Question

Short questions, from previous Exam II. Answer each of the following questions, with enough explanation to show that you are not guessing. Cascading two causal finite impulse response (FIR) filters of different lengths will result in an FIR filter that remains causal.

True
False

Answer 1

Cascading two causal FIR filters results in a combined FIR filter that remains causal, as the system's output depends solely on current and past input values.

Step-by-step explanation:

Cascading two causal finite impulse response (FIR) filters of different lengths will indeed result in an FIR filter that is also causal. The causality of an FIR filter implies that the output of the filter at any time depends only on the current and past input values, not on future values. Hence, when the first filter is applied to the input signal, it produces an output that is still causal. Passing this output through the second causal FIR filter results in an output that is dependent on the outputs of the first filter, which were based on the input's current and past values. Thus, the overall system remains causal because no part of the system relies on future input values. The result is a combined FIR filter whose impulse response is a convolution of the two individual FIR filters' impulse responses, maintaining the property of causality.