequency spectrum of a finite sequence of discrete samples. In contrast, the Discrete-time Fourier Transform (DTFT) represents a continuous function of frequency for a discrete-time signal, allowing for the analysis of signals in the frequency domain over an infinite range. Essentially, the DFT is a sampled version of the DTFT, applied to a finite number of samples, whereas the DTFT provides a broader, continuous frequency representation of the signal.
What is the need for fourier transform in analog signal processing?
The fourier transform is used in analog signal processing in order to convert from time domain to frequency domain and back. By doing this, it is easier to implement filters, shifters, compression, etc.
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.
Why Laplace transform is used in analysis of control system why not Fourier?
it is used for linear time invariant systems
