Flashcards on Statistics for Digital Signal Processing
Statistics for Digital Signal Processing: A Student Guide
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Digital Signal Processing Statistics
21 cards
Card 1
Question: What is a signal in the context of digital signal processing statistics?
Answer: A description of how one parameter is related to another; can be continuous (both parameters continuous) or discrete/digitized (formed from quantized
Card 2
Question: What distinguishes a continuous signal from a discrete (digitized) signal?
Answer: A continuous signal allows both parameters to assume a continuous range of values; a discrete signal is formed from quantized parameters (samples).
Card 3
Question: What does the domain of a signal refer to on a graph?
Answer: The type of parameter shown on the horizontal axis (the independent variable).
Card 4
Question: How is the mean (μ) of a signal defined for N samples?
Answer: Mean μ = (1/N) * sum over i of x_i — the average value of the signal.
Card 5
Question: How is the standard deviation (σ) of a signal defined for N samples?
Answer: σ = sqrt((1/N) * sum over i of (x_i - μ)^2) — a measure of how far the signal fluctuates from the mean.
Card 6
Question: What does the variance (σ^2) represent for a signal?
Answer: The power of the signal's fluctuation; variance = σ^2 = (1/N) * sum (x_i - μ)^2.
Card 7
Question: What is the RMS (root-mean-square) and how does it differ from σ?
Answer: RMS = sqrt((1/N) * sum x_i^2); it measures both AC and DC components. For a signal with no DC, rms = σ.
Card 8
Question: How is the relationship between σ and peak-to-peak value relevant?
Answer: Different waveforms have characteristic relationships between their standard deviation σ and their peak-to-peak amplitude (used to estimate spread fro
Card 9
Question: What numerical issues arise when computing mean and standard deviation directly for large μ compared to σ?
Answer: When μ >> σ subtracting two nearly equal numbers causes excessive round-off error; running statistics that involve all samples in each new calculation
Card 10
Question: What is one solution to numerical instability when computing running statistics?
Answer: Use formulas or algorithms that avoid subtracting large nearly equal numbers (e.g., incremental/update formulas that maintain numerical stability).