Question

DFT converts

• A. Time domain to Frequency domain
• B. Frequency domain to Time domain
• C. Voltage to Current
• D. Analog to Digital

Hint:

- Forward DFT: Transforms data from the Time Domain to the Frequency Domain. - Inverse DFT (IDFT): Restores spectral components from the Frequency Domain back into the Time Domain.

Answer 1

The Correct Option is A

Concept: In signal processing, signals can be analyzed in two distinct ways: the time domain, which shows how a signal changes over time, and the frequency domain, which reveals its component frequencies. The acronym DFT stands for the Discrete Fourier Transform. The DFT is a mathematical transform designed to process a discrete sequence of sampled signal values. It maps a sequence of uniformly spaced time-domain samples into a corresponding sequence of frequency-domain coefficients. This conversion reveals the specific frequency, phase, and amplitude components that make up the original time-domain waveform. Mathematically, let \(x[n]\) represent a discrete-time signal sequence of finite length \(N\), sampled at regular intervals over time. The forward Discrete Fourier Transform algorithm converts this sequence into a discrete-frequency sequence \(X[k]\) using the following formula: \[ X[k] = \sum_{n=0}^{N-1} x[n] \cdot e^{-j \frac{2\pi}{N} k n} \] where:
• \(n\) represents the discrete time-domain index variable (\(0 \le n < N\)).
• \(k\) represents the discrete frequency-domain index variable (\(0 \le k < N\)).
• \(e^{-j \frac{2\pi}{N} k n}\) is the complex exponential basis function using Euler's formula: \(\cos(\frac{2\pi}{N}kn) - j\sin(\frac{2\pi}{N}kn)\). The output sequence \(X[k]\) represents the complex spectral density values across the frequency spectrum. This confirms that the transform shifts representation from the time domain to the frequency domain.