Flashcards on Fundamentals of Digital Signal Processing Systems
Fundamentals of Digital Signal Processing Systems
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Linear Time-Invariant Systems (LTI) and Signal Flow Diagrams
10 cards
Card 1
Question: What is the definition of a causal system in discrete time?
Answer: A causal system is one whose output y at time m depends only on current and past input samples x[n] with n ≤ m and possibly past outputs y[n] with n <
Card 2
Question: For a causal LTI system, what property does the unit impulse response g[n] have for negative indices?
Answer: The unit impulse response g[n] is zero for all negative indices (g[n]=0 for n<0).
Card 3
Question: Name the three basic functional blocks used to describe or implement a causal LTI system in a signal flow diagram.
Answer: Addition (summation), multiplication by a constant, and unit delay.
Card 4
Question: What is a signal flow diagram and what is its primary use?
Answer: A signal flow diagram is a graphical representation of the system's difference equations used to describe and implement an LTI system; it serves as a
Card 5
Question: How can any causal LTI system be described mathematically?
Answer: Any causal LTI system can be described by a set of difference equations.
Card 6
Question: Why are temporary variables (like x1, x2) used when implementing difference equations from a signal flow diagram on a computer?
Answer: Temporary variables let you implement the system as a set of first-order difference equations so you don't need to store whole sequences—only a few sc
Card 7
Question: Given a signal flow with two unit delays and gains 1 and 2 summing to y[n]=1·x[n−1]+2·x[n−2], what are the corresponding first-order update equations
Answer: x1[n]=x[n−1], x2[n]=x[n−2] can be implemented by updates x1[n]=x[n], x2[n]=x1[n−1]; one practical set from the diagram: x1[n]=x[n−1], x2[n]=x1[n−1]; y
Card 8
Question: When testing a signal flow diagram implementation using the unit impulse input, what initial conditions are used for n<0 and for n=0?
Answer: For n<0, all internal states and outputs are zero; at n=0 the input x[0]=1 (impulse) and other past inputs are zero—these initial conditions are used
Card 9
Question: What are the two phases recommended for implementing an LTI system from a signal flow diagram on a computer?
Answer: Initial phase: define variables and initial values (index n, input x[n], temporary scalars, output y[n]). Calculation phase: iterate the difference eq
Card 10
Question: Why is the unit delay block sometimes represented by z^{-1} in diagrams?
Answer: z^{-1} is an alternative symbol associated with the Z-transform that denotes a one-sample unit delay.