Which one of the following statements not correct for convolution?

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UPSC IES Electrical 2022 Prelims Official Paper
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  1. The convolution of an odd and even function is an odd function
  2. The convolution of two odd functions is an even function. 
  3. The convolution. of two even functions is an even function.
  4. The convolution of two odd functions is an odd function.

Answer (Detailed Solution Below)

Option 4 : The convolution of two odd functions is an odd function.
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Detailed Solution

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 Properties of convolution of two signals:

→ Convolution of an odd and even function is an odd function.

→ Convolution of two odd functions is an even function.

→ Convolution of two even function is an even function

 Convolution of two causal functions is causal function.

→ Convolution of two Anti causal function is Anticausal function.

→ Convolution of two unequal length rectangular pulse is trapezium.

→ Convolution of two equal length rectangular pulses is triangle.

→ Convolution of signal with periodic train of impulses is periodic representation of signal.

Therefore option (4) statement is not correct.

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