Table of Contents
What is the disadvantage of exponential Fourier series?
Explanation: The major disadvantage of exponential Fourier series is that it cannot be easily visualized as sinusoids. Moreover, it is easier to calculate and easy for manipulation leave aside the disadvantage.
Which of the following is not a Dirchlet’s condition for the Fourier series expansion?
(c) f(x) must have a finite number of discontinuities in any given bounded interval, and the discontinuities cannot be infinite. Hence, the correct option is (b) i.e.f(x) has finite number of discontinuities in only one period.
Why wavelet transform is better than fourier transform?
Wavelet transform (WT) are very powerful compared to Fourier transform (FT) because its ability to describe any type of signals both in time and frequency domain simultaneously while for FT, it describes a signal from time domain to frequency domain.
When different Fourier components are suppressed by different amount it causes?
Clear responses at 2F1 Hz and 2F2 Hz are evident in the section of the evoked response spectrum shown in Figure 10(A), but there was no (F1 + F2) Hz component.
What are the limitations of Fourier series?
The major disadvantage of the Fourier transformation is the inherent compromise that exists between frequency and time resolution. The length of Fourier transformation used can be critical in ensuring that subtle changes in frequency over time, which are very important in bat echolocation calls, are seen.
Is Fourier Transform only for periodic functions?
Fourier originally defined the Fourier series for real-valued functions of real arguments, and using the sine and cosine functions as the basis set for the decomposition. A Fourier series, however, can be used only for periodic functions, or for functions on a bounded (compact) interval.
For which Fourier series Cannot be defined?
For which of the following a Fourier series cannot be defined? For 1 which is a constant, Fourier series exists. For exp (-|t|) sin (25t), due to decaying exponential decaying function, it is not periodic. So Fourier series cannot be defined for it.
Which of the following Cannot be the Fourier series expansion of a periodic function?
Which of the following cannot be the Fourier series expansion of a periodic signal? Since x2(t) is not periodic, so it cannot be expanded in Fourier series.
Which of the following function Cannot be expanded as a Fourier series?
→ The frequency of first term frequency of 2nd term is ω2 = 1. So, x(t) is a periodic or not periodic. Since function in (b) is non periodic. So does not satisfy Dirichlet conditionand cannot be expanded in Fourier series.
What is the difference between FFT and Fourier Transform?
Discrete Fourier Transform (DFT) is a transform like Fourier transform used with digitized signals. Fast Fourier Transform (FFT) is just an algorithm for fast and efficient computation of the DFT.
Why DWT is better than DCT?
Both techniques have its’ own advantages and disadvantage. Like DWT gives better compression ratio [1,3] without losing more information of image but it need more processing power. While in DCT need low processing power but it has blocks artifacts means loss of some information.
What is the difference between wavelet and Fourier transform?
In layman’s terms: A fourier transform (FT) will tell you what frequencies are present in your signal. A wavelet transform (WT) will tell you what frequencies are present and where (or at what scale). If you had a signal that was changing in time, the FT wouldn’t tell you when (time) this has occurred.
Why is SSB not used for broadcasting?
In addition, the occupied spectrum is less than half that of a full carrier AM signal. SSB reception requires frequency stability and selectivity well beyond that of inexpensive AM receivers which is why broadcasters have seldom used it.
Does Fourier transform of constant function exist?
One of the requirements for the existence of Fourier transform of f(x) is that: ∫∞−∞|f(x)|dx exists. However, the table says that the Fourier transform of constant functions (\emph{i.e.}, f(x)=1) do exist and it is δ(k) although ∫∞−∞1dx=∞ .
What is the relationship between fourier series and Fourier transform?
Fourier series is an expansion of periodic signal as a linear combination of sines and cosines while Fourier transform is the process or function used to convert signals from time domain in to frequency domain.
Why Fourier series is important?
Fourier series is just a means to represent a periodic signal as an infinite sum of sine wave components. A periodic signal is just a signal that repeats its pattern at some period. The primary reason that we use Fourier series is that we can better analyze a signal in another domain rather in the original domain.
What is Fourier’s Theorem?
FOURIER THEOREM A mathematical theorem stating that a PERIODIC function f(x) which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each of which has specific AMPLITUDE and PHASE coefficients known as Fourier coefficients.
What is the difference between Laplace and Fourier Transform?
Fourier transform is defined only for functions defined for all the real numbers, whereas Laplace transform does not require the function to be defined on set the negative real numbers. Every function that has a Fourier transform will have a Laplace transform but not vice-versa.
Is Fourier series always periodic?
The Fourier series is applicable only to functions assumed to be periodic. A generalization called the Fourier transform is applicable to non periodic functions; the Laplace transform is applicable to functions defined only for non negative argument.
Are Fourier series continuous?
The Fourier cosine series of f(x) will be continuous and will converge to f(x) on 0≤x≤L 0 ≤ x ≤ L provided f(x) is continuous on 0≤x≤L 0 ≤ x ≤ L .
Why Fourier transform not used in periodic signals?
The Fourier series itself is a periodic function, so any function that equals its Fourier series must be periodic as well. A non-periodic function cannot equal its Fourier series, hence it is not that useful to use Fourier series to analyze non-periodic functions.
