Which of the following statements is true? If more than one statement is true, identify all the statements which are true. [ 1 point for identifying all true statements, ‐ 0 . 5 points for choosing a wrong combination even if some of the statements chosen are true, 0 points for not answering ] ( i ) An all ‐ pass filter passes through all frequencies unchanged, but can change the phase of the signal ( ii ) If the FIR filter coefficients are symmetric, then it has linear phase ( iii ) FIR filter is computationally more efficient than an IIR filter of comparable performance ( iv ) A filter that does not operate in real ‐ time can be non ‐ causal

Answer: Statements (i), (ii), and (iv) are true.

Explanation:

  • (i) An all-pass filter passes through all frequencies unchanged, but can change the phase of the signal: This is true. An all-pass filter is designed to allow all frequencies to pass through with the same gain, but it can alter the phase of the signal.
  • (ii) If the FIR filter coefficients are symmetric, then it has linear phase: This is true. Symmetric FIR filter coefficients (either even or odd symmetry) result in a linear phase response, which means that all frequency components of the input signal are delayed by the same amount.
  • (iii) FIR filter is computationally more efficient than an IIR filter of comparable performance: This is generally false. FIR filters typically require more coefficients (and thus more computations) than IIR filters to achieve the same level of performance, especially in terms of sharpness of the filter response.
  • (iv) A filter that does not operate in real-time can be non-causal: This is true. Non-causal filters can use future input values to compute the current output, which is possible when the filter does not need to operate in real-time.
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