Which of the following statements accurately describes the relationship between the DFT and the continuous Fourier transform (CFT)?Select one:a. The DFT is the discrete-time equivalent of the Laplace transform.b. The DFT is obtained by sampling the frequency domain of the CFT.c. The DFT is the discrete-time equivalent of the Z-transform.d. The DFT is a sampled version of the CFT

Which of the following statements accurately describes the computational complexity of the Fast Fourier Transform (FFT) algorithm for computing the DFT of a sequence of length 𝑁?Select one:a.The computational complexity is 𝑂(𝑁log⁡𝑁).b.The computational complexity is 𝑂(𝑁).c. The computational complexity depends on the specific properties of the input sequence and can vary.d.The computational complexity is 𝑂(𝑁2).

The Discrete Fourier Transform (DFT) is a mathematical operation that decomposes a discrete signal into its constituent frequency components. It is a powerful tool in digital signal processing (DSP) with a wide range of applications, including:Signal analysis: The DFT can be used to identify the frequency components of a signal, which can be useful for understanding the signal's properties and characteristics.Filter design: The DFT can be used to design filters that selectively pass or attenuate certain frequency components of a signal.Signal compression: The DFT can be used to compress signals by removing frequency components that are not important or audible.Convolution: The DFT can be used to efficiently compute the convolution of two signals.The Fast Fourier Transform (FFT) is a family of algorithms for efficiently computing the DFT. The FFT is much faster than the direct computation of the DFT, making it practical to compute the DFT of large signals.Here is a brief introduction to the DFT and FFT, and their applications in digital signal processing:DFTThe DFT of a discrete signal x[n] is defined as follows:X[k] = \sum_{n=0}^{N-1} x[n] e^{-j2\pi kn/N}where N is the length of the signal.

Identify among the following assertions that  represents a necessary condition for the existence of Fourier Transform of discrete time signal (DTFT).Group of answer choicesDiscrete Time Signal should be absolutely differentiableDiscrete Time Signal should be absolutely integrableDiscrete Time Signal should be absolutely summableDiscrete Time Signal should be absolutely multipliable

Which of the following identifies the purpose of using the Fourier Transform while analyzing any elementary signals at different frequencies?Group of answer choicesbothPlotting of amplitude & phase spectrumnoneTransformation from time domain to frequency domain

Which of the following techniques is commonly used to compute the inverse DFT (IDFT) from the DFT coefficients?Select one:a. Windowingb. Fast Fourier Transform (FFT)c. Direct summationd. Discrete cosine transform (DCT)