Throughput requirements in digital signal processing The statement “Digital signal processing must be at least half as fast as the incoming signal to be processed” is evaluated in the context of sampling theory and real-time processing constraints.

Introduction / Context:
Real-time DSP systems must process sampled data fast enough to keep up with the stream without underflow or overflow. The Nyquist criterion states that the sampling rate must exceed twice the highest input frequency component to avoid aliasing, not that the processor can be half as fast as the signal.

Given Data / Assumptions:

• The input is sampled at Fs samples per second, where Fs > 2*Fmax of the signal.
• The DSP must sustain an average throughput equal to or greater than Fs times operations per sample.
• Buffering is finite; steady-state throughput must meet or exceed input rate.

Concept / Approach:
Processing speed relates to operations per sample and sample rate, not the analog signal frequency directly. If 50 operations are required per sample and Fs is 1 MS/s, the processor must execute at least 50 Mops/s in real time. The “half as fast” statement confuses sampling criteria with processing throughput.

Step-by-Step Solution:

Verification / Alternative check:
Profile the implementation to confirm that average and worst-case cycle budgets meet real-time deadlines with safety margin.

Why Other Options Are Wrong:
“Correct” misstates Nyquist and ignores throughput. The other qualifiers do not rescue the incorrect blanket claim.

Common Pitfalls:
Confusing Nyquist with CPU speed; ignoring algorithmic complexity; neglecting I/O and DMA overheads.

Final Answer:
Incorrect