Flashcards on Digital Signal Processing: DFT and FFT
Digital Signal Processing: DFT and FFT Explained for Students
Tap to flip · Swipe to navigate
Discrete Fourier Transform
45 cards
Card 1
Question: Why is spectrum analysis important in DSP?
Answer: It's used frequently for tasks like recognition (speaker, keyword, language) and diagnosis; it evaluates signal spectral content.
Card 2
Question: What are the main Fourier tools for discrete-time signals and when are they used?
Answer: For periodic signals use discrete-time Fourier series (requires knowing signal frequency for coherent sampling). For non-periodic signals use DTFT (co
Card 3
Question: Why is using DFT/FFT a compromise and what caution does it require?
Answer: DFT/FFT samples the DTFT and provides relative discrete spectral values; this compromise can lead to inaccuracies or misleading results, so use DFT/FF
Card 4
Question: How should the spectrum of a real signal be displayed?
Answer: As two graphs showing magnitude and phase (polar complex representation); magnitude often in Volts and frequency in Hz; phase typically normalized to
Card 5
Question: What is the nature of frequency information returned by a DFT/FFT?
Answer: Frequency info is relative: DFT outputs indices of coefficients that correspond to samples of the DTFT; indexes must be recalculated to actual frequen
Card 6
Question: How do you convert a DFT coefficient index k to actual frequency f?
Answer: Actual frequency f = (k/N) * Fs, where k is DFT index, N is DFT (FFT) length, and Fs is sampling frequency.
Card 7
Question: How are DFT coefficients related to amplitude and how do you obtain spectral amplitudes?
Answer: DFT coefficients represent spectral density per relative frequency. Dividing coefficients by N yields spectral coefficients of the periodic extension.
Card 8
Question: How can you compute the magnitude of a DFT coefficient from its real and imaginary parts?
Answer: Magnitude = sqrt((Re Xk)^2 + (Im Xk)^2); in MATLAB/Python use abs(X)/N.
Card 9
Question: How is phase of a DFT coefficient computed and what ambiguity must be handled?
Answer: Phase ϕ = arctan(Im Xk / Re Xk), but arctan is ambiguous by ±π; corrections are needed for 2nd (+π) and 3rd (−π) quadrants. Use MATLAB angle() or nump
Card 10
Question: In what units and interval is phase usually displayed?
Answer: Phase is usually displayed in degrees in the interval <−180°, 180°>, less often in radians in <−π, π>.