Discrete Fourier Transform Questions and Answers for Viva

Answer-1: The Discrete Fourier Transform (DFT) is a mathematical technique used to convert a sequence of sampled data points into its frequency domain representation.

Answer-2: The DFT is commonly used in digital signal processing to analyze and manipulate discrete-time signals.

Answer-3: The formula for calculating the DFT of a sequence x[n] of length N is: X[k] = Σ(x[n] * e(-j * 2π * k * n / N)), where k = 0, 1, ..., N-1.

Answer-4: The main components are the input sequence x[n], the output sequence X[k], and the complex exponential term e(-j * 2π * k * n / N).

Answer-5: The length of the input sequence determines the number of frequency components in the DFT output. For a sequence of length N, there are N frequency components.

Answer-6: The Nyquist frequency is half of the sampling frequency and represents the maximum frequency that can be accurately represented by the DFT.

Answer-7: The inverse Discrete Fourier Transform (IDFT) is the process of converting a frequency domain representation back to the time domain.

Answer-8: The IDFT is calculated using a similar formula to the DFT, but with a conjugate complex exponential term in the denominator.

Answer-9: The FFT is an efficient algorithm for calculating the DFT, particularly for sequences with a power of 2 length.

Answer-10: Common applications include signal processing, spectral analysis, image processing, and digital communication systems.

Answer-11: Windowing reduces spectral leakage and improves the frequency resolution of the DFT by tapering the edges of the input sequence.

Answer-12: Zero-padding increases the frequency resolution of the DFT by interpolating additional data points between the original samples.

Answer-13: The magnitude represents the amplitude of each frequency component, while the phase represents the phase shift of each component.

Answer-14: The sampling frequency determines the frequency range over which the DFT operates and affects the spacing between frequency bins.

Answer-15: The DC component represents the average value of the input sequence and corresponds to the 0th frequency bin.

Answer-16: The computational complexity of the DFT scales quadratically with the length of the input sequence, making it inefficient for large sequences.

Answer-17: The main limitation is its computational complexity for large input sequences, which can be addressed using more efficient algorithms like the FFT.

Answer-18: Aliasing can distort the frequency domain representation of a signal if the sampling frequency is not sufficiently high to accurately capture its frequency components.

Answer-19: Frequency resolution determines the ability to distinguish between closely spaced frequency components in the DFT output.

Answer-20: The DFT can be extended to handle real-valued input sequences by exploiting symmetry properties and efficiently calculating only half of the output spectrum.